MathsDim 7 TE

Teacher’s Edition

PDF version

Maths Dimensions essential learning

7

Homework Book Answers

Whole Number Revision 1

1A Place value1 a 31 b 703 c 2000 d 400 900

2 a Twelve

b Four thousand and ten

c Seven million

d Forty-five thousand, three hundred and thirteen

3 7 hundreds 4 306 804

5 a 87 621 b 12 678 6 2057

Puzzle‘ten-two’

1B Addition1 a 669 b 5190

2 a 9523 b 7420

3 $148 4 11 808 km

5 a South Australia: 23 035Western Australia: 28 468

b July c 51 503

d Add the totals for each of the 4 months.

1C Subtraction1 a 716 b 9279

2 a 88 b 894

3 162 minutes

4 Geelong to Lorne: 66 kmLorne to Port Campbell: 141 kmPort Campbell to Warrnambool: 66 km

Puzzle12

Whole Number Revision 2

1D Multiplication1 a 3114 b 28 956

2 a 2033 b 19 110

3 $169 4 19 5 $785

1E Division1 a 413 b 89

2 a 1247 b 8041

3 292 litres

4 a 129

b the number of students who paid for tickets

1F Doubling and halving1 a 10 × 69 = 690 b 36 × 100 = 3600

c 18 × 100 = 1800 d 100 × 97 = 9700

e 1000 × 19 = 19 000

2 a 560 b 800 c 330 d 392 e 600

3 a 1400 b 1670 c 342 000

4 $500

Puzzle• Pour from a full 7-litre bucket into the 5-litre bucket—

this leaves 2 litres in the 7-litre bucket.

• Empty the 5-litre bucket.

• Pour the 2 litres into the 5-litre bucket.

• Fill the 7-litre bucket.

• Pour water from it into the 5-litre bucket until the 5-litre bucket is full (this will remove 3 litres from the 7-litre bucket).

• 4 litres of water will remain in the 7-litre bucket.

1G Order of operations1 a 16 b 18 c 4 d 11 e 4 f 36

2 a 6 × (5 − 2) b 20 − (8 − 6) c 36 ÷ (6 ÷ 3)

3 a (3 + 8) × 2 b 62 − (10 × 5)

4 a 7 b 8 c 6

5 a 15 b 9 c 34 d 10 e 16 f 5

6 a 63 b 2 c 25 d13

e 2 f 36 g 27 h 8

i 36 j 130 k 44 l 12

7 a 2 × $800 + 3 × $500 + $100 b $3200

8 a 8 × (29 + 11) b 320

9 Multiplying and dividing take priority over addition and subtraction.

Puzzle‘thousand’

1H Estimation1 b 41 + 503 ≈ 40 + 500 = 540

c 793 − 58 ≈ 790 − 60 = 730

d 49 × 11 ≈ 50 × 10 = 500

e 798 ÷ 10 ≈ 800 ÷ 10 = 80

f 102 × 39 ≈ 100 × 40 = 4000

2 $160 ÷ $19 ≈ $160 ÷ $20 = 8 gifts

3 299 + 433 + 318 + 960 ≈ 300 + 450 + 300 + 950 = 2000; 2000 km

The four 4s puzzle1 = 4 − 4 + 4 ÷ 4 2 = 4 ÷ 4 + 4 ÷ 4

3 = (4 + 4 + 4) ÷ 4 4 = (4 − 4) × 4 + 4

5 = (4 × 4 + 4) ÷ 4 6 = (4 + 4) ÷ 4 + 4

7 = 4 + 4 − 4 ÷ 4 8 = 4 × 4 − (4 + 4)

9 = 4 + 4 ÷ 4 + 4

1J Number systems of the past1 a 13 b 51 c 20 d 156

e 1353 f 1500

2 a VI b XIV c XXI d LXI

e XXIX f MM

3 Roman numerals are harder to read quickly, and the filmmaker or TV network does not want viewers to realise that the film may be fairly old.

4 a XIV = 14 b LXIV = 64

5 a MDC = 1600 b MDCL = 1650

Two logic puzzles1 Inhabitant 1: elf, Inhabitant 2: elf, Inhabitant 3: troll

2 The bar should be cut immediately in two places—to make three pieces.

The three separate pieces will be one-seventh, two-sevenths and four-sevenths.

Instalment 1: Bank pays the person a one-seventh bit

Instalment 2: The person returns the one-seventh bitand the bank pays the person a two-sevenths bit

Chapter 1

1Homework Book Answers

2


Instalment 3: The bank gives the one-seventh bitback to the person

Instalment 4: The person returns the one- and two-sevenths bits, and then the bank pays them with a four-sevenths bit

Instalment 5: The bank gives the one-seventh bit to the person

Instalment 6: The person returns the one-seventh bit and the bank pays the person a two-sevenths bit

Instalment 7: The bank gives the one-seventh bit to the person

Number Patterns 1

2A Exploring number patterns1 a 21, 26, 31, 36 b 13, 17, 23, 30

c 64, 55, 46, 37 d 26, 37, 50, 65

2 a b 1, 3, 6, 10, 15

c 2, 3, 4, 5 d 21, 28, 36, 45

2B Multiples1 a 8, 16, 24, 32, 40 b 20, 40, 60, 80, 100

2 The list gives the multiples of 4.

3 56, 63, 70, 77, 84, 91, 98

4 a 12, 24, 36 b 36, 72, 108

5 a 40 b 60

6 a 12 days b 84 days

2C Factors1 a {1, 2, 4, 8} b {1, 3, 5, 15}

c {1, 2, 3, 4, 6, 8, 12, 24} d {1, 11}

2 1 3 7 is not a factor of 99

4 a 2 × 36, 3 × 24, 4 × 18, 6 × 12, 8 × 9 b 12

5 {1, 3, 9}

6 a 2 b 1 7 $20

2D Divisibility tests1 a no b yes c no d yes

2 0, 2, 4, 6, 8

3 A number is divisible by 5 if it ends in 0 or 5.

4 7 + 1 + 5 + 5 = 18, which is divisible by 9.

5 a 8004 b 8001

Number Patterns 2

2E Exploring primes and composites1 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

Multiples of 4 and 6 are also multiples of 2, and numbers divisible by 2 have already been removed.

2 53 3 1 has only 1 factor

4 a 91

b 91 = 7 × 13 so it has more than two factors Its factors are {1, 7, 13, 91}.

2F Index notation1 a 54 b 673

2 a 8 × 8 b 9 × 9 × 9 × 9 × 9 × 9

3 a 32 b 216

4 a false b true

5 a 4 × 25 = 100; 1003 = 1 000 000

6 a 2 + 22 + 23 b 14

2G Squares and square roots1 a 36 b 144 c 64

2 0 and 1

3 a 5 b 10 c 9

4 a 625 b 2025 c 12 544 d 139 129

5 a 33 b 216 c 0·72

6 1

Extended-answer question: Larger and smaller squares1

2 39, 2, 15, 1·2, 5·001

3 0·3, 0·767, 0·98

4 1, because 12 = 1; and also 0

5 a numbers greater than 1

b numbers between 0 and 1

2H Prime factors1 60 = 2 × 2 × 3 × 5

2 a 24 = 2 × 2 × 2 × 3

b 400 = 2 × 2 × 2 × 2 × 5 × 5

c 50 = 2 × 5 × 5

d 98 = 2 × 7 × 7

e 120 = 2 × 2 × 2 × 3 × 5

f 57 = 3 × 19

Extended-answer question: Goldbach’s conjectureSeveral answers are possible. Here is one (with some alternatives):

4 = 2 + 2 6 = 3 + 3

8 = 3 + 5 10 = 5 + 5

12 = 7 + 5 14 = 7 + 7

16 = 3 + 13 (or 5 + 11) 18 = 7 + 11

20 = 3 + 17 22 = 11 + 11

24 = 5 + 19 (or 13 + 11) 26 = 13 + 13

28 = 11 + 17 30 = 13 + 17

32 = 3 + 29 34 = 17 + 17

36 = 5 + 31 38 = 19 + 19

40 = 17 + 23 42 = 5 + 37

44 = 3 + 41 46 = 23 + 23

48 = 5 + 43 50 = 3 + 47

Chapter 2

Number Square The square is ______ than the number

39 1521 bigger

2 4 bigger

0·3 0·09 smaller

0·767 0·588 289 smaller

15 225 bigger

1·2 1·44 bigger

0·98 0·9604 smaller

5·001 25·010 001 bigger

Maths Dimensions 7 Teacher’s Edition CD


Second part:

21 = 3 + 7 + 11 23 = 5 + 7 + 11

25 = 3 + 5 + 17 27 = 3 + 5 + 19

29 = 5 + 11 + 13

2I Odds and evens1 a even b odd c even

2 13 Pluto Place, 17 Pluto Place

3 4 4 4 + 6 + 8

5

6 a either odd or even b 8 ÷ 4 = 2 which is even

6 ÷ 2 = 3 which is odd

Extended-answer question: Oddities1 a 4 b 9 c 16

2 100 3 202: 20 × 20 = 400

4 the sum of the first n odd numbers is n × n.

Extended-answer question: Last digits

a

b 1 c 1 d 1, 5, 6, 10

Fractions 1

3A Shaded diagrams

1 a b or c or

2 3 or 4

5 6 7 or

8 a B and D b ,

9 a b c d

3B Mixed numbers and improper fractions

1 a 1 b 3 c 1

2 6 minutes

3 a b c

4 a b 19

3C Adding with the same denominator

1 a b c 1 d

e 8 f 9

2 a Helena should not have added the two bottom numbers (denominators).

b c

Fractions 2

3D Adding with different denominators

1 a b c d 3

e 4 f 5

2 3 a 8 b 2

3F Subtracting with the same denominator

1 a b c d 2 e 1 2

3G Subtracting with different denominators

1 a b c d 1 e

2 3

3I Multiplying fractions

1 a b c 16 d

e 3 f 3 g 1

2

Fractions 3

3J Dividing fractions

1 a b 3 c

2 a b

3 a b 5 c

4 a b c d 8

5 a 3 b c

+ Odd Even − Odd Even

Odd Even Odd Odd Even Odd

Even Odd Even Even Odd Even

× Odd Even

Odd Odd Even

Even Even Even

Powers of 7 Value Last digit

71 7 7

72 49 9

73 343 3

74 2401 1

75 16 807 7

76 117 649 9

77 823 543 3

Chapter 3

12--- 4

12------ 1

3--- 4

12------ 1

3---

47--- 7

28------ 1

4--- 8

13------

750------ 3

5--- 6

16------ 3

8---

34--- 6

8---

12--- 2

5--- 2

3--- 4

9---

12--- 3

5--- 1

10------

34---

132

------ 237

------ 378

------

195

------

47--- 1

2--- 3

5---

35--- 2

5---

45---

920------ 19

20------ 19

24------ 2

3---

1720------ 5

6---

1320------

15--- 1

4--- 1

4--- 1

2--- 2

5--- 3

10------

524------ 3

10------ 1

24------ 7

20------ 4

5---

110------ 7

20------

635------ 1

8--- 1

5---

13--- 1

3---

110------

14--- 1

2---

38--- 3

14------

98--- 1

12------

1027------ 5

8--- 7

50------

211------ 7

9--- 134

35------


4


6 2 pies 7 3 ÷ 5 = × = =

8 7 books per hour

3K Fractions of quantities1 a 14 b 28 c 15 d 69

2 a $20 b 21 cm c 70 kg

3 × 60 = 45

4 $36 5 7 hours

6 160 minutes or 2 hours, 40 minutes

7 a b × 60 = 12; 12 minutes

Fractions 4

3L Squares and square roots of fractions

1 a b c

2 a 6 b 1 c 5

3 a b c

4 a 1 b 2

3M Order of operations

1 a 9 b 6

2 a b c d 6

e 5 f

Decimals and Percentages 1

4A Place value and notation

1

2 a 50·4 b 9·39 c 6034·1

d 300·2 e 0·005

3 a 9 tens b 9 tenths

c 9 units d 9 hundredths

e 9 thousandths

4 a False b True c False d True

5 a Thousandths b 0·03 g

6 a 0·8 b 12·8 c 1·2 d 17·001

7 0·043, 0·403, 0·43, 4·03, 4·3

8 a Apples b Apples c Apples

4B Estimation of decimals

1

2 a 90 ÷ 50 = 1·8 b $1·95 3 600

4C Rounding decimals1 a 5·8 b 13·1 c 0·5 d 42·6

2 a 3·63 b 0·17

3 a 1·438 b 16·259 c 0·001

4 6·7 kg 5 a $7·99 b $8·00


4D Adding decimals1 a 5·6 b 1·7 c 15·01 d 5·844

2 $12·25 3 42·1°C 4 47·4 kg

4E Subtracting decimals1 a 0·25 b 1·75 c 13·35 d 0·28

2 10·84 seconds 3 0·85 litres 4 154·8 cm

4F Multiplying decimals1 a 0·12 b 0·4 c 0·12 d 9·6 e 0·6

2 a 0·12 b 0·143 c 13·44 d 0·0002

3

4 a 25·2 b 29·13 c 2·216 d 24·7538

5 $18·80 6 a $7·80 b $2·20

7 $91·52

8 a $8·31 b $29·44 c $10·55 if given in cash

4G Dividing by whole numbers1 a 6·91 b 0·113 c 63·3 d 0·2175

2 $5·35 ÷ 3 = $1·78 or $1·80 if paying in cash

3 $8·79

12--- 3

4--- 15

4------ 1

5--- 15

20------ 3

4---

12---

34---

12---

15--- 1

5---

2564------ 1

9--- 16

121---------

14--- 7

9--- 41

64------

56--- 1

8--- 7

10------

13--- 1

3---

12---

1316------ 13

24------ 11

15------ 1

2---

112------

Chapter 4

Thousands Hundreds Tens Units · Tenths Hundredths

a 63·1 6 3 · 1

b 510·91 5 1 0 · 9 1

c 4000·2 4 0 0 0 · 2

d 0·07 0 · 0 7

e 31·59 3 1 · 5 9

Question Approximate question

Estimated answer

Actual answer

(calculator)

49·11 ÷ 5·1 50 ÷ 5 10 9·629

13·98 + 1·9 14 + 2 16 15·88

1·88 − 0·93 2 − 1 1 0·95

6·07 × 5·97 6 × 6 36 36·2379

× 0·2 4 0·05 1·2

0·1 0·02 0·4 0·005 0·12

0·3 0·06 1·2 0·015 0·36

0·08 0·016 0·32 0·004 0·096

0·12 0·024 0·48 0·006 0·0144




4H Dividing by decimals1 a 2 b 48·2 c 9830 d 1·8 ÷ 9

2 a 155 b 9·64 c 4915 d 0·2

3 a 21 b 210 c 21 d 21 000

4 a 0·296 b 4·4 c 2·099 d 615·9

5 50 6 250 7 87·9 cents 8 25 days

4I Exploring powers of 101 a 29 b 538·1 c 4·9

d 6300 e 57·91 f 0·438

2 a 2·345 b 0·0036 c 0·732

d 0·001 56 e 60·034 f 0·007

4K Fractions and decimals1 a 0·8 b 0·75 c 0·875 d 0·35

2 a 0·3125 b 1·5 c 3·175

3 a 0·444 444 444 b 0·232 323 232

c 5·188 888 888 d 60·658 658 658

4 a 0· b 3· c 14·0 d 3·

5 a 0· b 0·

4L Converting decimals to fractions

1 a b c d

e f

2 a 1 b 2 c 5 d 76

e 14 f 9


4M Percentages1 35%

2

3 a 86% b 14%

4 a b c d

5 Less than half; half would be 50%.

6 a 80% b 15% c 24%

7 a 49% b 5% c 71·8%

4N Finding percentages of quantities1 a $30 b 38 c 72 m d $112

2 $180 3 144 kg

4O Calculating percentages1 300 students 2 30 3 a 75 b 325

4 a $45·90 b $195·50

5 The Eski fridge is cheaper: it costs $1300 − 35%of $1300; $1300 − $455 = $845The Chillaway costs $1150 − 20% of $1150; $920

Extension: Squares and square roots1 a 9·61 b 0·16 c 39·0625

d 0·000 144 e 52·2729 f 0·023 104

2 a 0·7 b 2·7 c 2·88

d 0·13 e 0·587 f 14·28

Length and Perimeter 1

5A Units used to measure lengths1 a m b cm c km d m e mm

2 a 20 mm b 20 cm c 20 km

d 20 m e 2 m

3 a Ruler b Odometer

c Trundler wheel d Dressmaker’s tape

e Ruler f Dressmaker’s tape

g Ruler h Tape measure

5B Estimating by using known values1 a 10

b 30 cm. The height of the page is the length of about 10 paper clips, and 10 × 3 cm = 30 cm.

2 Car = 1·7 m wide and 2 cm wide in photoGarage is 7 cm wide in photo

= = 6 m wide

5C Estimating lengths1 40 mm

2 Depends on individual measurements—possible answers are:

a 200 mm b 218 mm c 220 mm

5D Reading scales when measuring 11 a = 4·8 b = 7·2 c = 2·5 d = 9·3

2 a 2 ÷ 5 = 0·4 or 4 ÷ 10 = 0·4 b 0·8, 1·6, 3·2

c

3 a 5 km/h b 75, 90 c 70 km/h


5D Reading scales when measuring 21 p = 16 kg, q = 74 kg

2 a 1 decibel b between 30 and 60

c a = 15, b = 24, c = 36, d = 53

5E Measuring lengths accurately1

2

2̇ 18 7̇ 192

8̇ 27

45--- 6

25------ 1

20------ 17

25------

58--- 201

250---------

34--- 2

5--- 1

125--------- 63

200---------

325------ 7

8---

15--- 3

4--- 2

25------ 16

25------

to nearest cm to nearest mm

A 1 cm 12 mm

B 3 cm 25 mm

C 4 cm 38 mm

D 6 cm 64 mm

in cm in mm

A 1·6 cm 16 mm

B 5 cm 50 mm

C 0·4 cm 4 mm

D 3·7 cm 37 mm

Chapter 5

7 cm 1·7 m×2 cm

-------------------------------

0 0.8 1.6 2 42.5 3.2


6


3

4 30mm

5 a 12 mm b 33 mm c 27 mm d 40 mm

5F Converting length units1 a 4800 m b 6 m c 0·042 m d 500 m

2 a 400 cm b 30 cm c 6·7 cm d 182 cm

3 a 5 km b 380 mm c 6·6 m d 5 cm

4 a 8 cm b 16 cm c 6·25 years

5 48 pieces

6 The book is 52 mm thick. Thickness of one sheet = total thickness ÷ number of sheets = 52 ÷ 784 = 0·066 mm


5G Adding and subtracting lengths1 a 246 cm b 287 mm

c 3000 m or 3 km d 3350 m

2 a 9750 m b 9·75 km

3 a 4710·4 km

b 52 193·8 km; 100 000 − 47 806·2 = 52 193·8

5H Perimeter of shapes with straight sides

1 a 16 cm b 24 cm c 52 m d 76 cm

2 a 24 cm b 48 cm c 30 cm

Extended-answer question: The fibre-optic network1 376 km

2 318 kilometres are used.

3

The network length is 536 km.

Puzzle30 cm

5I Exploring measurement in the past1 a 18 422 cm b 184·22 m

2 a km b m c km/h

3 a 38·85 km/h b 5050 km c 8 m

Area and Volume 1

6A Finding and comparing areas1 B, C, A

2 a 6 cm2 b 12 cm2 c 8 cm2 d 6 cm2

6B Using grids to find areas1 a 21 cm2 b 13 or 14 cm2 2 32 km2

6D Area of rectangles1 a 50 cm2 b 6 cm2 c 870 cm2

2 108 m2

3 484 cm2 4 40 m2

5 a 111 m2

b 444; the area of 1 tile is 0·5 × 0·5 m2 = 0·25 m2

so the number of tiles is or 444.

6E Area of parallelograms1 a 18 m2 b 25 cm2

2 Other answers are possible.

3 a 540 cm2 b 15 cm

Area and Volume 2

6G Area of triangles 1 a 15 cm2 b 120 cm2 c 30 cm2 d 15 m2

2 a x = 4 m, y = 5 m

b The area of the shaded quadrilateral will be the area of the rectangle − the sum of the areas of the four triangles.8 × 10 − (4 + 10 + 15 + 8) = 80 − 37 = 43; 43 m2

3 a 16 cm2 b 66 cm2 c 3 cans

4 a 140 cm2 b

c The height in part b is 2·6 cm on the plan, so is 130 cm in the road sign.

The area of ∆ABC = × 140 × 130 = 9100 cm2.

∆ACD has the same area as ∆ABC.

The total area is 2 × 9100 = 18 200 cm2.

Extended-answer question: Pick’s rule1 a 4 cm b 3 cm c 12 cm2

d n = 6 e p = 14

f Area = n − 1 + p = 6 − 1 + × 14

= 5 + 7 = 12

The area is 12 cm2.

g yes

in mm in m

A 3117 mm 3·117 m

B 3063 mm 3·063 m

C 3135 mm 3·135 m

D 3080 mm 3·08 m

E 3100 mm 3·1 m

Echuca

Seymour

Ballarat

Bendigo

Echuca

Seymour

Ballarat

Bendigo

Horsham

Castlemaine

93218 101

86

38

Chapter 6

1110.25----------

A

B

C

D

12---

12--- 1

2---



Area and Volume 3

6H Volume as a measure of space1 a 9 cm3 b 24 cm3 c 18 cm3 d 23 cm3

2 3

6J Volume of rectangular prisms1 a 80 cm3 b 280 cm3 c 5 cm3

2 64 cm3

3 A = 40 cm3, B = 24 cm3, C = 3 cm, D = 0·25 cm

4 12 000 cm3

6K Volume of prisms1 a 85 cm3 b 168 cm3

2 a Area = 10 × 3 + × (10 × 2)

= 30 + 10

= 40 m2

b 1000 m3 c 333

3 a 40 cm3 b 4800 cm3

c 4800 ÷ 40 = 120

Time and Mass 1

7A Timelines1

2 a

b The twelve months of the year are not all the same length.

4 a 7:15 pm b 7:55 pm

c

7B Time conversions1 a Minutes b Hours

c Seconds d Years

2 a 300 seconds b 5 weeks

c 7 centuries d 35 years

3 150 minutes 4 5:05 pm

5 6 hours 45 minutes 6 168 hours in a week

7 365 ÷ 7 8 4 9 14

10 a 13th birthday b 6 837 480 minutes

c 28 900 days

7C Time differences and the calendar1 Monday 2 14 November, Tuesday

3 a Leap year b Not a leap year

c Not a leap year d Leap year

4 a 31 b 30 c 31 d 30 e 28

5 a 12 October 2004 b 1 March 2000

c 29 February 2012

Time and Mass 2

7D Time differences in hours and minutes1 a 9:15 am b 2:30 pm

c 11:10 pm d 12:55 pm

2 a 0830 b 2030 c 1200 d 1345

3 a b

4 105 minutes, or one and three-quarter hours

7E Using timetables1 a 5:15 pm b 5:40 pm

c 12:25 pm d 40

e Saturday, Sunday f 1 hour 10 minutes

g Airline B has the most flights. A: 20, B: 22

2 a 5 hours 24 minutes

b

c Ararat and Geelong

3 a 2 pm b 3

c Mon, Tue, Wed, Thu, Fri, Sat

d Monday, 1:30 am

7F Time zones1 a 8 pm Monday b 11 pm Wednesday

2 a 2:30 pm Friday b 2 am Monday

3 a Evening b Sunday

Time and Mass 3

7G Ordering events and flow charts1 a every 2 seconds

b the ‘Wait for 2 seconds’ box would need to bechanged

c

2 cut toenails, put on socks, put on shoes, tie shoelaces

12---

Chapter 7

1940 1960 1980 2000

Sydney1938

Perth1962

Brisbane1982

SydneyMelbourne

1 Jan 31 Dec

G A M J

7:15 7:20 7:25 7:30 7:35 7:40 7:45 7:50 7:55 8:00 8:05 8:10 8:15

A E C D B

Station Eastbound Westbound

Horsham dep. 2:46 pm arr. 2:06 am

Ararat dep. 4:08 pm dep. 12:44 am

Geelong dep. 6:21 pm dep. 11:19 pm

Melbourne arr. 8:10 pm dep. 9:30 pm

19:50

START

Are thelights closer than

100 m

Wait for2 seconds

STOPGo throughintersection

Are thelights red?

Brake

Are thelights amber?

Are thelights closer than

50 m?

YES

NO

NO

NO

NO

YES

YES

Maintainspeed


8


3

Extended-answer question:Daylight saving1

2 a 4:57 am, 11:21 am, 5:26 pm, 11:37 pm

b More than 12 hours. On 9 October, for example, the time difference between one high tide and the next is 12 hours 16 minutes (2337 − 1121).

c 1, 17, 31 October

d 0153 (no adjustment needed because it is before 2 am), 0849, 1510, 2121

e There is a higher tidal range at new moon.

Puzzlea entrance–lions–crocodiles–giraffes–kiwis–kiosk–

snakes–exit (62 minutes).Other answers are possible.

b entrance–kiwis–kiosk–giraffes–crocodiles–snakes–lions–exit (58 minutes).Other answers are possible.

Time and Mass 4

7H Mass and conversion of units of mass

1 a kg b mg c tonne d g

e kg f tonne g kg h g

2

3 a 3000 g b 650 g c 5 g d 0·375 g

4 a 4000 kg b 680 kg c 94 kg d 8·25 kg

5 3 kg 6 125 cups 7 35 g

8 a Cocoa, espresso b 20 cups c 80 mg

d 1 can of cola contains 40 mg of caffeine.

To be poisoned by caffeine you would need toconsume 5 g = 5000 mg.

The number of cans for5000 mg = 5000 ÷ 40 = 125.

There are 60 minutes in an hour, so drinking2 per minute would give 120 cans.

Angles 1

8A Naming angles1 a ∠ACB or ∠BCA b ∠EDF or ∠FDE

2 1 = ∠ADB or ∠BDA 2 = ∠BDC or ∠CDB

3 = ∠ADC or ∠CDA

3 1 = ∠EDF or ∠FDE 2 = ∠DFE or ∠EFD

3 = ∠DEF or ∠FED

8B Types of angles1

2 a 1 b 2 c 4 d 3

3 a 8 b 12

4 a i 2 ii 3

b i 11 o’clock ii 5 o’clock

5 a Obtuse b Acute c Reflex

6

7 8 reflex

8C Measuring angles1 a 70° b 35°2 a 310° b 222°

8D Using a protractor to draw angles

1 a b

Perth Melbourne

August 5 5 pm 7 pm

January 2 5 pm 8 pm

June 18 11 am 1 pm

July 1 2 pm 4 pm

December 9 9:30 am midday

November 7 8:30 pm 11:30 pm

A paper clip: 1 g

A delivery van: 1·8 tonnes

A bar of chocolate: 100 g

A sumo wrestler: 175 kg

A tray of 24 soft-drink cans: 8 kg

STOP

YES

START

Is the lightgreen?

Wait for1 second

Drive off

NO

Type of angle Example

acute p°, t°, x°, w°

obtuse r°, s°, u°

reflex q°, v°

Chapter 8

N

NW

SW SE

NE

EW

S

A

A

A

AA

R

R

RO

O

62° 288°



Angles 2

8E Complementary angles1 x = 24°, y = 30°2 a 40° b 84° c 7°3 45° 4 p = 28°, q = 59° 5 61°

8F Supplementary angles1 a 40° b 171° c 127°2 a a = 120° b b = 70° c c = 126°

d d = 54° e e = 69° f f = 60°3 5°4 35°. The obtuse angle at the top of the diagram is 145°

because of supplementary angles on a straight line.

8G Angles in a circle1 a a = 20° b b = 250° c c = 95°

d d = 120° e x = 120°f y = 36° (the angles are 36°, 72°, 108°, 144°)

2 a 270° b

3 a 360° ÷ 12 = 30° b 15°

c d 105°

4 40°

Puzzle11

Polygons 1

9A Triangles: Side properties1 a Scalene b Equilateral c Isosceles

2 a Scalene b Isosceles

3 a Isosceles b Equilateral c Scalene

d Isosceles

4 a b 4 c false

Extended-answer question: Impossible trianglesa Not possible

b i Impossible ii Impossible

iii Possible iv Impossible

c add up to more

9B Triangles: Angle properties1

2 a b Impossible

9C Finding the third angle in a triangle1 a x = 70° b x = 120° c x = 53° d x = 55°2 a 110° b 9°3 a x = 65° b x = 60°4 x = 72°, y = 36°, z = 25°

9D Exterior angle properties of triangles 1 a x = 110° b x = 59° c x = 40° d x = 59°

Polygons 2

9F Quadrilaterals1 Rhombus, parallelogram, trapezium

2 a b trapezium

3 Kite

9G Angle sum of a quadrilateral1 a x = 38° b x = 80° c x = 115° d x = 250°

9H Polygons1 a Hexagon b Triangle c Hexagon

d Quadrilateral e Pentagon f Decagon

9I Angle sum of polygons1 6 triangles

2 a 360° b 1080° c 3240°3 a x = 85° b x = 120° c x = 64°4 3x + 210° = 540°

3x = 330°x = 110°

Location 1

10A Directions in two dimensions1 a Skeleton b Cannon

c Dead Man’s Reef d Shipwreck

2 a N13 b I3 c A5 d G15

3 a i A ii G iii C iv D

b i 420 320 ii 455 298

iii 443 328 iv 468 343

10B The coordinate number plane1 A = (4, 4), B = (2, 1), C = (1, 5), D = (0, 1), E = (3, 0)

2 (a, b) c None d Obtuse

3 W 4 Bread winner

Size of AngleType of triangle

∆ABC ∠A = 90° ∠B = 50° ∠C = 40° Right-angled

∆DEF ∠D = 36° ∠E = 114° ∠F = 30° Obtuse

∆GHI ∠G = 74° ∠H = 48° ∠I = 58° Acute

34---

9

12

3

678

1011 1

2

45

Chapter 9

A

B

C

D

keystone

Chapter 10

2

4

2 4

y

x


10


Location 2

10D Scale diagrams and maps1 a 34 mm on the map, 680 m to walk

b 45 mm on the map, 900 m to walk

c 38 mm on the map, 760 m to walk

2 3 × 250 = 750; 750 m 3 18·5 cm

4 a 4·5 cm, 2·3 cm b 90 m, 46 m

c 100 m

5 a 11·4 m b 1350 cm

c 4·8 m by 4·5 m

6 a 60 m b 76 m c 67 m 7 7·2 m

Location 3

10E Maps and bearings1 a 100° b 340° c 260° d 020°2

3

4 a 054° b 243° c 320° d 140° e 300°

Co-interior angles property gives the angle marked 60°, then use angles in a circle to get the bearing of 300°.

5 a 135° b 310°

6 a b c

d e

7 a 042° b 104° c 249° d 280°

PuzzlePossible positions for the roads are as shown:

Algebra Symbols 1

11A Writing expressions

1 a x − 1 b 9x c x + 100 d

2 a 6 more than x b 6 less than x

c x divided by 6 d 6 times x

3 a 2x b c 50y d

4 a 4 less than p b p divided by 4

5 A fraction line shows division in algebra.

11B Pronumerals1 a 6c b 3y c 2x

2 a 8h b 3x c 3x d 9y e 13x

3 a 18x b 3x c 6x d 2x

4

Other answers are possible.

5 a 7x and x b 4c and c c 3ab and 5ab

6 a Like b Unlike c Unlike d Unlike

7 a 5x + 12y b 5x + 8y c 3p + 7q

d 7x + 9 e 13y + 6 f 6x + 5

g 3x + 2y h 8p + q

8 a 15 tyres and 3 batteries

b 6t + 2b + 9t + b = 15t + 3b

9 a 2x + 10y b 8x + 8y c 4x + 1

d 6p + 9q e x + 1 f 2x + 2

g x h 2x − 7

Algebra Symbols 2

11C Multiplying and dividing pronumerals1 a 12x b 5x c pq d 14x e 3cd

f 4xy g 20xy h abc i 40cde j 12qr

2 a 3x + 2 b 8q + 5 c y − 6

d 10 + 2x e pq + 1 f ab − c

g 5x + 6y h 10p − 10q

3 True

True bearing Compass bearing

a 010° N10°E

b 190° S10°W

c 070° N70°E

d 330° N30°W

e 355° N5°W

f 160° S20°E

g 250° S70°W

h 150° S30°E

N000°

S180°

NE045°

NW315°

SE135°

SW225°

E090°

W270°

120°

60°

300°

N

N

Broken Hill

CooberPedy

N

075°

210°

N

315°

N

20°

NN20°W

15°

N

S15°E

x 2x 3x 4x

4x 3x 2x x

2x x 4x 3x

3x 4x x 2x

Chapter 11

x22------

x3--- 6

x---



4 a b c d

5 c cannot be simplified

11D The distributive law: Expanding brackets

1 a 5 b 12 c 15, 13

d 4 e x, 10

2 a 2x + 2y b 15x + 15y c 9p − 9q

d 10x + 10y + 10z e 8c + 8d − 8e

3 a 2x + 6 b 5x + 10 c 4x − 36

d 10x − 70 e 12x + 36 f 18x − 6

g 8x + 28 h 120x − 50

4 a xy + xz b cd − ce c px + 2x

d x2 + 8x e 2x2 − 3x f 4x2 − x

g 2pq + 2pr h 6x2 − 8x i 6x2 + 12x

5 a 7x + 7y b 10x + 6y c 12x + 15y

d 6x + 30

Algebra Symbols 3

11E Substituting into expressions1 a 8 b 20 c 24 d 6 e 1

f 18 g 5 h 144

2 a 19 b 75 c –1

3 a 43 b 21 c 10 d 4 e 0 f 8

4 a the number of shirts

b 160 pins c 32

d When there are 9 shirts, 72 pins are used.

a The number of hinges b 20

c No, because 38 is not divisible by 3.

d 2x

6 a $200 b $150 c $50

7 a 18 b 45 c 45 d 20 e 78

f 5 g 180 h 12 i 150 j 90

8 a 21 b 27 c 48 d 90 e 42 f 70

9 a 20

b When 4 trucks make 5 journeys each there are 20 deliveries altogether.

10 a x = the number of cats and y the number of dogs.

b 28

c When there are 10 cats and 8 dogs in the shelter there are 28 meals served each day.

Algebra Symbols 4

11G Exploring dot patterns

1 a

b 6, 12, 18

c Each shape has 6 more dots than the previous one.

d 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72

2 a 9 b

c We start with 1 dot, and then each shape has four more dots than the previous one.

11H Exploring match patterns

1 a

b

c 24 d Multiply the shape number by 3

2 a

b 9

c

d We start with 4 matches, and then add 9 matches each time.

3 a

b

c i 17 ii 21 iii 201

d To work out the number of matches, double thenumber of dots and add 1.

Extended-answer question: Calendar patterns3 The sums of the numbers in each pair of diagonally

opposite cells are equal.

4

5 x + (x + 8) = 2x + 8; (x + 7) + (x + 1) = 2x + 8

Algebra Symbols 5

11I Rules and formulas1 a 16 b 4

2 a 9 b i 3 ii 21

c No, the formula (n − 1) × (n − 1) only works when there are 4 nappies. A formula must work for all the values.

d No, because you cannot have half a nappy.

3 a i $3 ii $4·75

b 25 cents is $0·25, and 0·25t means 25 cents times the number of minutes

c C = 1·75t + 2

4 a 10 b 45 strands

c You get 0 strands. A fence with only 1 post can’t have any strands!

d No. The number of posts must be a whole number.

5 a $94 b $26 c $50

x4--- 2y

3------ 3x

2------ 8

x---

25x24

---------

Shape number 1 2 3 4

Number of matches 3 6 9 12

Shape number 1 2 3

Number of matches 4 13 22

Shape number 1 2 3 4 5

Number of matches 4 13 22 31 40

Number of dots (d) 1 2 3 4 5 6

Number of matches (m) 3 5 7 9 11 13

x x + 1

x + 7 x + 8


12


6 a $7·20 b $20

7 a

b Calculator Street

Equations and Inequations 1

12A Solving equations by inspection1 a 5 b 7 c 4 d 44 e 41

2 a 9 b 24 c 40 d 43 e 99

3 a 2 b 6 c 9 d 3 e 8

4 a 20 b 48 c 45 d 5 e 0

5 a x + 5 = 33 b 6x = 42

c = 2 d 3x = 18

6 a When 7 is subtracted from some number the result is 18.

b When some number is multiplied by 8 the result is 24.

c When 11 is added to some number the result is 19.

d When some number is divided by 5 the result is 10.

12B Solving equations with flow charts

1 a b

c d

2 a

b

3 a

b

c


12C Solving equations by inverse operation1 a x = 5 b x = 17 c x = 7 d x = 21

e x = 4 f x = 24

2 a x + 14 = 27 b x = 13

3 a x + 20 = 100 b x = 80

4 a 3x = 27 b x = 9

5 a 4x = 500 b x = 125

6 a C b x = 10 litres

7 a D b 75 boys

12D Solving two- and three-step equations 1

1 a x = 3 b x = 6 c x = 6 d x = 2

e x = 3 f x = 13 g x = 75 h x = 4


12D Solving two- and three-step equations 2

1 a x = 6 b p = 10

2 a the number of passengers

b x = 37

3 a t = 2n + 5

b 2n + 5 = 45

n = 20

4 4x + 35 = 75

5 a $1 b t = 5 c 5

d 3t − 2 = 40

t = 14 hours

6 a 8x + 2 = 50 b $6

12E Inequations 11 a 8 > 7 b 2 × 12 < 5 × 5

c 14 + 1 = 3 × 5 d 12 × 9 < 112

2 a

b

c

3 a x < 6

b p ≥ 3

c 2 ≤ x < 5

d 10% ≤ x < 15%

4 a 70 ≤ x ≤ 110

b

Number of pedestrians

(p)

Number of vehicles

(v)

Result ofp × v × v

Algebra Drive

350 500 87 500 000

Bracket Road

200 600 72 000 000

Calculator Street

60 1500 135 000 000

Chapter 12

x8---

÷ 7

x 7x× 7

568

=

x x + 14+ 14

− 142612

=

x x − 9− 9

+ 9 1120

=

÷ 3

927

x x3=

× 3

÷ 3

x 3x 3x + 2× 3 + 2

– 2 20186

=

÷ 6

x 3x 6x − 2× 6 − 2

+ 234366

=

÷ 2

x 2x 2x − 5× 2 − 5

+ 57126

=

x 12x 12x − 7

÷ 12

× 12 − 7

+ 765726

=

x x + 14÷ 3

× 3

+ 14

− 14443090

3

=

x3

13--- 1

3---

x0 1 2 3 4 5 6 7 8

x0 1 2 3 4 5 6 7 8

x0 1 2 3 4 5 6 7 8

6 x

3 x

2 5 x

10 15 x

70 110 x




12E Inequations 21 a x < 3 b x ≥ 4 c x < 3

d x ≤ 1 e x > 2 f x ≥ 24

12F Exploring the coordinate plane1 A = (−1, 3), B = (−2, −4), C = (5, −2),

D = (3, 4), E = (0, −2)

2 Y

3 Eyes down

4 a i octopus ii lifeguard

iii edge of the water

b i (−4, −1) ii (−7, 3)

iii (5, 4)

c i ground ii air

iii water iv ground

v air

Extended-answer question: The queen rules1 64 2 d1, e4, b7, g8

3 a sum of the numbers is odd

b sum of the numbers is even

Probability 1

13A The language of chance1 a Photo taken: 12·7% Accident: 0·2%

b i unlikely ii likely iii very unlikely

2 a equally likely to occur or not occur

b very likely c very unlikely

d impossible e likely

3

4 a unlikely b likely

c very unlikely d almost certain

13B Theoretical probability

1 a b c

2 a or 0·2 b or 0·85 c 0

3 a or 0·6

b Alert Taxis. The probability of a female driver at

Alert Taxis is = 0·4, which is higher than at

Business Taxis, where the probability of a female

driver is = 0·375.

4 a or 0·2 b 0 5 or 0·25

6 or 0·2 7 a b

8 a getting a 1 when you throw a fair six-sided dienumbered 1–6

b getting a blue pen when choosing a pen at random from a box containing 4 blue pens, 5 red pens and 1 black pen

Probability 2

13F Exploring card games

1 a b c

d e f

g h

13G Spinners

1 a b c

2

3 a A

b i B, white ii B, black

c Spinner B is unlikely to stop on a grey sector.

13I Using statistics to find probabilities1 a

b i likely ii very unlikely iii unlikely

2 a × = 14%

b i = ii 36%

c adult d life member

3 a unlikely

b old: = 0·15 new: = 0·4

c The old computers seem more reliable because only 15% needed repair compared with 40% of the new computers.

Statistics 1

14A Collecting data1 a numerical b ordinal c numerical

d categorical e numerical

Chapter 13

d c

impossible unlikely likely certainequallylikely tooccur ornot occur

a e b

16--- 5

6--- 2

3---

15--- 17

20------

35---

25---

38---

15--- 1

4---

15--- 1

3--- 7

12------

Result of call Frequency Relative frequency

Answered 61 = 0·61

Not answered 22 = = 0·22

Answer phone 11 = 0·11

Out of order 1 = 0·01

Engaged 5 = = 0·05

113------ 1

52------ 1

13------

14--- 3

4--- 1

2---

313------ 5

13------

14--- 3

8--- 1

8---

win

lose

61100---------

22100--------- 11

50------

11100---------

1100---------

5100--------- 1

20------

750------ 100

1---------

1850------ 9

25------

75500--------- 16

40------

Chapter 14


14


2 a discrete c continuous e continuous

3 a

b 6 tickets

c 1 ticket—this number of tickets occurs most frequently

4 a 8 b 2

c 56—this is the total number of houses

5 a

b 291 c $157·05

Extended-answer question: Frequency tables

6

a 6 b 17 c 32% d

Statistics 2

14B Creating and interpreting tables1 a

b 2 c $560 000

d 137 Ralph Road e 3

f 336A Downing Road , 14B Terry Crescent

2 a Rocky Road b Rocky Road c Snickers

d Crunchie, Rocky Road, Double Yum, Snickers, Toblerone

14C Column and bar graphs

1 a

b Homogenised c 23 cartons

2 a

b 26 c Corporate lunch d 3

3 a 3 b Oliver

c Mark and Sally d 16

4 38

Statistics 3

14D Interpreting line graphs1 a 23°C, January, February

b 5°C, July

c July

2 a

b The long-term trend is for the number of driverskilled to decrease.

c Trend is for the number of drivers killed to increase.

d decreasing trend

14E Pie graphs 1

1 a Netball b c 72° d 36

2 a

Number of tickets

Tally Frequency

0 10

1 12

2 5

3 3

4 2

5 0

6 1

Coin Frequency Value

5c 33 $1·65

10c 49 $4·90

20c 80 $16·00

50c 35 $17·50

$1 71 $71·00

$2 23 $46·00

Totals 291 $157·05

Weight (kg) Frequency

0–<1 kg 0

1–<2 kg 2

2–<3 kg 6

3–<4 kg 11

4–<5 kg 6

Address Price Section area

Type of dwelling

Road access

15 Murray St

$355 000 684 m2 town-house

corner section

336A Downing Road

$239 000 775 m2 separate house

right-of-way

68 Fairlie Ave


road-front section

137 Ralph Road


road-front section

14B Terry Crescent

$249 000 637 m2 town-house

right-of way

| | | | | | | || | | | | | | | | || | | || | || |

|

1725------

Day of week Opens/closes Hours open

Monday 9 am–6 pm 9

Tuesday 9 am–6 pm 9

Wednesday 9 am–6 pm 9

Thursday 9 am–6 pm 9

Friday 9 am–9 pm 12

Saturday 10 am–5 pm 7

Sunday 10 am–3 pm 5

Total 60

2

4

6

8

Hom

ogen

ised

Red

. fat

Tri

m

Phys

ical

Flav

oure

d

Num

ber

sold

2

4

6

8

Wed

ding

s

21st

Cor

pora

te lu

nch

Xm

as

Oth

er

Num

ber

of f

unct

ions

Catering for functions

1986 1988 1990 1992 1994 1996 1998

20

40

60

80

100

120

0

Number of drivers (18–25) killed

110------



b × 360° = 54° c

3 a × 360° = 171·9° (calculator)

b Used to smoke: 122°; Smoke now: 66°

c

Statistics 4

14E Pie graphs 2

1 a 2·5 people b

2 a Black coal

b Black coal, Brown coal, Other, Gas

c 92% d

14F Dot plots and the mode1 a 19 b 6

2 The driver should also be included. Each column of dots would then move one space to the right.

3

4 a 14 b No mode

c 0 d Two modes: 14 and 17

5 a 16

b The number with the most dots above it gives the mode of a dot plot.

6 a 7 b 3 c 1 d 41

7

8 Pippa was correct—there were 5 nectarines, which is more than the other types of fruit.

Statistics 5

14G The mean1 a 5 b 45 c 15

2 8·9

3 a 64·55 b 620·95

4 62 cents 5 691 kg

6 The schoolboy pack (combined weight of 496 kg) is heavier than the adult pack (combined weight of 486 kg).

7 $34

8 a 61·2 seconds b Eun-Wah

9 a 8·5 b 7, 8, 9, 10

10 158 cm

14H The median and the range1 a 22 b 10

2 a 19 b 20

3 a 49 b 6 c 34·5

4 a 31 b 8 c 32

5 a 35 cents b $1·80

c The mean gives information about the total sold: 24 × $0·25 = $6. Three bags were sold.

6 a

b 156·0 km on Thursday

Puzzle12

Statistics 6

14I Stem-and-leaf plots1 a 2 b 26

c Likely—18 out of 26 (more than two-thirds) of her ancestors lived until they were over 70 years of age.

d

2 a $119 b $42

3 a

b 86 minutes c 18 minutes

4 24

14J Venn diagrams1 a 30 b 24

c d 7

2 a b 10

960------ MSu

Sa

F

ThW

T

191400---------

Neversmoked

Nowsmoke

Used tosmoke

email

Phone/fax

Postcards/letters

Nuclear

Wind,solar

Fossilfuels:coal,oil,gas

2 3 4 5 6 7 8 9 10

27 28 29 30 31 32 33Number of students in Year 8 classes

34 35

Day of week

Odometer at start of day

Odometer at end of day

Distance travelled

(km)

Sunday 4018·6 4122·7 104·1

Monday 4122·7 4346·3 223·6

Tuesday 4346·3 4435·5 89·2

Wednesday 4435·5 4548·2 112·7

Thursday 4548·2 4704·2 156·0

Friday 4704·2 4897·3 193·1

Saturday 4897·3 5060·7 163·4

0 | 0 8

87654321

62030118

8153229

729

84

84

95

6

6

6

7

9

9

1119 13

M DVD

217 10

71

Glasses Braces


16


c students who wear neither glasses nor braces

14K Two-way tables1 a 167

b the number in the group who plan to visit both WA and SA

2 a

b 104 c 7

3

Short-answer questions1 7624 km

2 a 20 b 2 c 9 d 10

3 2 4 { 1, 2, 4 }

5 40 6 72 = 2 × 2 × 2 × 3 × 3

7 Count the number in one column and then multiply it by 28.

8 A number is divisible by 3 if the sum of its digits is divisible by 3.

9 a b

10 a b

11 a b 14

12 a b

13 a $8 b 105 m

14 a 48 b 24

15 Bruce, Donald, Adrian, Colin

16 a b

17 a 0·8 b 0·05

18 a 60% b 85%

19 a 2·9 m b 2900 mm

20 a x = 3 m, y = 6 m b 129 m2

21 46 cm2 22 12 cm3 23 108 hours

24 a Thursday b Wednesday c Saturday

25 2140 26 67 minutes

27 103° 28 101° 29 100°

30 a x = 31° b y = 20°

31 24° 32 92°

33 a 2a + c + p b 4a + 29c

34 a 6x b 9x + 23 c p + 13q

35 a 10xy b 24x2 c d

36 a 4x + 8 b 5y – 15 c 30x + 20

37 a 24x + 8 b x2 + 6x + 12

38 a $15 b $(2n + 9)

39 4x + 3 = 15; x = 3

40 a a = 31 b b = 20

c c = 7 d

41 10x = 35; x = 3·5 m

42 a x = 75 b y = 18 c x = 12

43 7x – 50 = 160; x = 30

44 a x < 12 b x ≥ 9 c x < 7

45 if ‘t’ is included as a word, otherwise

46

47 a 5 b New Zealand c 4

48 a 35 000 b False

c 220 000 d World War II

49 a August b September c $20

d May e decreasing

50 a 7

b There are 90 students. 360° ÷ 90 = 4°c

d

51 a 10

b In a dot plot, the mode is the number with the most dots above it.

52 86

Multiple-choice questions1 C 2 A 3 C 4 C 5 C 6 C

7 B 8 B 9 D 10 C 11 A 12 C

13 B 14 C 15 C 16 C 17 B 18 D

19 C 20 C 21 C 22 A 23 B 24 A

25 C 26 D 27 A 28 A 29 D 30 C

31 C 32 B 33 C 34 C 35 D 36 D

Own microwave

Do not own

microwave

Totals

Own dishwasher

59 7 66

Do not own dishwasher

21 17 38

Totals 80 24 104

Play cricket Do not play cricket

Totals

Play football 57 12 69

Do not play football

11 30 41

Totals 68 42 110

Chapter 15

45--- 3

8---

13--- 2

3---

310------

67--- 5

8---

625------ 5

8---

Day of the week

Number of students

Angle at centre

Sunday 9 36°

Monday 12 48°

Tuesday 18 72°

Wednesday 15 60°

Thursday 15 60°

Friday 11 44°

Saturday 10 40°

5x3

------ 2yx

------

d 12---=

1017------ 9

16------

Red

Blue

White

Sat Sun

Mon

Tues

Wed

Thurs

Fri



Short-answer questions

1 $667 290 2 $1·12 3 91

4 a b 5·3333 cm2

5 73, 64, 37, 55, 46

6 a 324 b 1 048 576

7 a 37 b 0·71

8 3 × 3 × 7 × 13

9 10

11 261·25 km

12 18 cakes and 2 cups left over

13 $111 700 14 15 2·38

16 a b

17 a 4 b 5·08 c 24·35 d 25·65

18 3 hours 19 $21

20 106 bottles—round down because the last bottle would not be completely filled

21 $20·65 22 $3506·25

23 a $14·85 b $196·90

24 a 2·1845 b 0·0266 c 3·7934 d 0·3421

25 152 mm or 15·2 cm 26 4·09 m2

27 24 472 cm3 28 252°

29 111° 30 25·04 cm

31 a 80·9295 b 1·156 c 24·8004

32 a x = 5 b x = 89·093

33 0·26 34

35 a 449 b 0·2472 c 0·3853

36 a

b If the first card is black, that leaves 25 black cards

out of 51, giving a probability of .

c

d

37 $926·99

610------

116------ 0.0625 cm2=

23--- 42

3---

135---

1725--- 431

70------

1st card is black 0·5

1st and 2nd cards are black 0·2451

1st 3 cards are black 0·1176



Black

White

Red

12---

2551------

12--- 25

51------× 25

102--------- 0.2451= =


1Fully Worked Solutions

Fully Worked Solutions

Exercise 1A1 a 24 b 612 c 204

d 6458 e 37 000 f 5 006 001

g 600 000 h 40 000 067 i 215 099

j 140 530 k 809 087 920

2 a Forty-eight

b Two hundred and ninety-one

c One hundred and twenty-five thousand, nine hundred and nine

d Three thousand, four hundred and ninety

e Two thousand and sixty-three

f Nine million, seven hundred and forty-five thousand, one hundred

g Sixty-seven thousand, four hundred and five

h Nine thousand and three

i Two hundred and twenty-four million

j Eight hundred and seventy-two thousand and four

k Four million and sixteen

l Two hundred and thirteen thousand, five hundred

3 a Units b Thousands

c Millions d Hundreds

e Tens f Ten thousands

g Ten thousands h Units

i Hundred millions j Tens

k Hundred thousands l Hundreds

4 a Three b Thirty

c Three thousand d Three hundred

e Three hundred thousand f Thirty thousand

g Three million h Three million

5 a 32 343 b 420 520 c 940 311

d 45 481 e 3 040 300 f 12 578

6 a 860 b 30 056 c 4830

d 80 050 030 e 10 687 f 5 406 007

7 a 841 b 9853 c 61

d 96 421 e 976 410 f 98 743 210

8 a 58 b 013 567 c 3569

d 0 234 579 e 478 f 23 467

9 a 12, 16, 35, 123, 145, 245, 321

b 303, 306, 316, 360, 366, 603, 660

c 4007, 4070, 4707, 4770, 4777

d 55 789, 55 796, 55 809, 55 976, 55 980

e 3, 34, 56, 345, 467, 721, 5005

f 12 405, 20 451, 42 510, 52 401

10 a $215 b $123 c $132 d $224

Exercise 1B1 a 157 b 1138 c 3840 d 392

e 1570 f 9682 g 16 825 h 6820

i 4821 j 5833 k 9068 l 9608

2 a b

c d

e f

3 4

5 6

7

8 a Alice has to travel 26 km.

b Bonnie has to travel 20 km.

c Celeste’s house is 22 km from Melbourne.

d Bonnie travels the shortest distance.

e The girls have to travel a total of 68 km.

f Alice has to travel 46 km, Celeste has to travel 42 km.

9 a NSW $12 917, Qld $13 006, WA $9172

b Queensland

c October $13 489, November $12 292, December $9314

d October e Total sales $35 095

Exercise 1C1 a 824 b 312 c 111 d 44

e 146 f 4943 g 5633 h 2791

i 584 j 1690 k 7576 l 2677

2 a b

Chapter 1 2 2658 642

+ 2 451

13 358

45 671+ 89 065

134 736

45 651+ 3 459

49 110

492571

+ 3 490

4 553

3 56156

+ 8 900

12 517

34645 698

+ 445 621

491 665

45821616

+ 28

$187

Sarah spent $187 altogether.

436134

+ 75

$645

Matthew spent $645 altogether for his skate gear.

785862804930

+ 912

$4 293

Mr Young spends $4 293 on his cattle.

45 95527 35016 97520 890

+ 35 420

$146 590

Total sales for the week are $146 590.

193374203

+ 103

873

The shortest distance between Melbourne and Sydney is 873 km.

8642− 3851

4791

98 642− 54 739

43 903

2



c d

e f

3 Emily has $312 left.

4 The Jones family must borrow $201 250 from the bank.

5 174 days left in the year.

6 11 255 kg of wheat can be added to the silo.

7 The Matterhorn is 319 m higher.

8 a It is 725 km from Euroa to Sydney.

b It is 310 km from Melbourne to Albury.

c It is 563 km from Albury to Sydney.

d It is 215 km from Holbrook to Yass.

e It is 680 km from Melbourne to Goulbourn.

9 a 312 000 – 23 880 = 288 120288 120 ML are required to fill the lake.

b 40 000 – 36 981 = 30193019 ML are required to reach the capacity.

c 3 038 000 – 928 330 = 2 109 6702 109 670 ML are required to take the Hume up to capacity.

d 411 000 – 182 738 = 228 262228 262 ML are needed to fill Waranga Basin up to capacity.

e 190 230 – 129048 = 6118261 182 ML are required to take Glenmaggie up to capacity.

f 1 068 000 – 496 382 = 571 618571 618 ML are required to fill Thomson Dam.

Exercise 1D

1 a b c

2 a 568 b 855 c 1664

d 6335 e 10 246 f 16 430

g 81 673 h 294 831 i 41 976

j 31 518 k 407 442 l 1 538 570

3 a b

c d

e

4 55 × 120 = 6600cSo it costs $66 to fill up the car.

5 Sasha earns $3060 for the year.

6 Mia’s clothes cost $323.

7 The farmer received $25 425 for his lambs.

8 a 4564 hours

b $299 000 per crossing

c $14 000 per crossing

d $10 850 per crossing

e Total revenue per crossing carrying maximum load = $323 850

9 It takes the winner 192 min, or 3 hours 12 min, to complete 24 laps.

10 a 21 km b 210 km c 658

d 34 216 e $336 f $2184

Exercise 1E1 a 2143 b 211 c 310 d 433

e 208 f 53 g 6589 h 510

i 267 j 562 k 914 l 982

2 a b c

d e f

g h i

j k l

3 a b c

d

4 Maria earns $96 per day.

5 John has 11 880 sheep.

6 The hiker walked 16 km per day.

7 a 1980 sheep

b 220 sheep per day

c There are 594 sheep in each flock.

8 The piggery has 1574 sows.

9 a 24 cars are sold per month.

b 6 cars are sold per week.

10 a The Chans travelled 480 km.

b 6 hours per day

11 a Each machine produces 144 000 bottles per week.

b 28 800 bottle are produced per machine per day.

c 60 bottles are produced per machine per minute.

d 2 litres in each bottle

12 a

$2031·12 is spent on groceries per family member per year.

5651− 999

4652

30 500− 876

29 624

56 000− 32 879

23 121

34 232− 659

33 573

4× 3

12

4× 4

16

5× 4

20

625× 92

1 25056 250

57 500

238× 6

1428

287× 24

11485740

6888

410× 162

82024 60041 000

66 420

742× 47

519429 680

34 874

2153)645

3674)1468

6015)3005

996)594

2917)2037

1 2708)10 160

9999)8991

48010)4800

2 65111)29 161

6 24712)74 964

5088)4064

20 6137)144 291

15253)4575

3 2846)19 704

60411)6644

688)544

2031·124)8124·48



b

The family spends $677·04 on groceries per month, on average.

c

The family spends $156·24 on groceries per week, on average.

13

The fertiiser costs $67.65 per tonne.

Exercise 1F1 a 20 × 5 × 4 = 100 × 4 = 400

b 25 × 4 × 9 = 100 × 9 = 900

c 10 × 10 × 56 = 100 × 56 = 5600

d 50 × 2 × 37 = 100 × 37 = 3700

e 10 × 10 × 321 = 100 × 321 = 32 100

f 4 × 25 × 34 = 100 × 34 = 3400

g 50 × 2 × 66 = 100 × 66 = 6600

h 5 × 20 × 19 = 100 × 19 = 1900

I 10 × 10 × 99 = 100 × 99 = 9900

j 2 × 50 × 33 = 100 × 33 = 3300

k 20 × 5 × 71 = 100 × 71 = 7100

l 4 × 25 × 15 = 100 × 15 = 1500

2 a (8 + 2) × 3 = 10 × 3 = 30

b (8 + 2) × 55 = 10 × 55 = 550

c (15 + 5) × 14 = 20 × 14 = 280

d (5 + 7) × 6 = 12 × 6 = 72

e (19 + 31) × 12 = 50 × 12 = 600

f (18 + 2) × 14 = 20 × 14 = 280

g (14 − 6) × 8 = 8 × 8 = 64

h (34 − 24) × 21 = 10 × 21 = 210

i (65 − 15) × 3 = 50 × 3 = 150

j (98 − 18) × 7 = 80 × 7 = 560

k (63 − 13) × 12 = 50 × 12 = 600

l (85 − 15) × 11 = 70 × 11 = 770

3 a 56 × 3 × 10 = 168 × 10 = 1680

b 21 × 2 × 10 = 42 × 10 = 420

c 7 × 8 × 2 × 10 = 112 × 10 = 1120

d 6 × 15 × 10 = 90 × 10 = 900

e 2 × 34 × 100 = 68 × 100 = 6800

f 5 × 12 × 100 = 60 × 100 = 6000

g 2 × 45 × 10 = 90 × 10 = 900

h 85 × 4 × 10 = 340 × 10 = 3400

i 19 × 3 × 10 = 57 × 10 = 570

j 5 × 23 × 10 = 115 × 10 = 1150

k 9 × 9 × 2 × 10 = 162 × 10 = 1620

l 66 × 2 × 10 = 132 × 10 = 1320

4 a 28 × 100 ÷ 2 = 2800 ÷ 2 = 1400

b 91 × 100 ÷ 2 = 9100 ÷ 2 = 4550

c 36 × 1000 ÷ 2 = 36 000 ÷ 2 = 18 000

d 52 × 1000 ÷ 2 = 52 000 ÷ 2 = 26 000

e 387 × 10 ÷ 2 = 3870 ÷ 2 = 1935

f 46 × 10 ÷ 2 = 460 ÷ 2 = 230

5 (28 + 32) × 4 = 60 × 4 = $240

Mario and Eliza spent $240 in total.

6 (1·4 + 1·6) × 5 = 3 × 5 = $15

The boys spent a total of $15.

7 (39 + 41) × 8 = 80 × 8 = 640 s = 10 min 40 s

Combined time is 10 min 40 s

Exercise 1G1 a 14 ÷ 2 + 3 × 4 = 7 + 12 = 19

b 60 ÷ 3 ÷ 4 + 2 = 5 + 2 = 7

c (16 + 4) ÷ 5 × 3 = 20 ÷ 5 × 3 = 12

d 5 × (4 − 3) + 9 = 5 × 1 + 9 = 14

e 6 × (2 + 7) − 2 × 7 = 6 × 9 − 14 = 40

f 5 + 7 − 3 × 2 = 12 − 6 = 6

g 3 × 15 − 6 × 5 = 45 − 30 = 15

h 18 ÷ 2 × 10 − (7 × 8) = 90 − 56 = 34

i 6 × 9 + 4 = 54 + 4 = 58

j 55 − 3 × 9 = 55 − 27 = 28

k (34 + 6) × 6 = 40 × 6 = 240

l 8 + 4 × (26 − 15) = 8 + 44 = 52

m 5 + 24 − 13 = 16

n (144 ÷ 6) − 3 × 7 = 24 − 21 = 3

o (15 + 6) ÷ 7 × 2 = 6

p 6 × 2 ÷ 3 = 4

q (9 − 4) × (6 + 3) ÷ 15 = 3

r (8 + 7) ÷ 5 × 3 − 1 = 8

s 3 × 3 × 3 − (4 × 5) = 7

t (1 + 2 + 3) × 10 + 40 = 100

u (6 + 2 × 8) ÷ 2 + 32 = 43

v 2 × 9 + 7 = 18 + 7 = 25

w 16 ÷ 4 + 5 = 4 + 5 = 9

x 16 − 3 × 2 = 10

2 a of 16 × 5 – 2 × (10 – 7)

= 8 × 5 – 2 × 3 = 34

b 6 + 34 ÷ 17 – 66 ÷ 11 = 6 + (34 ÷ 17) – (66 ÷ 11)= 6 + 2 – 6 = 2

c 9 – 8 × 7 ÷ 14 + 10 = 9 – 4 + 10 = 15

d 13 + + – 2 × 6

= 13 + 4 + – 12 = 6

e 11 – 64 ÷ 8 + 5 × 11 = 11 – 8 + 55 = 58

f (4 – 24 ÷ 8 ) × 55 – 9 × 5= 1 × 55 – 45 = 10

3 a 6 + 8 − 1 = 13

b 54 ÷ (6 + 3) + 2 = 8

c (6 + 34 ÷ 2 + 3) ÷ 2 = 13

d 42 ÷ (5 + 2) × 5 = 30

e 15 + 4 × (5 − 5) = 15

f 81 ÷ 9 ÷ (2 + 1) = 3

g (12 − 2) × 5 = 50

h 120 ÷ (10 + 2) + 5 = 15

i 8 + (4 − 3) × 2 = 10

j 45 ÷ 3 × 2 + 16 = 46

677·0412)8124·48

156·2452)8124·48

67·6530)2029·50

12---

14--- 18×

12---

12--- 1

2---

4



k 18 ÷ 9 × (5 + 7) = 24

l 4 + 3 × (3 + 4) = 25

m (4 − 2) × 100 ÷ 25 = 8

n 100 ÷ 25 × 5 + 6 = 26

o (48 ÷ 16 + 5) × 2 = 16

4 a (2 + 8) ÷ 5 = 2 b (14 − 5) × 9 = 81

c 6 × (8 − 3) = 30 d (21 + 5) ÷ 2 = 13

e 12 − 8 + 5 = 9 f 40 − 14 ÷ 7 = 38

g (10 − 8) × (5 + 4) = 18

h (34 − 12) × (12 ÷ 4) = 66

i 36 ÷ 9 + (10 − 4) = 10

j (64 ÷ 16) × 16 ÷ 8 = 8

k 20 + 100 ÷ 25 = 24

l (9 + 3) × (8 – 3) = 60

5 a 16 ÷ (3 + 1) × 3 + 6 = 16 ÷ 4 × 3 + 6= 4 × 3 + 6= 18 ≠ 36FALSE

b (2 + 3 × 5) – (3 + 16 ÷ 4) = 17 – 7= 10 ≠ 18FALSE

c 5 × 10 + 3 × 8 ÷ 4 = 50 + 6 = 56TRUE

d 44 ÷ 4 + 7 × 2 – 3 = 11 + 14 – 3= 22 ≠ 5FALSE

e (16 + 3 × 2) ÷ 11 – 1 = 2 – 1 = 1TRUE

f (48 + 2) ÷ 5 – 18 ÷ 3 = 10 – 6 = 4TRUE

g 15 × 3 ÷ ( 6 + 3) + 1 = 5 + 1 = 6TRUE

h (14 + 5 – 1) ÷ (2 × 5 – 1) = 18 ÷ 9= 2 ≠ 3FALSE

i 100 ÷ 25 × (6 + 2) = 4 × 8 = 32 ≠ 26FALSE

j 64 ÷ 16 + 16 – 8 = 12TRUE

6 a ii 2 + 4 × 3 = 14

b i 3 + 62 × 2 = 75

c ii 4 × 8 + 2 = 34

d i 16 ÷ 4 + 4 = 8

e i (13 + 8) ÷ (3 + 4) = 3

f ii 81 ÷ 9 + 1 = 10

Exercise 1H1 a 54 + 234 ≈ 50 + 200

= 250

b 1249 + 90 ≈ 1000 + 90= 1090

c 651 + 16 + 270 ≈ 700 + 20 + 300= 1020

d 1239 + 854 + 45 ≈ 1000 + 900 + 50= 1950

e 789 − 88 ≈ 800 − 90= 710

f 1467 − 674 ≈ 1000 − 700= 300

g 358 − 104 − 55 ≈ 400 − 100 − 60= 240

h 2478 − 865 ≈ 2000 − 900= 1100

i 45 × 89 ≈ 50 × 90= 4500

j 478 × 12 ≈ 500 × 10= 5000

k 49 × 82 × 105 ≈ 50 × 80 × 100= 400 000

l 372 × 34 × 2 ≈ 400 × 30 × 2= 24 000

m 83 ÷ 12 ≈ 80 ÷ 10= 8

n 57 ÷ 6 ≈ 60 ÷ 6= 10

o 804 ÷ 37 ≈ 800 ÷ 40= 20

2 84 + 156 + 42 + 11 ≈ 80 + 200 + 40 + 10= $330

Michelle will need about $330 to cover her expenses.

3 2120 + 2871 + 3278 + 3091 + 2656 ≈ 2000 + 3000 + 3000 + 3000 + 3000= 14 000 km

The sum of the distances for the air travel is about 14 000 km.

4 a 70 b 100

Technology Activity 1I4 + 4 ÷ 4 + 4 = 9(4 + 4) ÷ 4 + 4 = 64 ÷ 4 + 4 – 4 = 1

Exercise 1J2 a LIX b CXXXVII c LXXIII

d XIV e CCCCLXXXII f CXXIV

3 a 24 b 255 c 311 d 309 e 45 f 99

4 a b

c d

e f

5 a 26 b 8 c 79

d 327 e 1012 f 556

6 a b c

d e f



Puzzles

1

2 a 8, 6, 9 b 12, 10, 17

c 4, 12, 8, 9 or 7, 9, 11, 6

d 24, 16, 6, 7 or 22, 18, 4, 9

e 11, 8, 5, 6, 4

f 9, 10, 21, 8, 16, 17 or 10, 9, 22, 7, 17, 16

3 a Dirk Hartog landed at Shark Bay

b A boomerang that won’t come back

Applications

Number puzzleA possible answer is 1, 2, 4, 6, 8, 10, 9, 7, 5, 3

Magic squares1 Magic number is 26 2 Magic number is 584

3 Magic number is 558

Basketball ladder

Word sumsa 79 422 b 1960

+ 3 104 + 1875

82 526 3835

Enrichment1 a 246 b 628

+ 18 + 399

429 1027

c 416 d 1212+ 495 + 643

911 1855

2 a 294 b 1628− 184 − 448

110 1180

c 692 d 4243− 199 − 1951

493 2292

3 a 128 b 224× 4 × 8

512 1792

c 426 d 283× 34 × 67

1704 198112 780 16 980

14 484 18 961

4 a b c

5 a b

c d

e f

g h

4 2 5 6 1 4 9 9

1 2 8 8 5 2 2 4

6 5 3 4 8 3 3

7 1 3 6 9 2 5 8 6

8 4 5 3 2 9 1 7

3 6 8 1 7 1

9 6 3 4 7 5 3 3

2 6 6 5 2 3 3 2

2 7 6 9 2 4 1 8

5 8 4 2 2 8 3 5

97 27 20 118 101 185 179 119

62 76 83 41 167 131 137 149

90 48 55 69 143 155 161 125

13 111 104 34 173 113 107 191

107 118 217 116

140 193 125 100

128 134 106 190

183 113 110 152

Team Foul

Goa

l

3 po

inte

r

Tota

l

WLD

%

Springfield 5 30 5 80 W 160

SA Sharks 6 22 2 56 W 137

Vic Vipers 5 17 1 42 W 108

Qld Quokkas 0 26 4 64 W 102

WA Wallabies 1 15 5 46 D 100

Tas Tigers 2 22 0 46 D 100

Sydney Stars 4 28 1 63 L 98

Melb Midgits 3 15 2 39 L 93

NT Newts 2 15 3 41 L 73

Shelbyville 1 23 1 50 L 63

457)315

52711)5797

6 2178)49 736

25727)6939− 54

153− 135

189− 189

000

24137)8917− 74

151− 148

37− 37

000

3 28719)62 453− 57

54− 38

165− 152

133− 133

000

6 58721)138 327− 126

123− 105

182− 168

147− 147

000

54913)7137− 65

63− 52

117− 117

000

1 62029)46 980− 29

179− 174

58− 58

000

25432)8128− 64

172− 160

128− 128

000

6 85724)164 568− 144

205− 192

136− 120

168− 168

000

6



i

6 a 5 b 8 c 13 d 28 e 85 f 469

g 56 h 512 i 2925

7 a 10110 b 1001111 c 100011

d 111000 e 1000000 f 1100100

g 10100100 h 100000000 i 1001010111

j 100000000000

8 a 1010 b 10000 c 10010

d 100010 e 1010000 f 110000000

g 1001101 h 1101011 i 10010100

9 a 100100 b 1010100 c 11000110011

Revision1 a 90 876, 3258, 2348, 567, 543, 65

b 726, 627, 626, 276, 267, 266

c 444, 440, 404, 400, 44, 40, 4

2 a Two hundred and thirty

b One hundred and twenty-three thousand, five hundred and sixty-two

c One thousand, eight hundred and seventy-two

d Twenty-one e Eight

3 a 4620 b 1 249 016 c 19 465

d 50 925

4 a i 7570 ii 15 177 iii 11 309

b c

5 a i 464 ii 3168 iii 14 204

b c

6 a i 3672 ii 33 150 iii 1 852 745

b c

7 a i 158 ii 1402 iii 4403

b c

8 a 44 × 500 = 22 × 1000 = 22 000

b 34 × 7 + 16 × 7 = 50 × 7 = 350

c 25 × 7 × 4 = 100 × 7 = 700

d 5 × 78 × 20 = 100 × 78 = 7800

e 345 × 20 = 690 × 10 = 6900

f 50 × 95 × 2 = 100 × 95 = 9500

g 6 × 67 + 67 × 4 = 67 × 10 = 670

h 4806 × 50 = 240 300

I 18 × 471 − 8 × 471 = 4710

J 471 × 50 = 23 550

k 34 × 200 = 68 × 100 = 6800

l 432 × 20 = 864 × 10 = 8640

9 a 56 ÷ 8 × 2 = 7 × 2 = 14

b 15 + 5 × 6 − 4 = 15 + 30 − 4 = 41

c (8 + 9) × 2 + 6 = 17 × 2 + 6 = 40

d 5 × (11 − 3) ÷ 4 = 5 × 8 ÷ 4 = 10

e (6 − 6) × 7 + 3 = 3

f 8 + 2 × 8 ÷ 16 = 8 + 1 = 9

g (25 − 8 × 2) ÷ 3 + 10 = 13

h 44 ÷ 2 ÷ 11 + 5 = 2 + 5 = 7

i 3 × 6 − 18 ÷ 9 = 18 − 2 = 16

10 1721 + 1723 + 1477 + 1419 ≈ 1700 + 1700 + 1500 + 1400= 6300 metres

The total height of the four peaks is approximately 6300 metres.

11 2399 + 875 + 120 + 340 + 2500 ≈ 2400 + 900 + 100 + 300 + 2500= 6200

Rosetta’s holiday cost approximately $6200

12 a 19 = XIX b 127 = CXXVII

c 63 = LXIII d 34 = XXXIV

e 401 = CDI f 1234 = MCCXXXIV

13 a XIV = 14 b CCLVI = 256

c CCXXII = 222 d CVI = 106

e XLV = 45 f CL = 150

Learning task 2A1 a 10, 11, 12, 13, 14 b 12, 14, 16, 18, 20

c 21, 28, 36, 45, 55 d 17, 21, 26, 31, 37

e 33, 45, 59, 75, 93 f 32, 64, 128, 256, 512

g 25, 19, 14, 10, 7 h 33, 65, 129, 257, 513

2 a 1, 121, 12 321, 1 234 321

b 6, 12, 18, 24

c 11, 101, 1001, 10 001

3 a 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765

b 4 c 7 d 12 e 20

f Twentieth term − 1= 6765 − 1= 6764

5 b 3, 8, 15, 24, 35, 48, 63, 80, 99, 120

c differences = 5, 7, 9, 11 ...

6 a i 6, 15 ii 10, 25

b i 9 ii 15

d i 6, 15, 28, 45, 66, 91, 120, 153, 190, 231

ii 10, 25, 40, 55, 70, 85, 100, 115, 130, 145

7 a 47, 95, 191 b 33, 65, 129

c 121, 249, 505 d 65, 129, 257

e 77, 157, 317 f 91, 187, 379

g 108, 220, 444 h 136, 280, 568

4 26117)72 437− 68

44− 34

103− 102

17− 17

00

3086670

+ 201

7179

568+ 631

1199

876− 235

641

7387− 4649

2738

740× 12

14807400

8880

489× 39

4 40114 670

19 071

4723) 1416

98511)10 835

Chapter 2



Exercise 2B1 a 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72,

78, 84, 90, 96

b 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98

c 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96

d 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99

e 10, 20, 30, 40, 50, 60, 70, 80, 90

2 a 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48

b 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39,42, 45, 48

c 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48

d 5, 10, 15, 20, 25, 30, 35, 40, 45

3 44, 55, 66, 77

4 144, 156, 168, 180, 192

5 a 10 b 12 c 63 d 42 e 24 f 30

6 a 10 b 60 c 72

7 Lowest common multiple is 420.10 circuits for Sarah = 42 × 10 = 420 seconds7 circuits for Emily = 60 × 7 = 420 secondsAfter 7 minutes they will be together again.

8 Lowest common multiple is 24. The machines produce lollies simultaneously every 24 seconds.

9 Lowest common multiple is 36. The restaurants will change their menus simultaneously in 36 weeks. If they change their menus on 1 January, they will change their menus only once again on the same day that year.

10 The lowest common multiple is 408. They touch the wall after 408 seconds.

Lulu does 17 laps and Lillian does 12 laps.

Exercise 2C1 a 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

b 1, 2, 3, 5, 6, 10, 15, 30 c 1, 2, 7, 14

d 1, 2, 4, 5, 8, 10, 20, 40

e 1, 2, 4, 13, 26, 52 f 1, 3, 5, 15

g 1, 2, 4, 8, 16, 32 h 1, 13

i 1, 2, 5, 10, 25, 50 j 1, 3, 9, 27

k 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

l 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

2 a 6 b 15 c 1 d 13 e 8

f 10 g 30 h 48 i 16

3 Highest common factor of 40 and 64 is 8, so the longest length which makes all the pieces the same size is 8 m.

4 The highest common factor of 150 and 180 is 30, so the longest length which uses all the wood is 30 cm.

5 a Highest common factor of 4, 6 and 10 is 2, so each piece of hose would be 2 m.

b Keiko will thus have 10 pieces of 2 m each.

6 Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. Mr Chan could split the class exactly into groups of any of these numbers. There would be 24, 12, 8, 6, 4, 3, 2 or 1 groups, respectively.

7 Highest common factor of 84, 126, 294, 462, is 42. So there will be 42 groups of scouts.

Exercise 2D1 a 45, 55, 6210 b 6210

2 a 234, 6780 b 234, 6780 c 234

3 a 32, 540, 5672, 54 984, 346 884

b 32, 540, 5672, 54 984, 346 884

c 32, 5672, 54 984

4 a 2, 3, 4, 5, 8, 9 b 3, 5 c 2, 3, 9

d 3 e 2, 4, 8 f 3, 9

g 3 h 2, 4, 5, 8 i 3, 9

Learning task 2E1 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53,

59, 61, 67, 71, 73, 79, 83, 89, 97

2 4, 6, 8, 9, 10, 12, 14, 15, 16, 18

3 10 = 3 + 7, 12 = 5 + 7, 14 = 3 + 11, 16 = 5 + 11, 18 = 7 + 11, 20 = 7 + 13, 22 = 3 + 19, 24 = 5 + 19, 26 = 7 + 19, 28 = 5 + 23, 30 = 7 + 23

Exercise 2F1 a 2 × 2 × 2 × 2 × 2 × 2 × 2 = 27

b 6 × 6 × 6 = 63

c 17 × 17 × 17 = 173

d 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 = 510

e 23 × 23 × 23 × 23 = 234

f 3 × 3 × 3 × 3 × 3 = 35

g 1 × 1 × 1 × 1 × 1 × 1 × 1 = 17

h 19 × 19 = 192

2 a 92 = 9 × 9 b 231 = 23

c 37 = 3 × 3 × 3 × 3 × 3 × 3 × 3

d 45 = 4 × 4 × 4 × 4 × 4

e 89 = 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8

f 193 = 19 × 19 × 19

g 610 = 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6

h 28 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

3 a 52 = 5 × 5 = 25

b 103 = 10 × 10 × 10 = 1000

c 013 = 0 × 0 × 0 × 0 × 0 × 0 × 0 × 0 × 0 × 0 × 0 × 0 × 0 = 0

d 28 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256

e 201 = 20

f 34 = 3 × 3 × 3 × 3 = 81

g 44 = 4 × 4 × 4 × 4 = 256

h 132 = 13 × 13 = 169

4 a 92 − 42 = 9 × 9 − 4 × 4 = 81 − 16 = 65

b 82 − 25 = 8 × 8 − 2 × 2 × 2 × 2 × 2 = 32

c 42 + 23 = 4 × 4 + 2 × 2 × 2 = 24

d 52 + 16 = 5 × 5 + 16 = 41

e 24 + 32 + 43 = 2 × 2 × 2 × 2 + 3 × 3 + 4 × 4 × 4 = 89

f 102 × 5 = 10 × 10 × 5 = 500

g 5 × 62 = 5 × 6 × 6 = 180

h 50 − 25 + 32 = 50 − 2 × 2 × 2 × 2 × 2 + 3 × 3 = 27

i 2 × 52 = 2 × 5 × 5 = 50

j (5 × 2)2 = 102 = 100

k 5 × 22 = 5 × 2 × 2 = 20

l 22 × 52 = 2 × 2 × 5 × 5 = 100

8



5 110, 25, 34, 53, 44, 252, 105

6 If each of the 4 breeders has 4 cats, then the total number of cats = 4 × 4 = 16

If each cat has 4 kittens, then the total number of kittens = 16 × 4 = 64

Therefore the total number of cages needed = 16 + 64 = 80 cages

7 Each tray can hold 6 × 6 = 36 cakes

Each shelf can hold 6 trays = 6 × 36 = 216 cakes

Each cupboard has 6 shelves = 6 × 216 = 1296 cakes

Therefore the three cupboards can hold a total of 3888 cakes between them.

Exercise 2G1 a 52 = 5 × 5 = 25 b 22 = 2 × 2 = 4

c 102 = 10 × 10 = 100 d 92 = 9 × 9 = 81

e 82 = 8 × 8 = 64 f 122 = 12 × 12 = 144

g 132 = 13 × 13 = 169 h 112 = 11 × 11 = 121

i 202 = 20 × 20 = 400 j 402 = 40 × 40 = 1600

2 a √36 = 6 b √9 = 3 c √25 = 5

d √121 = 11 e √49 = 7 f √100 = 10

h √81 = 9 h √225 = 15 i √144 = 12

j √900 = 30

3 a 172 = 17 × 17 = 289

b 262 = 26 × 26 = 676

c 302 = 30 × 30 = 900

d 1252 = 125 × 125 = 15 625

e 1002 = 100 × 100 = 10 000

f 522 = 52 × 52 = 2704

g 472 = 47 × 47 = 2209

h 332 = 33 × 33 = 1089

i 812 = 81 × 81 = 6561

j 632 = 63 × 63 = 3969

4 a √324 = 18 b √2916 = 54

c √676 = 26 d √10 201 = 101

e √12 321 = 111 f √7921 = 89

h √4761 = 69 h √19·36 = 4·4

i √1·44 = 1·2 j √2·25 = 1·5

Exercise 2H1 a 105 = 3 × 5 × 7 b 182 = 2 × 7 × 13

c 51 = 3 × 17 d 115 = 5 × 23

2 a 20 = 2 × 2 × 5 b 49 = 7 × 7

c 100 = 2 × 2 × 5 × 5 d 36 = 2 × 2 × 3 × 3

e 16 = 2 × 2 × 2 × 2 f 48 = 2 × 2 × 2 × 2 × 3

g 30 = 2 × 3 × 5 h 24 = 2 × 2 × 2 × 3

i 70 = 2 × 5 × 7 j 54 = 2 × 3 × 3 × 3

k 84 = 2 × 2 × 3 × 7 l 63 = 3 × 3 × 7

m 81 = 3 × 3 × 3 × 3 n 66 = 2 × 3 × 11

o 120 = 2 × 2 × 2 × 3 × 5

3 a 42 = 2 × 3 × 7 b 65 = 5 × 13

c 90 = 2 × 3 × 3 × 5 d 28 = 2 × 2 × 7

e 72 = 2 × 2 × 2 × 3 × 3

f 196 = 2 × 2 × 7 × 7

g 400 = 2 × 2 × 2 × 2 × 5 × 5

h 224 = 2 × 2 × 2 × 2 × 2 × 7

i 420 = 2 × 2 × 3 × 5 × 7

j 560 = 2 × 2 × 2 × 2 × 5 × 7

k 1000 = 2 × 2 × 2 × 5 × 5 × 5

l 603 = 3 × 3 × 67

m 110 = 2 × 5 × 11

n 525 = 3 × 5 × 5 × 7

o 13 860 = 2 × 2 × 3 × 3 × 5 × 7 × 11

Exercise 2I1 a even b odd c even

d even e neither f odd

g odd h even i even

j even k odd l odd

m even n odd o even

2 50, 52, 54, 56, 58, 60

3 88, 90, 92, 94, 96, 98, 100, 102, 104, 106

4 29, 31, 33, 35, 37, 39 5 3, 7, 11, 15, 19

6 6, 8, 10 7 10, 12, 14, 16

8 9, 11, 13 9 3, 5, 7, 9

10 a 2 + 4 = 6 b 6 + 10 = 16

c 12 + 4 = 16 d 4 + 16 = 20

e even

11 a 3 + 5 = 8 b 11 + 7 = 18

c 17 + 5 = 22 d 5 + 19 = 24

e even

12 a 3 + 8 = 11 b 4 + 11 = 15

c 10 + 7 = 17 d 12 + 11 = 23

e odd

13 a even (2 × 4 = 8) b odd (3 × 5 = 15)

c even (2 × 5 = 10) d even (9 − 3 = 6)

e even (10 − 4 = 6) f odd (11 − 4 = 7)

Puzzles1 Mount Augustus 2 Toadly awesome

3 Across Down

2 1728 1 3375

5 25 2 125

6 13 3 81

9 8 4 841

10 12 7 343

13 23 11 21

14 14 641 12 1681

13 21

4 Barbed wire

Applications

Factor puzzlea 1 b 2 c 4 d 6 e 16 f 12

Brick wallsa 5 patterns are possible for a wall four units wide.

b 8 patterns are possible for a wall four units wide.



c Four units wide: Five units wide:

d There are 13 different patterns for a wall of length 6 units.

e Six-unit wall:

f ii This pattern is called a Fibonacci sequence as the two previous numbers add to give the next.

g i 1, 2, 3, 5, 8, 13, 21, 34This means 34 different brick walls could be made for an 8-unit wall.

ii 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144This means 144 different brick walls could be made for an 11-unit wall.

iii 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10 946, 17 711, 28 657, 46 368, 75 025, 121 393, 196 418, 317 811, 514 229, 832 040, 1 346 269.This means 1 346 269 different brick walls could be made for a 30 unit wall.

Enrichment1 a The top and side signs flash together every

45 seconds.

b The top and bottom signs flash together every 63 seconds.

c The side and bottom signs flash together every 105 seconds.

d The three signs will flash together after 189 seconds, or at 2:03:09 a.m.

2 Odds: perfect squares 1, 4, 9, 16 …

Evens: all others 2, 3, 5, 6, 7, 8 …

3 a 32 matches are needed with 64 players

b 32 = 2 × 2 × 2 × 2 × 2 or 25

c 16 matches will played in third round

d 8 matches will be played in the fourth round

e Total number of matches would be 64 + 32 + 16 + 8 + 4 + 2 + 1 = 127 matches.

4 11, 13, 17, 31, 37, 71, 73, 79, 97

5 a 28 = 1 + 2 + 4 + 7 + 14496 = 1+ 2 + 4 + 8 + 16 + 31 + 62 +124 + 2488128 = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 127 + 254 + 508 + 1016 + 2032 + 4064

b The sum of the squares of the digits eventually result in an answer of 1.7 is a happy number72 = 4942 + 92 = 9792 + 72 = 13012 + 32 + 02 = 1012 + 02 = 1Hence 7 is a happy number.

c 1, 7, 10, 13, 19, 2312 = 17 as above10: 12 + 02 = 113: 2 + 32 = 10

12 + 02 = 119: 12 + 92 = 82

82 + 22 = 6862 + 82 = 100

23: 22 + 32 = 1312 + 32 = 1012 + 02 = 1

6 a 24 = 23 × 3

30 = 2 × 3 × 5

40 = 23 × 5

LCM = 23 × 3 × 5 = 120

b 693 = 3 × 3 × 7 × 11 = 32 × 7 × 11

9317 = 7 × 11 × 11 × 11 = 7 × 113

LCM = 32 × 7 × 113 = 83 853

c 1178 = 2 × 19 × 31

1444 = 2 × 2 × 19 × 19

HCF = 2 × 19 = 38

d 204 = 2 × 2 × 3 × 17

1380 = 2 × 2 × 3 × 5 × 23

HCF = 2 × 2 × 3 = 12

e Factors of 204: 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204

Factors of 1380: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 60, 69, 92, 115, 138, 230, 276, 345, 460, 690, 1380

f 5280

g 961, factors are 1, 31, 961

h 867, factors are 1, 3, 17, 51, 289, 867

i HCF of 245 700, 132 300, 114 660, 207 900 is 1260

7 a 2, 2, 4, 6, 10, 16, 26, 42, 68, 110Sum = 286

b 1, 4, 5, 9, 14, 23, 37, 60, 97, 157Sum = 407

c Sum = 143

Revision1 a 1, 3, 5, 7, 9, 11, 13, 15, 17, 19

b 1, 3, 6, 10, 15, 21, 28, 36, 45, 55

2 a 3, 8, 15, 24, 35, 48, 63, 80, 99, 120

b 12, 20, 28, 36, 44, 52, 60, 68, 76, 84

3 a 7, 14, 21, 28, 35

b 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 395, 10, 15, 20, 25, 30, 35

10



c 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 486, 12, 18, 24, 30, 36, 42, 48

Therefore common multiples are 12, 24, 36, 48

d 36 e 42 f 105

4 6, 12, 18, 24. At least 6 steps.

5 Dean: 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, 396, 432 ...

Aiden: 44, 88, 132, 176, 220, 264, 308, 352, 396 ...

Hudson: 66, 132, 198, 264, 330, 396 ...

They all touch the sall 396 seconds or 6 min 36 s after starting.

6 a 15: 1, 3, 5, 15 20: 1, 2, 4, 5, 10, 20

b HCF = 5

c 14: 1, 2, 7, 14 21: 1, 3, 7, 21

HCF = 7

d 36: 1, 2, 3, 4, 6, 9, 12, 18, 3642: 1, 2, 3, 6, 7, 14, 21, 4254: 1, 2, 3, 6, 9, 18, 27, 54HCF = 6

e 18: 1, 2, 3, 6 9, 1851: 1, 3, 17, 5163: 1, 3, 7, 9, 21, 63HCF = 3

7 25 cm × 25 cm, 26 tiles × 19 tiles

8 a Yes b No c Yes d No

9 3696 divisible by: 2, 3, 4, 6, 8580 divisible by: 2, 4, 5, 104752 divisible by: 2, 3, 4, 6, 8, 94599 divisible by: 3, 9

10 a Prime b Composite c Composite

d Composite e Composite f Prime

11 a 46 b 93 c 107 d 22

12 a 6 × 6 b 4 × 4 × 4 × 4 × 4

c 8 × 8 × 8 d 10 × 10 × 10 × 10

e 3 × 3 × 3 × 3 × 3 × 3

13 a 3 × 23 = 3 × 2 × 2 × 2 = 24

b 32 × 23 = 3 × 3 × 2 × 2 × 2 = 72

c (3 × 2)2 = 62 = 6 × 6 = 36

d (3 × 2)3 = 63 = 6 × 6 × 6 = 216

e 32 + 23 = 9 + 8 = 17

14 a 6 × 6 = 36 b 15 × 15 = 225

c √64 = 8 d √169 = 13

15 a 282 = 784 b 1072 = 11 449

c √2116 = 46 d √10 609 = 103

16 a 18 = 2 × 3 × 3

b 64 = 2 × 2 × 2 × 2 × 2 × 2

c 26 = 2 × 13

d 32 = 2 × 2 × 2 × 2 × 2

e 242 = 2 × 11 × 11

f 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2

17 a 46, 48, 50, 52, 54, 56, 58

b 19, 21, 23, 25, 27, 29, 31

c 5, 9, 13, 17 d 4, 6, 8

Exercise 3A

1 a b c d e f

g h i j k l

2 a P b M c P d I e M f P

g M h I i P j M k I l I

m M n P o I

3 a b

c d

e f

g h

i j

k l

m n

o p

q r

s

t

u = = v = =

w = = x = =

y = =

Exercise 3B

1 a 2 = =

b 3 = =

c 1 = =

d 4 = =

e 1 = =

f 2 = =

g 10 = =

Chapter 3

56--- 2

3--- 1

4--- 1

6--- 3

8--- 2

5---

45--- 7

8--- 1

3--- 1

2--- 1

8--- 3

4---

68--- 6 2÷

8 2÷------------ 3

4---= = 6

20------ 5 5÷

20 5÷--------------- 1

4---= =

816------ 8 8÷

16 8÷--------------- 1

2---= = 6

9--- 6 3÷

9 3÷------------ 2

3---= =

1040------ 10 10÷

40 10÷------------------ 1

4---= = 14

21------ 14 7÷

21 7÷--------------- 2

3---= =

3542------ 35 7÷

42 7÷--------------- 5

6---= = 12

30------ 12 6÷

30 6÷--------------- 2

5---= =

1326------ 13 13÷

26 13÷------------------ 1

2---= = 56

64------ 56 8÷

64 8÷--------------- 7

8---= =

1260------ 12 12÷

60 12÷------------------ 1

5---= = 6

18------ 6 6÷

18 6÷--------------- 1

3---= =

99108--------- 99 9÷

108 9÷------------------ 11

12------= = 12

40------ 12 4÷

40 4÷--------------- 3

10------= =

3556------ 35 7÷

56 7÷--------------- 5

8---= = 16

28------ 16 4÷

28 4÷--------------- 4

7---= =

5696------ 56 8÷

96 8÷--------------- 7

12------= = 45

72------ 45 9÷

72 9÷--------------- 5

8---= =

33121--------- 33 11÷

121 11÷--------------------- 3

11------= =

78169--------- 78 13÷

169 13÷--------------------- 6

13------= =

810------ 8 2÷

10 2÷--------------- 4

5--- 12

14------ 12 2÷

14 2÷--------------- 6

7---

2136------ 21 3÷

36 3÷--------------- 7

12------ 15

25------ 15 5÷

25 5÷--------------- 3

5---

96120--------- 96 24÷

120 24÷--------------------- 4

5---

12--- 2 2× 1+

2--------------------- 5

2---

25--- 3 5× 2+

5--------------------- 17

5------

14--- 1 4× 1+

4--------------------- 5

4---

13--- 4 3× 1+

3--------------------- 13

3------

35--- 1 5× 3+

5--------------------- 8

5---

56--- 2 6× 5+

6--------------------- 17

6------

15--- 10 5× 1+

5------------------------ 51

5------



h 3 = =

i 1 = =

j 2 = =

k 3 = =

l 5 = =

m 4 = =

n 1 = =

o 10 = =

p 9 = =

q = =

r = =

s = =

t = =

2 a 2 b 3 c 1 d 4 e 2

f 2 g 3 h 2 i 4 j 4

k 4 l 7 m 8 n 7 o 2

p 4 q r s t

3 a b

c d

e f

g h

i j

k = = l = =

4 a is bigger b is bigger

c and so is bigger

d and so is bigger

e and so is bigger

f and so is bigger

Exercise 3C

1 a b

c d

e f

g h

i j

k

l

m

n

o

p

q

r

s

t

2 a = =

b = =

c = =

d = =

e = =

f = =

3 a b

c d

e f

g h

47--- 3 7× 4+

7--------------------- 25

7------

512------ 1 12× 5+

12------------------------ 17

12------

79--- 2 9× 7+

9--------------------- 25

9------

16--- 3 6× 1+

6--------------------- 19

6------

34--- 5 4× 3+

4--------------------- 23

4------

38--- 4 8× 3+

8--------------------- 35

8------

1112------ 1 12× 11+

12--------------------------- 23

12------

49--- 10 9× 4+

9------------------------ 94

9------

311------ 9 11× 3+

11------------------------ 102

11---------

333--- 3 3 2+×

3--------------------- 11

3------

745--- 7 5 4+×

5--------------------- 39

5------

437--- 4 7 3+×

7--------------------- 31

7------

1258--- 12 8 5+×

8------------------------ 101

8---------

23--- 1

2--- 4

5--- 5

6--- 3

8---

14--- 3

8--- 2

7--- 3

7--- 1

5---

59--- 1

3--- 3

10------ 8

11------ 1

6---

34--- 41

8--- 64

7--- 94

5--- 7 7

10------

12--- 6

12------ 4

8---= = 2

3--- 10

15------ 14

21------= =

35--- 12

20------ 18

30------= = 3

4--- 12

16------ 21

28------= =

56--- 10

12------ 25

30------= = 2

7--- 18

63------ 22

77------= =

45--- 12

15------ 36

45------= = 1

4--- 8

32------ 5

20------= =

49--- 8

18------ 20

45------= = 3

10------ 18

60------ 33

110---------= =

18--- 2

16------ 4

32------ 5

9--- 20

36------ 35

63------

67--- 10

11------

23--- 5

5---× 10

15------= 3

5--- 3

3---× 9

15------= 2

3---

56--- 11

11------× 55

66------= 8

11------ 6

6---× 48

66------= 5

6---

49--- 5

5---× 20

45------= 2

5--- 9

9---× 18

45------= 4

9---

27--- 10

10------× 20

70------= 3

10------ 7

7---× 21

70------= 3

10------

15--- 2

5---+ 3

5---= 4

7--- 2

7---+ 6

7---=

613------ 5

13------+ 11

13------= 1

9--- 5

9---+ 6

9--- 2

3---= =

417------ 9

17------+ 13

17------= 3

10------ 5

10------+ 8

10------ 4

5---= =

916------ 3

16------+ 12

16------ 3

4---= = 5

14------ 3

14------+ 8

14------ 4

7---= =

56--- 5

6---+ 10

6------ 12

3---= = 4

5--- 3

5---+ 7

5--- 12

5---= =

38--- 5

8---+ 8

8--- 1= =

310------ 9

10------+ 12

10------ 11

5---= =

1721------ 11

21------+ 28

21------ 11

3---= =

1924------ 11

24------+ 30

24------ 11

4---= =

2031------ 5

31------+ 25

31------=

712------ 11

12------+ 18

12------ 11

2---= =

613------ 7

13------+ 13

13------ 1= =

1415------ 16

15------+ 30

15------ 2= =

1417------ 20

17------+ 34

17------ 2= =

2325------ 27

25------+ 50

25------ 2= =

23--- 1

3--- 2

3---+ + 5

3--- 12

3---

29--- 7

9--- 5

9---+ + 14

9------ 15

9---

18--- 5

8--- 3

8---+ + 9

8--- 11

8---

417------ 11

17------ 16

17------+ + 31

17------ 114

17------

922------ 11

22------ 19

22------+ + 39

22------ 117

22------

2140------ 37

40------ 39

40------+ + 97

40------ 217

40------

115--- 33

5---+ 44

5---= 43

8--- 21

8---+ 61

2---=

637--- 32

7---+ 95

7---= 5 1

10------ 2 3

10------+ 72

5---=

116--- 45

6---+ 6= 4 5

11------ 3 4

11------+ 7 9

11------=

2 512------ 1 1

12------+ 31

2---= 2 5

14------ 3

14------+ 24

7---=

12



i j

k l

m n

o p

4 a = 7

b =

c =

d =

e =

f =

5 a of the pie was eaten by the first child.

b of the pie was eaten by the second child.

c of the pie has been eaten.

6 metres of fabric has been sold.

7 kilograms of oranges were bought.

8 metres of shadecloth

was sold.

9 = 1 so the oven need to be

on for an hour and 20 minutes.

10 hours are spent on chores by Tran.

11 a so Mark ate 4 slices.

so Sue ate 2 slices.

Dale ate one slice.

b Therefore there were 5 slices left.

12 a Sonja 4 slicesAleisha 6 slicesJulia 2 slices

b 4 slices

c so of the 2 pizzas remains.

Exercise 3D

1 a

b

c

d

e

f

g

h

i = = =

j = = = =

k = = = =

l = = = =

2 a

b

c

d

e

f

g

h

i = = =

=

j =

k = =

=

l = = =

=

3 a b

c d

e f

g h

534--- 61

4---+ 12= 45

9--- 27

9---+ 71

3---=

3 815------ 2 7

15------+ 6= 113

20------ 211

20------+ 41

5---=

823--- 62

3---+ 151

3---= 513

18------ 417

18------+ 102

3---=

1 713------ 311

13------+ 5 5

13------= 2 8

11------ 3 7

11------+ 6 4

11------=

227--- 31

7--- 14

7---+ +

515--- 24

5--- 13

5---+ + 93

5---

678--- 53

8--- 15

8---+ + 137

8---

14 215------ 3 7

15------ 211

15------+ + 201

3---

4 720------ 511

20------ 813

20------+ + 1811

20------

13 911------ 11 8

11------ 5 9

11------+ + 31 4

11------

18---

38---

12---

134--- 41

4---+ 6=

325--- 24

5---+ 61

5---=

3 110------ 5 7

10------ 10 9

10------+ + 19 7

10------=

34--- 7

12------+ 9

12------ 7

12------+= 1

3---

27--- 5

7--- 4

7---+ + 14

7---=

13--- 4

12------=

16--- 2

12------=

416------ 1

4---= 1

4---

14--- 2

5---+ 1

4--- 5

5---× 2

5--- 4

4---×+ 5 8+

20------------ 13

20------= = =

16--- 4

7---+ 1

6--- 7

7--- 4

7---+ 6

7---×× 7 24+

42--------------- 31

42------= = =

25--- 1

5---+ 2

3--- 5

5---× 1

5--- 3

3---×+ 10 3+

15--------------- 13

15------= = =

23--- 7

8---+ 2

3--- 8

8---× 7

8--- 3

3---×+ 16 21+

24------------------ 113

24------= = =

25--- 3

10------+ 2

5--- 2

2--- 3

10------+× 4 3+

10------------ 7

10------= = =

34--- 1

8---+ 3

4--- 2

2--- 1

8---+× 6 1+

8------------ 7

8---= = =

29--- 1

6---+ 2

9--- 2

2--- 1

6--- 3

3---×+× 4 3+

18------------ 7

18------= = =

35--- 2

7---+ 3

5--- 7

7--- 2

7--- 5

5---×+× 21 10+

35------------------ 31

35------= = =

23--- 4

15------+ 2

3--- 5

5--- 4

15------+× 10 4+

15--------------- 14

15------

910------ 19

20------+ 9

10------ 2

2--- 19

20------+× 18 19+

20------------------ 37

20------ 117

20------

815------ 3

5---+ 8

15------ 3

5--- 3

3---×+ 8 9+

15------------ 17

15------ 1 2

15------

518------ 7

9---+ 5

18------ 7

9--- 2

2---×+ 5 14+

18--------------- 19

18------ 1 1

18------

212--- 41

5---+ 6 1

2--- 5

5--- 1

5--- 2

2---×+×+ 65 2+

10------------ 6 7

10------= = =

225--- 41

7---+ 6 2

5--- 7

7--- 1

7--- 5

5---×+×+ 614 5+

35--------------- 619

35------= = =

127--- 34

9---+ 4 2

7--- 9

9--- 4

9--- 7

7---×+×+ 418 28+

63------------------ 446

63------= = =

838--- 41

9---+ 12 3

8--- 9

9--- 1

9---+× 8

8---×+ 1227 8+

72--------------- 1235

72------= = =

214--- 31

2---+ 5 1

4--- 1

2--- 2

2---×+ + 51 2+

4------------ 53

4---= = =

437--- 22

9---+ 6 3

7--- 9

9--- 2

9--- 7

7---×+×+ 627 14+

63------------------ 641

63------= = =

516--- 41

2---+ 9 1

6--- 1

2--- 3

3---×+ + 91 3+

6------------ 92

3---= = =

135--- 21

8---+ 3 3

5--- 8

8--- 1

8--- 5

5---×+×+ 324 5+

40--------------- 329

40------= = =

1623--- 48

9---+ 20 2

3--- 3

3--- 8

9---+×+ 206 8+

9------------ 2014

9------

2159---

14 10 825------+ 24 8

25------

9 310------ 62

5---+ 15 3

10------ 2

5--- 2

2---×+ + 15 3 4+

10------------+

15 710------

234--- 41

2---+ 6 3

4--- 1

2--- 2

2---×+ + 6 3 2+

4------------+ 65

4---

714---

16--- 11

12------+ 1 1

12------= 2

5--- 7

10------+ 1 1

10------=

67--- 3

4---+ 117

28------= 7

9--- 5

6---+ 111

18------=

311------ 7

10------+ 107

110---------= 5

8--- 9

11------+ 139

88------=

1213------ 1

2---+ 111

26------= 7

8--- 4

5---+ 127

40------=



i j

k l

m n

o p

q r

s t

u

v

w

x

4 a =

= = =

b =

= = =

c =

= = =

d =

= = =

e =

= = = =

f =

= = = 2

g =

= = =

h =

= = =

i =

= = =

j =

= = =

k =

= = =

l =

= = =

5 a Common denominator of and is 35.

b , Tony has eaten of

the chocolate.

c , Michelle has eaten

of the chocolate.

6 a hours or 69 minutes

were spent on homework by Michael on Monday.

b hours were

spent by Michael on homework on Tuesday.

c of an hour was spent doing

homework on Wednesday.

d hours were

spent on homework on Thursday.

e

hours were spent on homework on Friday.

7 metres

of pipe were purchased.

8 kg

is the weight in Mr Bracken’s bag.

9 , Matthew has eaten of

the total pizza.

10

= hours would be the total

playback time for the 3 CDs.

11

hours would be the total playback time for the CDs.

Exercise 3F

1 a b

c d

912--- 3+ 121

2---= 45

6--- 22

3---+ 71

2---=

1278--- 5+ 177

8---= 11

2--- 23

4---+ 41

4---=

4 710------ 34

5---+ 81

2---= 65

8--- 15

6---+ 811

24------=

434--- 44

7---+ 9 9

28------= 7 9

10------ 33

8---+ 1111

40------=

3 425---+ 72

5---= 5 8

15------ 28

9---+ 819

45------=

21320------ 311

25------+ 6 9

100---------= 6 9

10------ 411

15------+ 1119

30------=

718------ 11

21------+ 115

126---------=

156--- 21

2--- 42

5---+ + 811

15------=

41125------ 6 7

20------+ 10 79

100---------=

5 710------ 211

25------+ 8 7

50------=

34--- 7

8--- 3

5---+ + 3

4--- 10

10------ 7

8--- 5

5--- 3

5--- 8

8---×+×+×

30 35 24+ +40

------------------------------ 8940------ 2 9

40------

25--- 5

6--- 3

10------+ + 2

5--- 6

6--- 5

6--- 5

5--- 3

10------ 3

3---×+×+×

12 25 9+ +30

--------------------------- 4630------ 1 8

15------

710------ 3

4--- 1

6---+ + 7

10------ 6

6--- 3

4--- 15

15------ 1

6--- 10

10------×+×+×

42 45 10+ +60

------------------------------ 9760------ 137

60------

1112------ 3

5--- 5

6---+ + 11

12------ 5

5--- 3

5--- 12

12------ 5

6--- 10

10------×+×+×

55 36 50+ +60

------------------------------ 14160

--------- 2 720------

17--- 4

5--- 23

35------+ + 1

7--- 5

5--- 4

5--- 7

7--- 23

35------+×+×

5 28 23+ +35

--------------------------- 5635------ 121

35------ 13

5---

14--- 5

6--- 11

12------+ + 1

4--- 3

3--- 5

6--- 2

2--- 11

12------+×+×

3 10 11+ +12

--------------------------- 2412------

312--- 15

6--- 23

4---+ + 6 1

2--- 6

6--- 5

6--- 2

2--- 3

4--- 3

3---×+×+×+

6 6 10 9+ +12

------------------------+ 62512------ 8 1

12------

235--- 5 7

10------ 17

8---+ + 8 3

5--- 8

8--- 7

10------ 4

4--- 7

8--- 5

5---×+×+×+

8 24 28 35+ +40

------------------------------+ 88740------ 10 7

40------

21011------ 33

4--- 11

2---+ + 610

11------ 4

4--- 3

4--- 11

11------ 1

2--- 22

22------×+×+×

6 40 33 22+ +44

------------------------------+ 69544------ 8 7

44------

5 213------ 31

2--- 43

4---+ + 12 2

23------ 4

4--- 1

2--- 26

26------ 3

4--- 13

13------×+×+×+

12 8 26 39+ +52

---------------------------+ 127352------ 1321

52------

458--- 1 9

11------ 81

2---+ + 13 5

8--- 11

11------ 9

11------ 8

8--- 1

2--- 44

44------×+×+×+

13 55 72 44+ +88

------------------------------+ 1317188

--------- 148388------

478--- 24

5--- 72

9---+ + 13 7

8--- 45

45------ 4

5--- 72

72------ 2

9--- 40

40------×+×+×+

13 315 288 80+ +360

------------------------------------+ 13683360--------- 14323

360---------

15--- 1

7---

15--- 7

7--- 2

7--- 5

5---×+× 17

35------= 17

35------

25--- 7

7--- 3

7--- 5

5---×+× 29

35------= 29

35------

34--- 5

5--- 2

5--- 4

4---×+× 1 3

20------=

27--- 9

9--- 8

9--- 7

7---×+× 56 18+

63------------------ 111

63------= =

14--- 2

2--- 3

8---+× 5

8---=

45--- 3

3--- 2

3--- 5

5---×+× 12 10+

15------------------ 1 7

15------= =

13--- 10

10------ 2

5--- 6

6--- 1

2--- 15

15------×+×+× 10 12 15+ +

30------------------------------ 1 7

30------= =

1212--- 102

3---+ 22 1

2--- 3

3--- 2

3--- 2

2---×+×+ 231

6---= =

225--- 4 13

4---+ + 7 2

5--- 4

4--- 3

4--- 5

5---×+×+ 8 3

20------= =

14--- 7

7--- 2

7--- 4

4---×+× 15

28------= 15

28------

134--- 32

5--- 1

4---+ + 4 3

4--- 5

5--- 2

5--- 4

4--- 1

4--- 5

5---×+×+×+=

415 8 5+ +20

------------------------ 525---=

8 114--- 4 35

60------ 2 2×+×+× 10 21

3--- 4+ + 161

3---= =

58--- 1

8---– 4

8--- 1

2---= = 7

9--- 1

9---– 6

9--- 2

3---= =

511------ 2

11------– 3

11------= 11

12------ 5

12------– 6

12------ 1

2---= =

14



e f

g h

i j

k

l

m

n

o

p

2 a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q

r

s

t

3 a =

b =

c =

d =

e =

f = =

g =

h =

i = =

j =

k =

l =

4 of the cake is left.

5 bags of lollies are left.

6 metres of carpet are left

on the roll.

7 the tin of ice-cream needs to

be eaten before the new tin is ordered.

8 a boxes of soft drink

are left at the warehouse.

b boxes of chips are left

at the warehouse.

c boxes of

cups are left at the warehouse.

9 litres of fuel remains on board.

10 a 37 months in total is year

5 months taking photos of Mars is year

23 months collecting data is year

b 37 − 23 − 5 = 9 months is spent travelling:

year is spent travelling.

513------ 2

13------– 3

13------= 30

31------ 15

31------– 15

31------=

1719------ 12

19------– 5

19------= 97

100--------- 37

100---------– 60

100--------- 3

5---= =

87--- 1

7---– 7

7--- 1= = 12

8------ 3

8---– 9

8--- 11

8---= =

2013------ 5

13------– 15

13------ 1 2

13------= =

1611------ 10

11------– 6

11------=

3025------ 3

25------– 27

25------ 1 2

25------= =

429

------ 219

------– 219

------ 213---= =

3310------ 13

10------– 20

10------ 2= =

185

------ 65---– 12

5------ 22

5---= =

478--- 13

8---– 34

8--- 31

2---= =

10 910------ 3 3

10------– 7 6

10------ 73

5---= =

61013------ 3 4

13------– 3 6

13------=

9 811------ 3 4

11------– 6 4

11------=

318--- 2– 11

8---=

14 615------ 8– 6 6

15------ 62

5---= =

4 37---– 37

7--- 3

7---– 34

7---= =

8 59---– 79

9--- 5

9---– 74

9---= =

12 235---– 115

5--- 23

5---– 92

5---= =

16 8 710------– 1510

10------ 8 7

10------– 7 3

10------= =

121021------ 6 4

21------– 62

7---=

81920------ 1 7

20------– 712

20------ 73

5---= =

141619------ 811

19------– 6 5

19------=

427--- 15

7---– 39

7--- 15

7---– 24

7---= =

815--- 24

5---– 76

5--- 24

5---– 52

5---= =

1238--- 27

8---– 1111

8------ 27

8---– 94

8--- 91

2---= = =

1329--- 57

9---– 1211

9------ 57

9---– 74

9---= =

11 511------ 6 8

11------– 1016

11------ 6 8

11------– 4 8

11------= =

7 512------ 411

12------– 617

12------ 411

12------– 2 6

12------ 21

2---= = =

5 110------ 4 7

10------– 411

10------ 4 7

10------– 4

10------ 2

5---= = =

911------ 2

11------– 5

11------– 2

11------

1013------ 7

13------– 2

13------– 1

13------

2225------ 7

25------– 2

25------– 13

25------

4215------ 21

15------– 8

15------– 13

15------

3724------ 13

24------– 7

24------– 17

24------

3136------ 17

36------– 11

36------– 3

36------ 1

12------

14 2 411------– 510

11------– 5 8

11------

8 219---– 37

9---– 21

9---

141115------ 4 1

15------– 3 7

15------– 7 3

15------ 71

5---

12 518------ 811

18------– 217

18------– 13

18------

81120------ 3 7

20------– 213

20------– 211

20------

51124------ 2 1

24------– 117

24------– 117

24------

88--- 3

8---– 5

8---=

234--- 11

4---– 12

4--- 11

2---= =

1678--- 103

8---– 64

8--- 61

2---= =

810------ 3

10------– 5

10------ 1

2---= =

1678--- 35

8---– 132

8--- 131

4---= =

1034--- 21

4---– 82

4--- 81

2---= =

38 101625------– 3725

25------ 1016

25------– 27 9

25------= =

845--- 71

5---– 13

5---=

3712------ 3 1

12------=

512------

2312------ 111

12------=

912------ 3

4---=



c 9 of the 37 months or of the time are spent

travelling.

d 5 of the 37 months or of the time are spent

taking photos on Mars.

Exercise 3G

1 a

b

c

d

e

f

g

h

i = = =

j = = =

k = = =

l = =

2 a

b

c

d

e

f

g

h

i

j

k

l

3 a b

c d

e f

g h

i j

k l

m n

o p

q r

s t

u v

w x

4 a = b =

c = d =

e = f =

g =

h =

i =

j =

k =

l =

5

= of a hectare is left for garden.

6 , so the

chocolate cake takes of an hour more to bake

than a fairy cake.

7

metres of wire is left on the coil

937------

537------

25--- 3

10------– 2

5--- 2

2--- 3

10------–× 4 3–

10------------ 1

10------= = =

710------ 3

5---– 7

10------ 3

5--- 2

2---×– 7 6–

10------------ 1

10------= = =

1112------ 1

6---– 11

12------ 1

6--- 2

2---×– 11 2–

12--------------- 9

12------ 3

4---= = = =

23--- 1

5---– 2

3--- 5

5--- 1

5--- 3

3---×–× 10 3–

15--------------- 7

15------= = =

25--- 1

4---– 2

5--- 4

4--- 1

4--- 5

5---×–× 8 5–

20------------ 3

20------= = =

34--- 1

6---– 3

4--- 3

3--- 1

6--- 2

2---×–× 9 2–

12------------ 7

12------= = =

35--- 1

6---– 3

5--- 6

6--- 1

6--- 5

5---×–× 18 5–

30--------------- 13

30------= = =

67--- 2

3---– 6

7--- 3

3--- 2

3--- 7

7---×–× 18 14–

21------------------ 4

21------= = =

27--- 1

9---– 2

7--- 9

9--- 1

9--- 7

7---×–× 18

63------ 7

63------– 11

63------

56--- 2

5---– 5

6--- 5

5--- 2

5--- 6

6---×–× 25

30------ 12

30------– 13

30------

911------ 2

5---– 9

11------ 5

5--- 2

5--- 11

11------×–× 45

55------ 22

55------– 23

55------

1213------ 2

2--- 1

2--- 13

13------×–× 24

26------ 13

26------– 11

26------

312--- 11

4---– 22

4--- 1

4---– 21

4---= =

612--- 21

5---– 4 5

10------ 2

10------– 4 3

10------= =

1012--- 41

6---– 63

6--- 1

6---– 62

6--- 61

3---= = =

678--- 13

4---– 57

8--- 6

8---– 51

8---= =

925--- 41

7---– 514

35------ 5

35------– 5 9

35------= =

335--- 11

4---– 212 5–

20--------------- 2 7

20------= =

612--- 4– 21

2---=

8 2 710------– 710

10------ 2 7

10------– 5 3

10------= =

9 1419------– 819

19------ 14

19------– 8 5

19------= =

718--- 3

4---– 69

8--- 6

8---– 63

8---= =

735--- 3 9

10------– 4 6

10------ 9

10------– 3 7

10------= =

10 710------ 34

5---– 917

10------ 3 8

10------– 6 9

10------= =

78--- 2

11------– 61

88------= 4

7--- 1

8---– 25

56------=

27--- 2

9---– 4

63------= 7

9--- 3

4---– 1

36------=

56--- 3

11------– 37

66------= 7

10------ 5

8---– 3

40------=

911------ 1

2---– 7

22------= 12

13------ 4

5---– 8

65------=

925--- 31

6---– 6 7

30------= 35

7--- 13

8---– 219

56------=

349--- 12

7---– 210

63------= 23

5--- 11

8---– 119

40------=

612--- 42

5---– 2 1

10------= 75

8--- 1

3---– 7 7

24------=

18 3 710------– 14 3

10------= 8 14

17------– 7 3

17------=

10 710------ 34

5---– 6 9

10------= 105

8--- 21

9---– 837

72------=

447--- 23

4---– 123

28------= 73

8--- 3 9

10------– 319

40------=

425--- 15

6---– 217

30------= 21

4--- 11

3---– 11

12------=

31125------ 113

20------– 1 79

100---------= 1011

15------ 6 9

10------– 35

6---=

1118------ 1

6---– 1

3---– 1

9--- 14

15------ 2

5---– 3

8---– 19

120---------

1920------ 1

4---– 2

5---– 3

10------ 35

36------ 4

9---– 1

4---– 5

18------

2122------ 5

11------– 1

4---– 1

4--- 41

48------ 3

4---– 1

12------– 1

48------

10 25---– 43

4---– 417

20------

19 412---– 62

7---– 8 3

14------

1214--- 22

5---– 51

6---– 441

60------

1456--- 41

8---– 22

3---– 8 1

24------

81112------ 54

7---– 13

4---– 125

42------

925--- 35

6---– 13

8---– 4 23

120---------

34--- 1

12------– 3

4--- 3

3--- 1

12------–× 9 1–

12------------ 8

12------= = =

23---

23--- 1

4---– 2

3--- 4

4--- 1

4--- 3

3---×–× 8 3–

12------------ 5

12------= = =

512------

1082 910------ 8421

4---– 240 9

10------ 2

2--- 1

4--- 5

5---×–× 24018 5–

20---------------= =

2401320------=

16



8 = =

= = metres of material is left.

9 Fraction of money spent is

Subtracting this from 1 gives

a Therefore Jess put of her pocket money in the

bank.

b $160 × = $20, $160 × = $32

10 a b remains

c $125 on rollerblades and $50 on snacks.

Learning task 3H

1 is the equivalent of finding one-half of

one-quarter, meaning one-eighth

2 If you cut a pie into quarters, then took one of those pieces and cut it in half, you would have one-half of one-quarter of the pie, or one-eighth.

3 is the same as . Using the analogy

above, if you had a pie and cut it in half, then took one of those pieces and cut it into quarters, you would have one-quarter of one-half, which is also one-eighth.

4 Using a calculator confirms this answer.

5 a b

c d

e f

g h

i j =

k = l =

m = n =

o =

Exercise 3I

1 a

b During multiplication of two fractions, the numerators are multiplied together and the denominators are multiplied together to form the answer.

c The calculator might multiply numerators, multiply denominators, then simplify the fraction by cancelling common factors.

2 a

b

c

d

e

f

g

h

i

j

k

l

3 a

b

c

d

e

f

g

h

i

j

k

l

4 a = = =

b = = =

827--- 51

2---– 5

14------– 29

7--- 2

2--- 1

2--- 7

7--- 5

14------–××× 218 7– 5–

14------------------------

2 614------ 23

7---

18--- 1

5---+ 1

8--- 5

5--- 1

5--- 8

8---×+× 5 8+

40------------ 13

40------= = =

4040------ 13

40------– 27

40------=

2740------

18--- 1

5---

58--- 1

4---+ 7

8---= 1 7

8---– 1

8---=

12--- 1

4---×

12--- 1

4---× 1

4--- 1

2---×

34--- 6

9---× 1

2---= 5

6--- 2

5---× 1

3---=

23--- 3

5---× 2

5---= 4

5--- 1

2---× 2

5---=

14--- 5

7---× 5

28------= 3

10------ 3

7---× 9

70------=

15--- 2

3---× 2

15------= 3

4--- 1

4---× 3

16------=

13--- 3

4---× 1

4---= 1

2--- 2

7---× 1

7---

13--- 2

5---× 2

15------ 1

2--- 2

5---× 1

5---

34--- 3

5---× 9

20------ 2

3--- 1

4---× 1

6---

16--- 2

3---× 1

9---

15--- 1

2---× 1

10------= 1

5--- 7

10------× 7

50------=

34--- 3

7---× 9

28------= 5

6--- 5

7---× 25

42------=

34--- 8

9---× 1

1--- 2

3---× 2

3---= =

13--- 9

10------× 1

1--- 3

10------× 3

10------= =

25--- 10

11------× 2

1--- 2

11------× 4

11------= =

58--- 3

5---× 1

8--- 3

1---× 3

8---= =

27--- 1

2---× 1

7--- 1

1---× 1

7---= =

45--- 10

13------× 4

1--- 2

13------× 8

13------= =

56--- 7

10------× 1

6--- 7

2---× 7

12------= =

23--- 4

5---× 8

15------=

712------ 4

5---× 7

3--- 1

5---× 7

15------= =

29--- 6

7---× 2

3--- 2

7---× 4

21------= =

12--- 4

9--- 1

6---×× 1

1--- 1

9--- 1

3---×× 1

27------= =

25--- 2

3--- 1

4---×× 1

5--- 1

3--- 1

1---×× 1

15------= =

4 38---× 4

1--- 3

8---× 3

2--- 11

2---= = =

6 19---× 6

1--- 1

9---× 2

3---= =

23--- 0× 0=

89--- 1× 8

9---=

212--- 4× 5

2--- 4

1---× 10

1------ 10= = =

113--- 9× 4

3--- 9

1---× 12

1------ 12= = =

5 114---× 5

1--- 5

4---× 25

4------ 61

4---= = =

3 225---× 3

1--- 12

5------× 36

5------ 71

5---= = =

23--- 41

2---× 2

3--- 9

2---× 3

1--- 3= = =

213--- 22

7---× 7

3--- 16

7------× 16

3------ 51

3---= = =

145--- 2

3---× 9

5--- 2

3---× 6

5--- 11

5---= = =

79--- 32

7---× 7

9--- 23

7------× 23

9------ 25

9---= = =

216--- 11

2--- 3

4---×× 13

6------ 3

2--- 3

4---×× 39

16------ 2 7

16------

434--- 22

3--- 26

7---×× 19

4------ 8

3--- 20

7------×× 760

21--------- 36 4

21------



c = = 3

d = = =

e = = =

f = = =

g

h

i

j

k

l

5 , so Kelvin will have to pay

78 − 26 = $52.

6 , so it takes Carmel

hours to complete her project.

7 , so the family will

travel km.

8 a , so a worker

pays $166·40 in tax.

b 520 − 166·5 = 353·6, so a worker takes home $353·60 after tax.

9 a A double batch of cakes would require twice the amount of ingredients:

cups of flour

2 teaspoons of vanilla essence

cup of jam

kg of butter

cups of sugar 6 eggs

litre of cream

cup of milk

b A half batch would require half the amount of ingredients:

cup of flour

teaspoons of vanilla essence

cup of jam

kg of butter

cup of sugar

eggs

litre of cream

cup of milk

Exercise 3J

1 a

b

c

d

e

f

g

h

i

j

k

l

2 a

b

c

d

214--- 13

5--- 5

6---×× 9

4--- 8

5--- 5

6---××

134--- 17

9--- 3×× 7

4--- 16

9------ 3×× 28

3------ 91

3---

245--- 34

7--- 113

20------×× 14

5------ 25

7------ 33

20------×× 33

2------ 161

2---

116--- 21

4--- 111

14------×× 7

6--- 9

4--- 25

14------×× 75

16------ 411

16------

412--- 13

5--- 1

3---×× 9

2--- 8

5---× 1

3---× 12

5------ 22

5---= = =

25--- 31

2--- 11

4---×× 2

5--- 7

2---× 5

4---× 7

4--- 13

4---= = =

6 34--- 21

3---×× 6

1--- 3

4---× 7

3---× 21

2------ 101

2---= = =

56--- 10 14

5---×× 5

6--- 10

1------× 9

5---× 15

1------ 15= = =

223--- 41

2--- 14

5---×× 8

3--- 9

2---× 9

5---× 108

5--------- 213

5---= = =

418--- 51

3--- 11

6---×× 33

8------ 16

3------× 7

6---× 77

3------ 252

3---= = =

78 13---× 78

1------ 1

3---× 26= =

34--- 21

4---× 3

4--- 9

4---× 27

16------ 111

16------= = =

11116------

85 256---× 85

1------ 17

6------× 2405

6---= =

24056---

520 825------× 520

1--------- 8

25------× 1662

5---= =

112--- 2× 3

2--- 2

1---× 3= =

12--- 2× 1

2--- 2

1---× 1= =

18--- 2× 1

8--- 2

1---× 1

4---= =

23--- 2× 2

3--- 2

1---× 11

3---= =

310------ 2× 3

10------ 2

1---× 3

5---= =

14--- 2× 1

4--- 2

1---× 1

2---= =

112--- 1

2---× 3

2--- 1

2---× 3

4---= =

12---

12--- 1

2---× 1

4---=

18--- 1

2---× 1

16------=

23--- 1

2---× 1

3---=

112---

310------ 1

2---× 3

20------=

14--- 1

2---× 1

8---=

34--- 1

8---÷ 3

4--- 8

1---× 6= =

25--- 8

15------÷ 2

5--- 15

8------× 3

4---= =

12--- 6

11------÷ 1

2--- 11

6------× 11

12------= =

18--- 4

7---÷ 1

8--- 7

4---× 7

32------= =

13--- 4

9---÷ 1

3--- 9

4---× 3

4---= =

67--- 7

9---÷ 6

7--- 9

7---× 54

49------ 1 5

49------= = =

314------ 3

7---÷ 3

14------ 7

3---× 1

2---= =

215------ 10

21------÷ 2

15------ 21

10------× 7

25------= =

49--- 5

6---÷ 4

9--- 6

5---× 8

15------= =

310------ 11

12------÷ 3

10------ 12

11------× 18

55------= =

47--- 9

14------÷ 4

7--- 14

9------× 8

9---= =

712------ 5

6---÷ 7

12------ 6

5---× 7

10------= =

25--- 4

15------÷ 2

5--- 15

4------× 3

2--- 11

2---= = =

821------ 2

7---÷ 8

21------ 7

2---× 4

3--- 11

3---= = =

34--- 9

16------÷ 3

4--- 16

9------× 4

3--- 11

3---= = =

18--- 4

7---÷ 1

8--- 7

4---× 7

32------= =

18



e ÷

f ÷ =

g ÷ =

h ÷ =

i ÷ =

j ÷ =

k

l ÷ =

3 a ÷ =

b ÷ =

c ÷ =

d ÷ =

e ÷ =

f ÷ =

g ÷ =

h ÷ =

i ÷ =

j ÷ =

k ÷ =

l ÷ =

4 a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q ÷

r 9 ÷ =

s 20 ÷ =

t ÷ 2 =

5 ÷ 8 = of the cake

6 40 ÷ = days

7 25 ÷ =

a 11 tablecloths b metre

8 ÷ = bags

9 ÷ = blocks

10 tonnes

11 a × 2 = kilolitres

b × = weeks

c ÷ 4 = kilolitres

Exercise 3K

1 a

b

c

d

e

114--- 5

6--- 5

4--- 6

5---× 11

2---= =

914------ 1 1

17------ 9

14------ 18

17------÷ 9

14------ 17

18------× 17

28------= =

2121------ 12

7--- 12

21------ 9

7---÷ 12

21------ 7

9---× 4

9---= =

2 411------ 1

22------ 26

11------ 22

1------× 52=

512------ 11

4--- 5

12------ 5

4---÷ 5

12------ 4

5---× 1

3---= =

214--- 3

4--- 9

4--- 4

3---× 3=

47--- 9

14------÷ 4

7--- 14

9------× 8

9---= =

412--- 5

6--- 9

2--- 6

5---× 27

5------ 52

5---= =

212--- 41

6--- 5

2--- 25

6------÷ 5

2--- 6

25------× 3

5---= =

157--- 11

3--- 12

7------ 4

3---÷ 12

7------ 3

4---× 9

7--- 12

7---= = =

119--- 12

3--- 10

9------ 5

3---÷ 10

9------ 3

5---× 2

3---= =

114--- 31

2--- 5

4--- 7

2---÷ 5

4--- 2

7---× 5

14------= =

618--- 24

5--- 49

8------ 14

5------÷ 49

8------ 5

14------× 35

16------ 2 3

16------= = =

157--- 11

2--- 12

7------ 3

2---÷ 12

7------ 2

3---× 11

7---= =

247--- 21

4--- 18

7------ 9

4---÷ 18

7------ 4

9---× 11

7---= =

225--- 21

2--- 12

5------ 5

2---÷ 12

5------ 2

5---× 24

25------= =

334--- 4 1

11------ 15

4------ 45

11------÷ 15

4------ 11

45------× 11

12------= =

413--- 2 4

11------ 13

3------ 26

11------÷ 13

3------ 11

26------× 11

6------ 15

6---= = =

634--- 1 5

28------ 27

4------ 33

28------÷ 27

4------ 28

33------× 63

11------ 5 8

11------= = =

189--- 131

54------ 17

9------ 85

54------÷ 17

9------ 54

85------× 6

5--- 11

5---= = =

2 18---÷ 2

1--- 8

1---× 16= =

8 85---÷ 8

1--- 5

8---× 5= =

12 611------÷ 12

1------ 11

6------× 22= =

8 47---÷ 8

1--- 7

4---× 14= =

16 49---÷ 16

1------ 9

4---× 36= =

21 79---÷ 21

1------ 9

7---× 27= =

9 37---÷ 9

1--- 7

3---× 21= =

4 13---÷ 4

1--- 3

1---× 12= =

14 76---÷ 14

1------ 6

7---× 12= =

7 2112------÷ 7

1--- 12

21------× 4= =

27 98---÷ 27

1------ 8

9---× 24= =

26 136

------÷ 261

------ 613------× 12= =

25--- 4÷ 2

5--- 1

4---× 1

10------= =

8 27---÷ 8

1--- 7

2---× 28= =

34--- 6÷ 3

4--- 1

6---× 1

8---= =

8 45---÷ 8 5

4---× 10= =

114--- 6 5

4--- 1

6---× 5

24------= =

1 117------ 9

1--- 18

17------÷ 9

1--- 17

18------× 81

2---= =

127--- 20

1------ 9

7---÷ 20

1------ 7

9---× 140

9--------- 155

9---= = =

2 411------ 26

11------ 1

2---× 13

11------ 1 2

11------= =

212--- 5

2--- 1

8---× 5

16------=

114--- 40

1------ 4

5---× 32=

214--- 25 4

9---× 111

9---=

19---

1034--- 11

5--- 43

4------ 5

6---× 215

24--------- 823

24------= =

1625--- 2

5--- 82

5------ 5

2---× 41=

56--- 1

12------× 5

72------=

4058--- 325

8--------- 2

1---× 811

4---=

3254

--------- 223--- 325

4--------- 3

8---× 3015

32------=

223--- 8

3--- 1

4---× 2

3---=

14--- 16× 1

4--- 16

1------× 4= =

16--- 18× 1

6--- 18

1------× 3= =

19--- 18× 1

9--- 18

1------× 2= =

25--- 15× 2

5--- 15

1------× 6= =

34--- 12× 3

4--- 12

1------× 9= =



f

g

h

i

j

k

l

m = = 30

n = = 28

o = = 18

p = = 40

q = = 48

r = = 84

s = = 20

t = = 121

2 a

b

c

d

e

f

g

h

i

j min

k

l

m m = = 175m

n = = $1000

o = = $8197

p lollies = = 2800 lollies

q sheep = = 1920 sheep

r ML = = 283 850ML

3 h, so Ali slept 6 hours.

4 , so Bronwyn took

14 chocolates to school.

5 , so Brendan had to throw

back 15 fish, therefore he took home 9 fish.

6 a = = $43·50

b = = $29·00

c = = $14·50

7 a = = 8 tonnes

b = = 13 tonnes

c = = = tonnes

8 = = = metres

9 = 330 g sugar

= 375 mL milk

= 187·5 g butter

Exercise 3L

1 a

b

c

d

e

f

25--- 20× 2

5--- 20

1------× 8= =

56--- 30× 5

6--- 30

1------× 25= =

310------ 20× 3

10------ 20

1------× 6= =

25--- 5× 2

5--- 5

1---× 2= =

12--- 8× 1

2--- 8

1---× 4= =

35--- 40× 3

5--- 40

1------× 24= =

38--- 64× 3

8--- 64

1------× 24= =

23--- 45× 2

3--- 45

1------×

45--- 35× 4

5--- 35

1------×

37--- 42× 3

7--- 42

1------×

58--- 64× 5

8--- 64

1------×

49--- 108× 4

9--- 108

1---------×

78--- 96× 7

8--- 96

1------×

13--- 60× 1

3--- 60

1------×

1112------ 132× 11

12------ 132

1---------×

23--- $60× 2

3--- 60

1------× $40= =

45--- $400× 4

5--- 400

1---------× $320= =

29--- $360× 2

9--- 360

1---------× $80= =

14--- $1000× 1

4--- 1000

1------------× $250= =

12--- 500 m× 1

2--- 500

1---------× 250 m= =

25--- 200 m× 2

5--- 200

1---------× 80 m= =

56--- 300 km× 5

6--- 300

1---------× 250 km= =

27--- 14 cm× 2

7--- 14

1------× 4 cm= =

13--- 60 min× 1

3--- 60

1------× 20 min= =

34--- 15 min× 3

4--- 15

1------× 111

4---= =

38--- 40 s× 3

8--- 40

1------× 15 s= =

13--- 24 h× 1

3--- 24

1------× 8 h= =

78--- 200× 7

8--- 200

1---------×

56--- $1200× 5

6--- 1200

1------------×

712------ $14 052× 7

12------ 14 052

1----------------×

710------ 4000× 7

10------ 4000

1------------×

25--- 4800× 2

5--- 4800

1------------×

79--- 364 950× 7

9--- 364 950

1-------------------×

14--- 24 h× 1

4--- 24

1------× 6= =

23--- 21× 2

3--- 21

1------× 14= =

58--- 24× 5

8--- 24

1------× 15= =

12--- $87× 1

2--- 87

1------×

13--- $87× 1

3--- 87

1------×

16--- $87× 1

6--- 87

1------×

12--- 16× 1

2--- 16

1------×

12--- 26× 1

2--- 26

1------×

12--- 182

3---× 1

2--- 56

3------× 28

3------ 91

3---

71320------ 3÷ 153

20--------- 1

3---× 51

20------ 211

20------

440 34---×

500 34---×

250 34---×

14---

2 14--- 1

4---× 1

16------= =

25---

2 25--- 2

5---× 4

25------= =

56---

2 56--- 5

6---× 25

36------= =

13---

2 13--- 1

3---× 1

9---= =

23---

2 23--- 2

3---× 4

9---= =

12---

2 12--- 1

2---× 1

4---= =

20



g

h

i

j

k

l

2 a

b

c

d

e

f

g

h

i

j

k

l

3 a b

c d

e f

g h

i j

k l

4 a

b

c

d

e

f

g

h

i

j

k

l

5 a 0·76 b 0·59 c 0·58 d 0·45

e 0·94 f 0·94 g 1·66 h 2·31

i 2·92 j 2·63 k 2·36 l 1·06

Exercise 3M

1 a × 8 + 2 = 4 + 2 = 6

b × 9 − 2 = 6 − 2 = 4

c 5 + × = 5 + 6 = 11

d 26 − × = 26 − 20 = 6

e × − 3 = 4 − 3 = 1

f × − 2 = 6 − 2 = 4

g 3 + × = 3 + =

h

i

j

k

l

2 a

910------

2 910------ 9

10------× 81

100---------= =

38---

2 38--- 3

8---× 9

64------= =

512------

2 512------ 5

12------× 25

144---------= =

711------

2 711------ 7

11------× 49

121---------= =

47---

2 47--- 4

7---× 16

49------= =

89---

2 89--- 8

9---× 64

81------= =

112---

2 32--- 3

2---× 9

4--- 21

4---= = =

214---

2 94--- 9

4---× 81

16------ 5 1

16------= = =

127---

2 97--- 9

7---× 81

49------ 132

49------= = =

125---

2 75--- 7

5---× 49

25------ 124

25------= = =

313---

2 103

------ 2 100

9--------- 111

9---= = =

129---

2 119

------ 2 121

81--------- 140

81------= = =

215---

2 115

------ 2 121

25--------- 421

25------= = =

416---

2 256

------ 2 625

36--------- 1713

36------= = =

178---

2 158

------ 158

------× 22564

--------- 33364------= = =

256---

2 176

------ 176

------× 28936

--------- 8 136------= = =

1 910------

2 1910------ 19

10------× 361

100--------- 3 61

100---------= = =

267---

2 207

------ 207

------× 40049

--------- 8 849------= = =

14--- 1

2---= 1

9--- 1

3---=

125------ 1

5---= 9

25------ 3

5---=

81100--------- 9

10------= 36

49------ 6

7---=

144169--------- 12

13------= 64

100--------- 4

5---=

81121--------- 9

11------= 4

81------ 2

9---=

50338--------- 25

169--------- 5

13------= = 98

162--------- 49

81------ 7

9---= =

279--- 25

9------ 5

3--- 12

3---= = =

214--- 9

4--- 3

2--- 11

2---= = =

5 116------ 81

16------ 9

4--- 21

4---= = =

11125------ 36

25------ 6

5--- 11

5---= = =

614--- 25

4------ 5

2--- 21

2---= = =

1119--- 100

9--------- 10

3------ 31

3---= = =

51925------ 144

25--------- 12

5------ 22

5---= = =

1214--- 49

4------ 7

2--- 31

2---= = =

3 625------ 81

25------ 9

5--- 14

5---= = =

179--- 16

9------ 4

3--- 11

3---= = =

2014--- 81

4------ 9

2--- 41

2---= = =

2 249------ 100

49--------- 10

7------ 13

7---= = =

12---

23---

25--- 15

1------

56--- 24

1------

27--- 14

1------

25--- 15

1------

194

------ 21--- 91

2--- 121

2---

2 525------ 6

5---÷× 2

1--- 8

25------ 5

6---×× 8

15------= =

83--- 1 8

3---×+ 8 8+

3------------ 51

3---= =

6 13--- 18

1------ 1

3---××+ 6 2+ 8= =

9 12--- 6

1--- 1

2---××– 9 11

2---– 71

2---= =

4 25---+ 25

1------ 1

7---×× 4 10

7------+ 53

7---= =

12--- 8 2

3--- 6

7---×–× 4

1--- 4

7---– 33

7---= =



b

c

d ÷ =

e

f ÷ =

=

g

h

i

j

=

k

l ÷ =

m

n

o

3 a = = =

b = = =

c = =

= =

d =

= = =

e =

= = =

= =

f = =

= =

g = =

= = =

h = =

= = =

i = =

= = =

j =

= = = =

k =

= = =

l = = =

4 a = =

= = =

b = =

= = =

c = =

d =

= = = =

e = =

= =

f = =

= =

g =

= = =

h =

= = =

23--- 9

10------ 1

4---–× 3

5--- 1

4---– 12 5–

20--------------- 7

20------= = =

623--- 11

2---+ 22

5---× 20

3------ 3

2--- 12

5------×+ 20

3------ 18

5------+= =

100 54+15

--------------------- 10 415------=

6 212---– 5

6--- 6 5

2---– 6

5---× 6 3– 3= =

212--- 31

3---+

27---× 5

2--- 10

3------+

27---× 35

6------ 2

7---× 12

3---= = =

623--- 4

9--- 22

5---– 20

6------ 9

4--- 12

5------–× 15 12

5------–=

635

------ 1235---=

318--- 1

4--- 19

4------×– 25

8------ 19

16------– 31

16------ 115

16------= = =

214--- 8

25------ 6

5---÷× 9

4--- 8

25------ 5

6---×× 3

5---= =

212--- 2

3--- 13

4--- 22

3---×+× 5

2--- 2

3--- 7

4--- 8

3---×+× 5

3--- 14

3------+ 61

3---= = =

6 13--- 8 3

2--- 2

5---+

–×+ 6 83--- 15 4+

10---------------

–+=

6 80 57–30

------------------ + 623

30------=

25--- 2

5--- 1

10------ 3

5---×–× 4

25------ 3

50------– 1

10------= =

218--- 2

3--- 5

8---×– 22

3--- 21

8--- 2

3--- 5

8--- 3

8---××– 17

8------ 5

32------–=

6332------ 131

32------=

458--- 2

3--- 12 1

2--- 13

4------×–×+ 45

8--- 8 13

8------–+=

1258---= 15

8---– 11=

89--- 4

3---÷ 2

3--- 2×+ 8

9--- 3

4--- 4

3---+× 6

9--- 12

9------+ 2= = =

34--- 6

5--- 1

10------ 1+ +× 9

10------ 1

10------ 1+ + 2= =

23---

2 34--- 9

8---÷+ 4

9--- 3

4--- 8

9---×+ 4

9--- 2

3---+ 11

9---

12--- 3

4--- 2

5---

–×2 3

8--- 4

25------– 3 25 4 8×–×

200--------------------------------- 43

200---------

38--- 1

6---

×2 9

11------× 3

8--- 1

36------ 9

11------×+ 3

8--- 1

44------+

3 11 1 2×+×88

---------------------------------- 3588------

112--- 3

4---

2 13---–+ 3

2--- 9

16------ 1

3---–+

3 24 9 3 1 16×–×+×45

------------------------------------------------------- 8348------ 135

48------

56---

242

3--- 14

5---÷+ 25

36------ 14

3------ 9

5---÷+

2536------ 14

3------ 5

9---×+ 25

36------ 70

27------+ 25 3 70 4×+×

108-------------------------------------

355108--------- 3 31

108---------

712------

2 58--- 21

2---÷– 49

144--------- 5

8--- 2

5---×– 49

144--------- 1

4---–

49 36–144

------------------ 13144---------

3649------ 21

4--- 12

3---×+ 6

7--- 9

4--- 5

3---×+ 6

7--- 15

4------+

6 4 15 7×+×28

---------------------------------- 12928

--------- 41728------

323--- 4

81------÷ 43

4---– 11

3------ 9

2--- 19

4------–× 33

2------ 19

4------–

33 2 19–×4

--------------------------- 474

------ 1134---

125------ 12

3--- 24

5---+÷ 1

5--- 3

5--- 14

5------+× 3

25------ 14

5------+

3 14 5×+25

------------------------ 7325------ 223

25------

58--- 22

3--- 2 2

49------ 21

3---×+÷ 5

8--- 3

8--- 10

7------ 7

3---×+×

1564------ 10

3------+ 15 3 10 64×+×

192---------------------------------------- 685

192--------- 3109

192---------

112--- 2

5---+

179---– 3 5 2 2×+×

10------------------------------- 4

3---–

1910------ 4

3---– 19 3 4 10×–×

30------------------------------------ 17

30------

214--- 4

50------ 121

4---÷× 9

4--- 4

50------ 7

2---÷× 9

50------ 2

7---× 9

175---------

14---

2 23---

2× 51

2---+ 1

16------ 4

9--- 11

2------+× 1

36------ 11

2------+

1 11 18×+36

--------------------------- 19936

--------- 51936------

12--- 25

4------ 4

5--- 22

3---×+× 1

2--- 5

2--- 4

5--- 8

3---×+× 5

4--- 32

15------+

5 15 32 4×+×60

------------------------------------- 20360

--------- 32360------

34--- 81

25------ 1

2---–× 3

4--- 9

5--- 1

2---–× 17

20------

912--- 2

3--- 52

9--- 101

8---××+ 91

2--- 2

3--- 47

9------ 81

8------××+

192

------ 1414

---------+ 19 2 141+×4

------------------------------ 1794

--------- 4434---

4981------ 3

5--- 1

4--- 12

13------×–× 7

9--- 3

5--- 3

13------–× 7

15------ 3

13------–

7 13 3 15×–×195

------------------------------------ 46195---------

123---

2 14--- 2

5---×– 25

9------ 1

10------– 25 10 9–×

90---------------------------

24190

--------- 26190------

56--- 100

144--------- 11

4---

2–+ 5

6--- 10

12------ 25

16------–+

5 16 10 8 25 6×–×+×96

---------------------------------------------------------- 1096------ 5

48------

81920------ 22

3---

2– 27

9---+ 179

20--------- 64

9------– 5

3---+

179 9 64 20 5 60×+×–×180

---------------------------------------------------------------- 631180--------- 3 91

180---------

22



i = = =

j = =

= =

k = = =

=

l = =

= = =

m = = = 7

n = =

= =

o = = = =

Puzzles1 He is fully recovered.

2 It could see the future and pasture.

3 Reproductive organs.

Applications

Phases of the MoonAt new moon, the cycle begins and no days have passed.

At first quarter, 7·38 days have passed.

At full moon, 14·77 days have passed.

At last quarter, 22·15 days have passed.

Fraction patterns

The answer to the next question will be .

If the additions signs are replaced with subtraction signs, the answer will always be equal to the last fraction:

Chinese tangrams

, , , , , ,

Squares

a 5 b , , , c , , ,

Enrichment

1 a b

c d

e f

2 a and , so is larger.

b and , so

is larger.

c and , so is larger.

d and , so

is larger.

e and so

is larger.

f and , so

is larger.

3 a b

c

4 a Magic number is

b Magic number is

89--- 119

81------÷ 1

5---– 8

9--- 9

10------ 1

5---–× 4

5--- 1

5---– 3

5---

278---

211

2--- 3

4---×+ 529

64--------- 9

8---+ 529 9 8×+

64---------------------------

60164

--------- 92564------

214---

2 12--- 5

6---+

÷ 8116------ 8

6---÷ 81

16------ 3

4---× 243

64---------

35164------

356---

211

2---

2 34---×– 529

36--------- 9

4--- 3

4---×– 529

36--------- 27

16------–

529 4 27 9×–×144

--------------------------------------- 1873144

------------ 13 1144---------

4214--- 26

27------ 1

4---+÷ 13

2------ 27

26------ 1

4---+× 27

4------ 1

4---+

34---

211

4---

2 78---–+ 9

16------ 25

16------ 7

8---–+ 34 7 2×–

16------------------------

2016------ 11

4---

15--- 2

9--- 64

81------+× 2

45------ 8

9---+ 2 8 5×+

45--------------------- 42

45------ 14

15------

12--- 1

4---+ 2

4--- 1

4---+ 3

4---= =

12--- 1

4--- 1

8---+ + 4

8--- 2

8--- 1

8---+ + 7

8---= =

12--- 1

4--- 1

8--- 1

16------+ + + 8

16------ 4

16------ 2

16------ 1

16------+ + + 15

16------= =

12--- 1

4--- 1

8--- 1

16------ 1

32------+ + + + 16

32------ 8

32------ 4

32------ 2

32------ 1

32------+ + + + 31

32------= =

6364------

12--- 1

4---– 1

8---– 1

16------– 1

32------– 16

32------ 8

32------– 4

32------– 2

32------– 1

32------– 1

32------= =

14--- 1

4--- 1

16------ 1

8--- 1

18------ 1

16------ 1

8---

1

12--- 1

4--- 1

8--- 1

16------ 1

8--- 1

16------ 1

32------ 1

64------

34--- 1

2--- 1

4---+= 2

5--- 1

3--- 1

15------+=

23--- 1

2--- 1

6---+= 3

10------ 1

4--- 1

20------+=

37--- 1

3--- 1

11------ 1

231---------+ += 5

6--- 1

2--- 1

3---+=

56--- 1

2--- 1

3---+= 8

9--- 1

2--- 1

3--- 1

18------+ += 8

9---

89--- 1

2--- 1

3--- 1

18------+ += 9

10------ 1

2--- 1

3--- 1

15------+ +=

910------

34--- 1

2--- 1

4---+= 4

5--- 1

2--- 1

4--- 1

20------+ += 4

5---

49--- 1

3--- 1

9---+= 5

11------ 1

3--- 1

9--- 1

99------+ += 5

11------

45--- 1

2--- 1

4--- 1

20------+ += 7

9--- 1

2--- 1

4--- 1

36------+ += 4

5---

58--- 1

2--- 1

8---+= 7

11------ 1

2--- 1

8--- 1

88------+ += 7

11------

212---

114--- 63

4---

245---

315--- 13

5---

456---

34--- 31

3---

11112------

178---

14--- 11

8--- 4

8---

78--- 5

8--- 3

8---

34--- 1

8---

135---

13--- 4

5--- 7

15------

23--- 8

15------ 2

5---

35--- 4

15------ 11

15------



c Magic number is 17

d Magic number is

5 a Area = m × m = × = m2

b Area = 11 m × m = m2

c Fraction of court =

d Fraction of singles court = m × m

Fraction of court =

6 a b c d e f

Revision

1 a b c

2 a b c

3 a Improper fraction b Mixed number

c Proper fraction

4 a

b

5 a b c d

6 a 2 b 3 c 2 d 4

7 a b c d

8 a 4 b c 5 d 5

9 a

b

c

d

10

, so the Wade family has a total of 16 kg

of flour.

11 kg is

the total weight of Suzie’s fruit.

12 a

b

c

d

e

f

g

h

13 , so Wayne is taller by 40 cm.

14 , so Maria needs to buy another

m of material.

15 a

b

c

d

16 , so James has litres of

soft drink.

17 litres of orange juice

litres of pineapple juice and

litres of lemonade

7 2

6 3

4 5

1 8

3

2

4

1

12--- 71

2---

312--- 41

2---

512--- 21

2---

612--- 11

2---

1012---

134--- 11

4--- 41

2---

112--- 41

4--- 23

4---

34--- 31

2--- 21

4---

314--- 21

2--- 33

4---

4 110------ 62

5--- 41

10------ 32

5------ 26 6

25------

2345--- 2614

5---

26 625------ m

2

26145--- m

2--------------------- 656

25--------- 25

6545------------× 656

6545------------= =

815--- 234

5---

815--- 234

5---×

11 2345---×

---------------------- 415

------ 111------× 41

55------= =

18--- 1

4--- 1

2--- 1

2--- 1

2--- 1

16------

13--- 5

8--- 2

5---

2060------ 1

3---= 32

56------ 4

7---= 35

45------ 7

9---=

25--- 4

10------ 10

25------ 18

45------= = =

37--- 9

21------ 36

84------ 21

49------= = =

25--- 5

11------ 1

6--- 5

7---

25--- 2

3--- 6

7--- 5

8---

94--- 30

7------ 19

5------ 19

11------

67--- 1

2--- 3

11------

47--- 1

3---+ 4

7--- 3

3--- 1

3--- 7

7---×+× 12 7+

21--------------- 19

21------= = =

34--- 5

6---+ 3

4--- 3

3--- 5

6--- 2

2---×+× 9 10+

12--------------- 19

12------ 1 7

12------= = = =

278--- 31

2---+ 5 7

8--- 1

2--- 4

4---×+ + 5 7 4+

8------------+ 511

8------ 63

8---= = = =

145--- 34

9---+ 4 4

5--- 9

9--- 4

9--- 5

5---×+×+ 436 20+

45------------------= =

45645------= 511

45------=

418--- 35

8--- 6 27

8---+ + + 151 5 7+ +

8--------------------- 1513

8------= =

1658---= 5

8---

234--- 11

3--- 1

2---+ + 39 4 6+ +

12--------------------- 319

12------ 4 7

12------= = =

78--- 3

8---– 4

8--- 1

2---= =

21720------ 1 9

20------– 1 8

20------ 12

5---= =

5 411------– 55

11------ 5

1---– 51

11------ 4 7

11------= = =

312--- 2– 11

2---=

23--- 4

7---– 2

3--- 7

7---× 4

7--- 3

3---×– 14 12–

21------------------ 2

21------= = =

412--- 12

5---– 3 5

10------ 4

10------– 3 1

10------= =

6 258---– 58

8--- 25

8---– 33

8---= =

714--- 37

9---– 345

36------ 28

36------– 317

36------= =

1 710------ 1 3

10------– 2

5---=

445--- 22

5---– 22

5---=

225---

23--- 7

8---× 14

24------ 7

12------= =

34--- 10

15------ 12

25------×× 1

1--- 2

5--- 3

5---×× 6

25------= =

5 212--- 2

7---×× 5

1--- 5

2--- 2

7---×× 50

14------ 34

7---= = =

114--- 2

5--- 31

6---×× 1

2--- 1

1--- 19

6------×× 19

12------ 1 7

12------= = =

34--- 6× 3

4--- 6

1---× 41

2---= = 41

2---

25--- 41

2---× 2

5--- 9

2---× 14

5---= =

13--- 41

2---× 1

3--- 9

2---× 11

2---= =

212--- 41

2---× 5

2--- 9

2---× 111

4---= =

24



18 a

b ÷

c ÷

d ÷

19 a

b

c

20 a b

c

d

e f

g

h

21 a

b ÷

c ÷

Exercise 4A

1

2 a 23·678 Units

b 12·437 8 Hundredths

c 178·900 3 Ten-thousandths

d 0·346 Tenths

e 349·444 78 Hundreds

f 390·897 51 Hundreds

g 14·003 457 Thousandths

h 2·436 887 Hundredths

i 1278·463 76 Thousandths

j 567·890 32 Ten-thousandths

k 2·467 830 Hundred-thousandths

l 0·000 035 Hundred-thousandths

3 a 16·890 76 5 b 346·23 2

c 1·670 3 d 90·006 031 6

e 0·456 3 f 56·789 789 789 9

g 1·234 789 30 8 h 2·9 1

i 4·987 3 j 9 643·230 0 4

k 7·909 09 5 l 2·3 1

4 a 2 units + 6 tenths = 2·6

b 5 units + zero tenths + 7 hundredths = 5·07

c 8 thousandths = 0·008

d 9 tens + 2 hundredths + 4 thousandths = 90·024

e 9 ten-thousandths = 0·0009

f 7 tenths + 7 thousandths = 0·707

5 a 5·43 b 4·96 c 7·6

d 0·14 e 126·986 f 10·47

g 6 hundredths h 7 tenths

6 a 2·345 2·435 2·453 2·543 3·245

b 2·718 27·08 27·18 27·81

c 19·115 19·151 19·5 19·511

d 0·000 04 0·0004 0·004 0·4

e 0·907 0·909 0·997 1·003 1·909

f 0·9199 0·989 0·9909 0·999 89 0·9999

7

a The temperature was highest at 3 pm.

b The temperature with a value of 5 tenths is 28·5°C.

c The temperature at 6 pm in words is 2 tens + 4 units + 3 tenths °C or twenty-four point three °C.

d The temperatures in ascending order are: 17·8, 23·4, 24·3, 25·8, 28·5 (all °C).

8 a 8 hundredths is equal to 8 cents ($0·08).

b Mandy’s hat cost $27·92 + $0·08 = $28·00.

c Martin’s hat cost $29·72 and was the most expensive.

9 Aaron 1·45 m Joshua 1·85 mKarl 1·55 m Matthew 2·05 m

a Matthew had the highest jump.

b Aaron had the shortest jump.

c Joshua’s jump can be written as 1 unit, 8 tenths and 5 hundredths.

d The first, second and third placegetters were: Matthew, Joshua and Karl respectively.

e 1·45 + 1·85 + 1·55 + 2·05 = 6·9 mThe total height of the combined jumps of alll four students is 6·9 m.

a 3·12 3 · 1 2

b 12·890 1 2 · 8 9 0

c 123·5 1 2 3 · 5

d 8·5678 8 · 5 6 7 8

e 2·008 2 · 0 0 8

f 56·7071 5 6 · 7 0 7 1

g 0·1004 0 · 1 0 0 4

h 440·6 4 4 0 · 6

i 49·003 4 9 · 0 0 3

j 943·761 9 4 3 · 7 6 1

k 78·0002 7 8 · 0 0 0 2

l 0·0643 0 · 0 6 4 3

25--- 3

8---÷ 2

5--- 8

3---× 16

15------ 1 1

15------= = =

214--- 3

5--- 9

4--- 5

3---× 15

4------ 33

4---= = =

356--- 22

9--- 23

6------ 9

20------× 69

40------ 129

40------= = =

2 411------ 4 26

11------ 1

4---× 13

22------= =

14--- 32× 1

4--- 32

1------× 8= =

25--- 40× 2

5--- 40

1------× 16= =

38--- 24 h× 3

8--- 24

1------× 9 h= =

34---

2 916------= 2

7---

2 449------=

156---

2 116

------ 2 121

36--------- 313

36------= = =

215---

2 115

------ 2 121

25--------- 421

25------= = =

1649------ 4

7---= 9

100--------- 3

10------=

7 916------ 121

16--------- 11

4------ 23

4---= = =

11981------ 100

81--------- 10

9------ 11

9---= = =

23--- 4

5---× 61

3---+ 8

15------ 6 5

15------+ 613

15------= =

812--- 7– 12

5--- 81

2--- 7

1--- 5

7---×– 81

2--- 5– 31

2---= = =

34---

2 23--- 7

8---×– 12

5--- 9

16------ 2

3--- 7

8--- 5

7---××–=

916------= 5

12------– 7

48------=

Chapter 4

Time 9 am 12 noon 3 pm 6 pm 9 pm

Temperature 23·4°C 25·8°C 28·5°C 24·3°C 17·8°C



f Highest jump = 2·05Shortest jump = 1·45Difference = 2·05 – 1·45 = 0·6 m

Exercise 4B

1

2 Estimated cost = 6 + 4 + 3 + 1= $14

3 Estimated total cost = 80 + 20 +100 + 40 + 70 = $310

Exercise 4C1 a 7·8 ≈ 8 b 19·7 ≈ 20

c 124·5 ≈ 125 d 23·85 ≈ 24

e 47·13 ≈ 47 f 983·054 ≈ 983

g 0·9 ≈ 1 h 0·47 ≈ 0

2 a 2·345 = 2·3 b 0·243 = 0·2

c 4·5721 = 4·6 d 99·8732 = 99·9

e 0·09 = 0·1 f 689·0812 = 689·1

g 45·89 = 45·9 h 0·02 = 0·0

3 a 23·693 = 23·69 b 12·809 = 12·81

c 25·006 73 = 25·01 d 14·5573 = 14·56

e 56·222 351 = 56·22 f 12·1 = 12·10

g 14·999 = 15·00 h 88·0984 = 88·10

4 a 45·2535 = 45·254 b 97·024 78 = 97·025

c 19·6578 = 19·658 d 14·234875345 = 14·235

e 2·6097 = 2·610 f 107·9999 = 108·000

g 2·679 = 2·680 h 0·3 = 0·333

5 a 45·876 124 [5 dp] = 45·876 12

b 0·087 346 23 [7 dp] = 0·087 346 2

c 21·469 023 [4 dp] = 21·4690

d 0·004 562 [3 dp] = 0·005

e 34·99 [0 dp] = 35

f 17·090 457 [4 dp] = 17·0905

g 0·7 [ 3 dp] = 0·700

h 0·142 857 [4 dp] = 0·1429

i 43·4678 [4 dp]

j 1·54 [2 dp]

k 9·155 [3 dp]

l 0·0047 [4 dp]

Exercise 4D

1 a b c

d e f

g h i

2 a b c

d e f

g h i

j

3

The sum of 245·98, 34·07 and 1·88 is 281·93.

4

The total weight is 162·20 kilograms.

5

In one week Angela swam a total of 7·27 kilometres.

6

Sian spent a total of $9·80 at the supermarket.

Approximate question

Estimate answer

Calculator answer

≈ 120 + 20 = 140 = 148·01

a ≈ 1 + 15 = 16 = 15·67

b ≈ 236 + 7 = 243 = 242·8987

c ≈ 2 + 9 = 11 = 11·23

d ≈ 15 − 4 = 11 = 10·83

e ≈ 14 − 1 = 13 = 12·80

f ≈ 57 − 1 = 56 = 56·133

g ≈ 25 × 10 = 250 = 320·8321

h ≈ 5 × 10 = 50 = 55·0095

i ≈ 14 × 3 = 42 = 41·9058

j ≈ 240 ÷ 4 = 60 = 58·9925

k ≈ 640 ÷ 8 = 80 = 79·736 25

l ≈ 81 ÷ 9 = 9 = 8·954

23·21+ 13·54

36·75

127·3+ 45·6

172·9

1·25+ 6·51

7·76

45·91+ 12·73

58·64

237·72+ 56·91

294·63

12·909+ 93·007

105·916

34·95+ 6·86

41·81

1·78+ 8·56

10·34

1·42+ 92·08

93·50

0·653·98

+ 5·12

9·75

12·763+ 45·601

58·364

104·69+ 23·28

127·97

129·87+ 42·90

172·77

14·89342·09

5·01+ 12·77

374·76

160·8762·801

+ 0·083

163·760

1·054·99

+ 120·12

126·16

19·310·6

+ 250·9

280·8

136·8568·01

+ 3018·34

3723·15

44·821·7

1000·74+ 0·07

1047·33

245·9834·07

+ 1·88

281·93

45·7516·25

+ 100·20

162·20

0·672·51·450·85

+ 1·8

7·27

1·863·281·87

+ 2·79

9·80

26



7 a The collective weight of his parcels was

6·35 kg:

b The combined weight of the heaviest and lightest parcel was 3·02 kg :

8

Pia purchased a total length of 7·2 metres of material.

9 a Rochelle spent $21·50 at the market:

This would be rounded down to $21·50.

b Tyrone spent $22·25 at the market:

c Therefore, Tyrone spent more at the market.

d The total cost of the fruit and vegetables for the two weeks was $43·75:

10 a It will cost Morgan $12·85 to make spaghetti

bolognaise:

b Morgan has $14·80 to spend:

c Yes, Morgan has enough money, he will have $1·95 left.

11

The total cost was $12·75.

12 July electricity bill:

13

Exercise 4E

1 a b c

d e f

g h i

2 a b c

d e f

g h i

j k l

3 The difference between 34·7 and 21·8 is 12·9:

4 65·07 is bigger than 30·77 by 34·3:

5 The difference between 3·76 metres and

121·05 metres is 117·29:

6 The Chan family spent $143·35 at the supermarket on groceries and received $56·65 change from $200:

2·750·580·271·8

+ 0·95

6·35

2·75+ 0·27

3·02

2·33·1

+ 1·8

7·2

potatoes 5·99onions 1·10lettuce 0·97carrots 1·58apples 8·24bananas 2·28kiwi fruit + 1·36

21·52

potatoes 6·49onions 2·51capsicum 1·27pumpkin 0·86lettuce 0·99apples 3·95bananas 3·23oranges + 2·95

22·25

21·50+ 22·25

43·75

mince 4·26tomato paste 1·89onion 0·31tomatoes 3·64spaghetti + 2·75

12·85

9·60+ 5·20

14·80

exercise book 3·90pencil case 1·65pencils 3·95highlighters + 3·25

12·75

final cost 252·15discount + 52·75

initial cost 304·90

weight (5 years old) 20·65weight (birth) − 3·19

17.46

Emilia has gained 17·46 kg.

28·76− 13·54

15·22

187·9− 15·6

172·3

10·87− 7·54

3·33

85·81− 14·23

71·58

167·32− 94·96

72·36

22·72− 13·07

9·65

64·1− 6·9

57·2

9·56− 8·78

0·78

92·8− 9·7

83·1

80·98− 5·12

75·86

212·96− 85·61

127·35

140·39− 23·20

117·19

219·87− 32·44

187·43

14·3− 5·7

8·6

16·81− 0·08

16·73

1·99− 0·14

1·85

19·97− 9·29

10·68

1018·34− 568·20

450·14

1164·9− 246·86

918·04

176·8− 12·0

164·8

44·0− 3·8

40·2

34·7− 21·8

12·9

65·07− 30·77

34·30

121·05− 3·76

117·29

200·00− 143·35

56·65



7 The temperature at Ballarat rose by 17·7°C:

8 Ten years ago shares in a particular bank were priced at $9·35, however they are now priced at $31·12. The cost of these shares risen by $21·77:

9 a i The distance the Frazer family travelled on

Monday was 446·1 kilometres:

ii The distance travelled on Tuesday was 572·5 kilometres:

iii The distance travelled on Wednesday was 509·2 kilometres:

b They travelled furthest on Tuesday.

c The total distance travelled on their trip was 1527·8 kilometres:

10 a Clint is given $20 for his birthday which he deposits in the bank on 9 April. His balance is then equal to $91·91:

b On 14 April he places his left-over pocket money of $5·82 in the bank. His balance is then equal to $97·73:

c Clint needs $29·95 from his bank to buy a new shirt for himself and a present for his mate’s birthday party. He withdraws this money on 20 April. His balance is then equal to $67·78:

d Clint deposits $25·85 in the bank on 27 April. His balance is then equal to $93·63:

Exercise 4F

1 a b c

d e f

g h i

j k

l m

n o p

2 a 12·7 × 14Estimate = 10 × 15 = 150Calculator = 177·8

b 34·9 × 23Estimate = 35 × 20 = 700Calculator = 802·7

c 0·67 × 38Estimate = 1 × 38 = 38Calculator = 25·46

d 6·84 × 19Estimate = 7 × 20 = 140Calculator = 129·96

e 99·5 × 72Estimate = 100 × 72 = 7200Calculator = 7164

f 5·78 × 47Estimate = 6 × 50 = 300Calculator = 271·66

g 4·74 × 53Estimate = 5 × 50 = 250Calculator = 251·22

h 134·87 × 21Estimate = 135 × 20 = 2700Calculator = 2832·27

i 1·76 × 49Estimate = 2 × 50 = 100Calculator = 86·24

j 84·098 × 124Estimate = 90 × 120 = 10 800Calculator = 10 428·152

k 78·934 × 87Estimate = 80 × 90 = 7200Calculator = 6867·258

l 129·57 × 264Estimate = 130 × 300 = 39 000Calculator = 34 206·48

m 2·9 × 21·7Estimate = 3 × 22 = 66Calculator = 62·93

n 44·83 × 5·13Estimate = 50 × 5 = 250Calculator = 229·9779

o 149·56 × 32·9Estimate = 150 × 30 = 4500Calculator = 4920·524

23·5− 5·8

17·7

31·12− 9·35

21·77

108 818·8− 108 372·7

446·1

109 391·3− 108 818·8

572·5

109 900·5− 109 391·3

509·2

446·1572·5

+ 509·2

1527·8

71·91+ 20·00

91·91

91·91+ 5·82

97·73

97·73− 29·95

67·78

67·78+ 25·85

93·63

23·6× 7

165·2

14·9× 9

134·1

0·42× 7

2·94

124·75× 4

499·00

2·354× 3

7·062

56·89× 6

341·34

9·98× 9

89·82

4·874× 8

38·992

45·980× 7

321·860

9·807× 8

78·456

23·9087× 5

119·5435

19·087 45× 8

152·699 60

7·6× 0·4

3·04

41·5× 2·5

103·75

5·8× 9·3

53·94

25·3× 1·2

30·36

28



p 3·87 × 1·57Estimate = 4 × 2 = 8Calculator = 6·0759

3 a 1·82 b 5·04 c 2·82

d 2·36 e 3·28 f 20·52

g 76·96 h 13·32 i 14·792

j 0·6175 k 2·1624 l 47·5356

4 a 0·0276 b 0·004 55

c 0·000 018 d 0·000 264

e 0·000 04 f 0·0486

g 0·000 003 6 h 0·000 603

i 0.00301

5 a 23·29 b 175·11

c 93·22 d 121·929

e 373·221 f 82·705

g 365·976 h 45·408

i 83·5125 j 132·2411

k 353·2396 l 156·6661

6 a 10 768·146 b 1197·4843

c 394·643 84 d 872·295 681 6

7 $1181·97

8 a $173·25 b $28·88 c $202·13

9 $49·85 10 $1753·13

11 $11·89 12 $47·41

13 a i $6·39 ii $15·66 iii $1·42

iv $3·51 v $6·71 vi $1·85

vii $3·13

b $38·67

14 25 × 273·90 = $6847·50

Total cost of netting is $6847.50.

Exercise 4G

1 a b c

d e f

g h i

j k l

m n o

p

2 a 47·982 ÷ 12Estimate = 50 ÷ 10 = 5Calculator = 4·00

b 17·765 ÷ 9Estimate = 20 ÷ 10 = 2Calculator = 1·97

c 2·064 ÷ 4Estimate = 2 ÷ 4 = 0·5Calculator = 0·52

d 4·87 ÷ 2Estimate = 5 ÷ 2 = 2·5Calculator = 2·44

e 71·14 ÷ 5Estimate = 70 ÷ 5 = 14Calculator = 14·23

f 95·092 ÷ 7Estimate = 100 ÷ 5 = 20Calculator = 13·58

g 21·93 ÷ 11Estimate = 22 ÷ 11 = 2Calculator = 1·99

h 7·034 216 ÷ 8Estimate = 8 ÷ 8 = 1Calculator = 0·88

i 24·2424 ÷ 6Estimate = 24 ÷ 6 = 4Calculator = 4·04

j 177·390 ÷ 9Estimate = 180 ÷ 9 = 20Calculator = 19·71

k 143·618 ÷ 12Estimate = 140 ÷ 10 = 14Calculator = 11·97

l 962·3261 ÷ 8Estimate = 1000 ÷ 8 = 125Calculator = 120·29

3 Mrs Quick divides $9·45 equally between her three children. Therefore each child receives $3·15:

4 $9·75 for 5 days of train tickets to school. Therefore her ticket costs $1·95 per day:

5 A packet of 100 cups costs $3·56:

a Each cup costs approximately $0·04 (in dollars).

b Each cup costs approximately 4 cents.

6 A packet of biscuits costs $3·48 and contains 12 biscuits:

Therefore each biscuit costs $0·29 (29 cents).

7 a Plane travels 1555·5 kilometres in 3 hours

Therefore in 1 hour it travels 518·5 kilometres.

b 15 min = = hour

Therefore in 15 min, the plane travels 129·625 km.

Exercise 4H1 a 13 b 7 c 1·2 d 12

e 0·6 f 0·09 g 100 h 2100

i 110 j 0·002 k 0·04 l 5

m 90 n 15 o 1 p 0·5

q 2·275 r 0·0016 s 0·6 t 1360

2 a 4·58 b 3·5 c 316

d 6·4 e 0·258 f 45·6

3·94)15·6

29·15)145·5

32·43)97·2

3·127)21·84

4·288)34·24

7·549)67·86

0·05796)0·3474

29·275)146·35

0·0411)0·44

0·0095)0·045

39·666)237·96

1·838)14·64

23·40·2)46·8

·71·2)8·4

·412·5)10·25

3·512·1)73·71

3·153)9·45

1·955)9·75

0·0356100)3·56

0·2912)3·48

518·53)1555·5

1560------ 1

4---

129·6254)518·500



g 1·256 h 24·67 i 1·256

j 0·146 k 911·5 l 0·458 25

m 60 n 120·465 71 o 130

p 1·55 q 765·5 r 16·18

s 19·1325 t 49·9 u 3·768

3 a 4·56 b 1·569 c 0·045

d 23 e 3·54 f 74·809

g 0·018 h 0·9175 i 114·99

4 a 709·8775 b 971·21

5 245 6 18 7 18·5

Learning task 4I

1

2 a When a decimal is multiplied by 10 the decimal point moves one place to the right.

b When a decimal number is multiplied by a power of 10, say 100 or 1000, the decimal point moves to the right by the number of places equal to the number of zeros in the multiplying power.

3

4 a When a decimal is divided by 10 the decimal point moves one place to the left.

b When a decimal number is divided by a power of 10, say 100 or 1000, the decimal point oves to the left by the number of places equal to the number of zeros in the dividing power.

5 a 127·4 b 765·4 c 14·56

d 59·83 e 65 f 1587·39

g 35·89 h 0·67 i 123 678

j 8·76 k 2789·04 l 42 780

6 a 34 987 b 650 098 c 340·08

d 877·6402 e 285·7162 f 567 901·1

g 23 589·0 h 34 125·67

i 4 569 998·7 j 345 000

k 23 487 124·5 l 3 478 000

7 a

17·375 × 100 = 1737·5

b

1·023 585 × 10 000 = 10 235·85

c

76·735 × 10 = 767·35

8 a 0·3983 b 1·238 76

c 145·832 45 d 34·598

e 0·5699 f 0·087

g 9·8054 h 0·234 123

i 56·7329 j 60·6098

k 0·235 908 7 l 3·490

9 a 0·023 87 b 0·0098

c 0·002 349 8 d 0·000 123

e 6·7908 f 0·008 76

g 2·345 679 h 0·012 765 4

i 0·001 245 j 0·034 576

k 0·000 345 6 l 0·125 745

m 0·047 89 n 0·003 76

o 1·956 7 p 0·000 98

q 0·034 567 r 0·000 087 6

s 23·456 23 t 0·000 987

u 0·000 001 05

10 a

49·72 × 10 = 497·2

b

623·25 × 100 = 62 325

c

96·25 × 10 = 962·5

d

222·44 ÷ 100 = 2·2244

e

145·28 ÷ 10 = 14·528

f

16·59 ÷ 100 = 0·1659

g

17 172·75 × 1000 = 17 172 750

h

387·36 × 10 = 13 873·6

Question Answer

1·8 × 10 18

0·6 × 10 6

7·3 × 10 73

3·68 × 100 368

5·008 × 100 500·8

0·005 × 1000 5

1·612 × 1000 1612

1·75 × 1000 1750

Question Answer

40·3 ÷ 10 4·03

50·4 ÷ 10 5·04

0·24 ÷ 10 0·024

650·48 ÷ 100 6·5048

346·24 ÷ 100 3·4624

19·36 ÷ 100 0·1936

1087·4 ÷ 1000 1·0874

471·28 ÷ 1000 0·471 28

0·24 ÷ 100 0·0024

27

3·475× 5

17·375

0·341 195× 3

1·023 585

15·347× 5

76·735

24·86× 20

124·65× 500

19·25× 50

222·442)444·88

145·283)435·84

16·596) 99·54

3434·55× 5000

346·84× 40

30



i

47 391·75 × 10 = 473 917·5

j

2140 ÷ 100 = 21·4

k

4580 ÷ 100 = 45·8

l

7190 ÷ 100 = 71·9

m

3·36 × 1000 = 3360

n

14·75 × 100 = 1475

o

40·16 × 100 = 4016

Exercise 4K

1 a b

c d

e f

g h

i j

k l

m n

o p

q r

s t

2 a b

c d

e f

g h

3 a b c

d e f

g h

Exercise 4L

1 a 0·2 = = b 0·04 = =

c 0·9 = d 0·003 =

e 0·13 = f 0·45 = =

g 0·066 = = h 0·088 = =

i 0·25 = = j 0·375 = =

k 0·75 = = l 0·125 = =

2 a

b

c

d

e

f

g

h

3 a

b

c

d

e

f

g

h

i

j

k

9478·35× 50

21404)8560

45802)9160

7 1903) 21 570

1·68× 2

2·95× 5

10·04× 4

= 0·3)

0·333̇ 3̇1·000

0·45) 2·0

0·254)1·00

0·1258) 1·000

0·8757) 8·000

= 0·4112)

0·4166̇ 6̇5·0000

= 0·85)

0.833̇ 3̇6·000

0·754) 3·00

0·85)4·0

0·310) 3·00

= 0·9)

0·55̇ 5̇5·00

= 0·11)

0·2727 273·0000

0·6258) 5·000

= 0·9)

0·888̇ 8̇8·000

0·85)6·00

3̇ = 0·12)

0·666̇ 6̇2·0000

= 0·9)

0·222̇ 2̇2·000

0·25) 1·0

0·16 = 0·16)1·000

6̇ 6̇ 0·45 = 0·11)5·0000

45 45

1·7 = 1·9)16·00

7̇ 7̇ 3·3 = 3·3)10·00

3̇ 3̇

1·85) 9·0

1·45 = 1·11)16·0000

45 45

2·16 = 2·16)13·00

6̇ 6̇ 1·710)17·0

1·09 = 1·11)12·0000

09 09 1·083 = 1·0812)13·0000

3̇ 3̇

0·574)7·00

0·147)1·00

4·673)14·00

2·437)17·00

0·449)4·00

0·388)3·00

0·297)2·00

1·679)15·00

210------ 1

5--- 4

100--------- 1

25------

910------ 3

1000------------

13100--------- 45

100--------- 9

20------

661000------------ 33

500--------- 88

1000------------ 11

125---------

25100--------- 1

4--- 375

1000------------ 3

8---

75100--------- 3

4--- 125

1000------------ 1

8---

8·5 8 510------+ 81

2---= =

3·6 3 610------+ 33

5---= =

2·07 2 7100---------=

8·008 8 81000------------+ 8 1

125---------= =

1·06 106100--------- 1 3

50------= =

2·875 28751000------------ 2 875

1000------------ 27

8---= = =

3·625 36251000------------ 35

8---= =

4·07 407100--------- 4 7

100---------= =

0·104 1041000------------ 13

125---------= =

0·909 9091000------------=

0·705 7051000------------ 141

200---------= =

0·340 3401000------------ 17

50------= =

0·135 1351000------------ 27

200---------= =

0·996 9961000------------ 249

250---------= =

0·548 5481000------------ 137

250---------= =

0·625 6251000------------ 5

8---= =

1·25 1 25100---------+ 11

4---= =

2·75 2 75100---------+ 23

4---= =

1·02 1 2100---------+ 1 1

50------= =



l

m

n

o

p

q

r

s

t

Exercise 4M

1 a b c d

e f 1 g 1 h 3

2 a 3% b 81% c 70% d 30%

e 46% f 2% g 4% h 48%

i 50% j 20% k 25% l 100%

3 a 0·16 b 0·47 c 0·07 d 0·88

e 0·50 f 0·90 g 0·35 h 0·05

i 1·14 j 4·25 k 2·50 l 3·15

4 a 33% b 45% c 13% d 93%

e 19% f 5% g 1% h 2%

i 163% j 159% k 100% l 106%

5 a 0·8, 82%, , ,

(0·8, 0·82, 0·875, , )

b 0·6, 65%, , 67%,

(0·6, 0·65, , 0·67, )

c , 0·923, 92·5%, 0·96, 98%

(0·9, 0·923, 0·925, 0·96, 0·98)

d 24%, , 0·26, , 29%

(0·24, 0·25, 0·26, 0·28, 0·29)

Exercise 4N

1 a × 90 = 18 b × 88 = 22

c × 400 = 40 d × 660 = 198

e × 40 = 4 f × 250 = 37·5

g × 60 = 3 h × 350 = 42

i × 490 = 343 i × 175 = 63

k × 30 = 5·7 l × 400 = 8

2 a × 80 = 88 b × 150 = 300

c × 70 = 91 d × 100 = 225

e × 750 = 795 f × 1200 = 1260

g × 75 = 116·25 h × 12 = 42

3 a 6·5% of 200 = × 200 = 13

b 10·2% of 500 = × 500 = 51

c 3·3% of 11 000 = × 11 000 = 363

d 40·5% of 400 = × 400 = 162

e 0·25% of 800 = × 800 = 2

f 0·01% of 80 000 = × 80 000 = 8

g 9·8% of 3500 = × 3500 = 343

h 20·4% of 1250 = × 1250 = 255

4 × 10 000 = 6000

The motorbike would cost $6000.

5 a × 312 000 = 202 800

Lake Eppalock holds 202 800 megalitres when 65% full.

b × 3 390 000 = 135 600

Eildon Weir holds 135 600 megalitres when 4% full.

c × 64 200 = 2568

Pine lake holds 2568 megalitres when it is 4% full.

6 67% of 85 marks = × 85 = 56·95

Sonja obtained 57 marks in her maths test.

Exercise 4O1 a 100% − 10% = 90%

0·9 × $12 = $10·80

b 100% − 15% = 85%0·85 × $100 = $85

c 100% − 20% = 80%0·8 × $199 = $159·20

d 100% − 5% = 95%0·95 × $30 = $28·50

e 100% − 75% = 25%0·25 × $60 = $15

3·65 3 65100---------+ 313

20------= =

5·315 5 3151000------------+ 5 63

200---------= =

7·343 7 3431000------------=

9·384 9 3841000------------+ 9 48

125---------= =

12·648 12 6481000------------+ 12 81

125---------= =

10·105 10 1051000------------+ 10 21

200---------= =

12·018 12 181000------------+ 12 9

500---------= =

15·360 15 3601000------------+ 15 9

25------= =

20·045 20 451000------------+ 20 9

200---------= =

21100--------- 97

100--------- 1

2--- 1

4---

1320------ 73

100--------- 59

100--------- 33

100---------

78--- 0·87̇ 8

9---

0·87̇ 0·88̇

23--- 0·67̇

0·66̇ 0·67̇

910------

14--- 7

25------

20100--------- 25

100---------

10100--------- 30

100---------

10100--------- 15

100---------

5100--------- 12

100---------

70100--------- 36

100---------

19100--------- 2

100---------

110100--------- 200

100---------

130100--------- 225

100---------

106100--------- 105

100---------

155100--------- 350

100---------

6·5100---------

10·2100----------

3·3100---------

40·5100----------

0·25100----------

0·01100----------

9·8100---------

20·4100----------

60100---------

65100---------

4100---------

4100---------

67100---------

32



f 100% − 12·5% = 87·5%0·875 × $999 = $874·13

2 a 15% of 50 km0·15 × 50 km = 7·5 km

b 17% of 1000 metres0·17 × 1000 m = 170 m

c 125% of $701·25 × $70 = $87·50

d 95% of 20 litres0·95 × 20 L = 19 L

e 62·5% of $4000·625 × $400 = $250

f 35% of 8 centimetres0·35 × 8 cm = 2·8 cm

3 a $5 bag of cementGST = 0·1 × $5 = $0·50Total = $5·50

b $20 pair of sunglassesGST = 0·1 × $20 = $2Total = $22

c A $120 pair of jeansGST = 0·1 × $120 = $12Total = $132

d A $200 pair of runnersGST = 0·1 × $200 = $20Total = $220

e $25 compact discGST = 0·1 × $25 = $2·50Total = $27·50

f a $36·50 tieGST = 0·1 × $36·50 = $3·65Total = $40·15

Puzzles1 To see Miss Shell

2 Because he couldn’t see the point

3 The multiplication table

4 An adder machine

Applications

The price is right?1 $4·47 2 $3·49 3 $3·19

Magic squares

Magic number = 48·28

Magic number = 214·2

Currency (selected answers)1 Australian currency

There are 13 ways of having 50 cents using Australian currency.

2 US currency

12·78 8·52 21·3 5·68

22·72 4·26 14·2 7·1

2·84 18·46 11·36 15·62

9·94 17·04 1·42 19·88

56·7 37·8 94·5 25·2

100·8 18·9 63 31·5

12·6 81·9 50·4 69·3

44·1 75·6 6·3 88·2

50 cent coins

20 cent coins

10 cent coins

5 cent coins

1

2 1

2 2

1 3

1 2 2

1 1 4

1 6

5

4 2

3 4

2 6

1 8

10

50 cents 25 cents 10 cents 5 cents 1 cent

1

2

1 2 1

1 2 5

1 1 3

1 1 2 5

1 1 1 10

1 1 15

1 5

1 4 5

1 3 10

1 2 15

1 1 20

1 25

5

4 2

3 4

2 6

1 8

4 1 5

4 10

3 3 5

3 2 10

3 1 15

3 20

2 5 5

2 4 10

2 3 15

2 2 20

2 1 25

2 30



Using US currency there are 50 ways of having 50 cents.

5 Israel’s agorot

There are 7 ways of having 50 cents using Israel’s currency of agorots.

Enrichment

1 a 0·2

N = 0·2333… (1)100N = 23·2333… (2)(2) − (1)100N − N = 23·333…− 0·2333…99N = 23·1000

N = =

b 0·

N = 0·888… (1)100N = 88·888… (2)(2) − (1)100N − N = 88·888…− 0·888…99N = 88·000

N = =

c 0·7 s

N = 0·722222… (1)10N = 7·222222… (2)(2) − (1)10N − N = 72·22222…− 0·22229N = 6·5000

N = = =

d 0·

N = 0·555… (1)100N = 55·555… (2)(2) − (1)100N − N = 55·555…− 0·555…99N = 55·000

N = =

e 0·3

N = 0·34545… (1)1000N = 345·4545… (2)(2) − (1)1000N − N = 345·4545…− 0·345345…99N = 34·200000

N = =

f 0·2 (4 & 5 recur)

N = 0·2454545… (1)100N = 24·5454545… (2)(2) − (1)100N − N = 24·5454545…− 0·2454545…99N = 24·3000000

N = = =

g 0·1

N = 0·1888… (1)100N = 18·888… (2)(2) − (1)100N − N = 18·888…− 0·1888…99N = 18·7000

N = = =

h 0·4 (5 & 6 recur)

N = 0·4565656… (1)100N = 45·656565… (2)(2) − (1)100N − N = 45·656565…− 0·4565656…99N = 45·2000000

N = = =

1 7 5

1 6 10

1 5 15

1 4 20

1 3 25

1 2 30

1 1 35

1 40

10

9 5

8 10

7 15

6 20

5 25

4 30

3 35

2 40

1 45

50

50 agorot 10 agorot 5 agorot

1

5

4 2

3 4

2 6

1 8

10

50 cents 25 cents 10 cents 5 cents 1 cent

3̇

231990--------- 7

30------

8̇

8899------ 8

9---

2̇

6·59

------- 6590------ 13

18------

5̇

5599------ 5

9---

45

342990--------- 19

55------

45

24·399

---------- 243990--------- 27

110---------

8̇

18·799

---------- 187990--------- 17

90------

56

45·299

---------- 452990--------- 226

495---------

34



i 0·0

N = 0·0666… (1)100N = 6·6666… (2)(2) − (1)100N − N = 6·6666…− 0·060699N = 6·6000

N = =

j 2·4

N = 2·4777… (1)100N = 247·777… (2)(2) − (1)100N − N = 247·777…− 2·4777…99N = 245·3000

N = = =

k 0·30 (8)

N = 0·308888… (1)1000N = 308·888… (2)(2) − (1)1000N − N = 308·888…− 0·3088999N = 308·5800

N = = =

l 3·6

N = 3·6737373… (1)100N = 367·373737… (2)(2) − (1)100N − N = 367·373737…− 3·67373737…99N = 363·70000000

N = =

4 a Each structure costs $34·10 (2 posts at $8·25 each plus one rail at $17·60).

b 30 structures are needed.

c 60 posts are needed.

d Cost of the posts is $495.

e Two nuts and bolts per structure, at a total cost of $210.

f Total cost of fence materials = $1233.

g Total cost of labour = $1600.

h Cost of the materials and labour for the fence is $2833.

i GST charged = $2833 × 0·1 = $283·3 so the total cost is $2833 + 283·30 = $3116·30.

Revision1 a Units b Thousandths

c Tenths d Tens

e Hundredths f Thousand thousandths

g Tenths h Hundred thousandths

2 a 34·8762 b 1·35 c 19·606

d 0·01 e 0·0 f 0·5000

3 a 69·01 b 1198·143 c 2·43

d 13·563 e 1002·434 f 51·84

4 a $50·06 b $254·84

c Michael d $184·78

5 a 100·24 b 0·81 c 10·57

d 802·7 e 64·432 f 684·35

6 a 108 b 2·04 c 2·25

d 9·8 e 145·992 f 821·1

7 a $1·79 per kilogram b $1·75 per kilogram

c $2·50 per kilogram

d The 10 kg bag when it is on special

8 a 12·52 b 2·1 c 102·87

d 25 e 57·6 f 705

9 a 378·9 b 1 234 500 c 402 240

d 239·4 e 23·4875 f 1·245 674 32

10 a b 0·375 c 0·09

d e 1·8 f 1·375

11 a b c

d e 5 f 12

12 a , 0·23 b , 0·9

c , 0·35 d 3

e 2 , 2·25 f , 0·01

13 a $8 b 6 cm c $25

d 1 cent e $12 f $125

14 a $366·31 b $42·53 c $408·84

d $367·95 e $132·05

Exercise 5A1 a Centimetres b Metres c Metres

d Millimetres e Centimetres f Metres

g Metres h Metres i Millimetres

j Kilometres

2 a For example: distance of a marathondistance from Adelaide to Perthdiameter of the earthdistance from Earth to the Moonlength of the Amazon River

b For example: height of Mount Everestdistance jumped by a long jumperlength of the classroomheight of a giraffelength of a car

c For example: height of a chairlength of a rulerdimensions of a shoe boxsize of your waist

6̇

6990--------- 1

15------

7̇

245·399

------------- 2453990

------------ 22390

---------

8̇

308·58999

---------------- 30 85899 900---------------- 139

450---------

73

363·799

------------- 3637990

------------

0·583̇

0·7̇

12--- 7

1000------------ 67

100---------

173500--------- 809

1000------------ 29

500---------

23100--------- 9

10------

720------

14--- 1

100---------

Chapter 5



d For example: width of a pencilthickness of your shoelacediameter of your eyelength of a beediameter of a pea

3 For example: a highlighter a perfume bottlea car key a muga pair of scissors

4 For example: the width of the fridge a cereal boxa bottle of wine the height of the oventhe width of a wok

Exercise 5B1 a 1·4 m b 70 cm c 1·3 m

d 48 m e 17 m f 27 cm

2 a 3 m b 3·75 cm c 4·5 m

d 5·6 m e 15 m f 2·5 m

Exercise 5C1 Both circles are 1·9 cm in diameter.

2 Both lines are 3·1 cm.

3 Squares are the same size.

4 Rectangles are the same size.

5 They are the same size.

6 A and C are the same size, B and D are the same size and bigger than A, C.

7 The top and bottom ones are the same height, the middle one is taller.

8 The two on the left are the same size and the two on the right are the same size and bigger than the others.

9 A = 5 cm B = 6 cm C = 11 cm D = 8 cmE = 5·3 cm F = 4·5 cm G = 4·5 cmA, B & C are the easiest and the hardest are D & E.Horizontal and vertical are easier than diagonal

Exercise 5D1 a 9·4 cm b 6·7 cm c 11·9 cm

d 1·5 cm e 8·1 cm f 12·7 cm

2 a 4·1 b 4·1 c 2 d 3 e 3·4

3 A: inch B: 1 inch

C: inches D: inches

E: inches F: inches

G: 5 inches

Exercise 5E1 a Width: 34 mm, height: 23 mm,

bottom span: 10 mm

b Height: 9 mm, length: 33 mm

c Front length: 10 mm, height of front tyre: 11 mm, length: 33 mm

d Head height: 17 mm, height: 43 mm, shoe width: 11 mm

e Length: 30 mm, height: 21 mm

f Height: 40 mm, width: 31 mm

2 a 204 mm b 165 mm

c 144 mm d 122 mm

3 a 426 mm b 480 mm

4 a Length: 29·0 cm, cost: $348

b Length: 43 cm, cost: $516

Exercise 5F1 a Multiply by 100 b Divide by 10

c Divide by 1000 d Divide by 1000

e Divide by 100 f Multiply by 1000

g Multiply by 100 000 h Multiply by 10

2 a 3·9 km = 3900 m = 390 000 cm

b 0·0003 km = 0·3 m = 30 cm = 300 mm

c 0·14 m = 14 cm = 140 mm

d 0·57 m = 57 cm = 570 mm

3 a 1·2 m b 1·5 km c 20 cm

d 0·12 km e 4700 mm f 20 mm

g 12 cm h 0·8 km i 2 cm

j 350 cm k 4500 m l 24 mm

4 21·11 m 5 60 480 m, 60·48 km

6 84 cm or 0·84 m

7 a $100 ÷ $0.20 = 500 coins × 2 mm = 1000 mm= 1 m

b $212 ÷ %0.20 = 1060 coins × 2 mm = 2120 mm= 2.12 m

c $583.60 ÷ $0.20 = 2918 coins × 2 mm = 5836 mm= 5.836 m

Exercise 5G1 a 81 mm b 31 m c 80 mm

d 610 km e 340 mm f 15 cm

g 113 m h 3 mm i 293 m

j 28 mm k 72 km l 187 cm

2 a 858 cm b 8290 m c 398 cm

d 101 mm e 670 mm f 102 mm

g 736 m h 146 mm i 56 789 m

j 3280 cm k 701 mm l 1363 cm

3 a 7·124 km b 4·87 m c 17·0 cm

d 5·986 km e 75·3 m f 1·4 cm

g 0·502 km h 85·17 m i 3·2 km

j 81·7 cm k 88·7 km l 1·1 m

4

5 The 23·2 m kick was greater by 3·31 m.

6 Bill’s worm was longer by 33 mm.

7 Jin walks 2·5 + 0·56 = 3·06 km.Shan walks 2·5 km.

8 a 133·7 m b 36·7 m

9 a 27·3 mm, 3 cm, 0·045 m

b 43 mm, 8 cm, 153 mm, 0·0045 km

c 1450 mm, 6·8 km, 7932 m

d 180 cm, 3 m, 0·0045 km

e 0·12 cm, 3·5 mm, 0·009 m, 0·0058 km

f 0·2 cm, 15 mm, 0·04 m, 0·006 km

616------ 3

8---=

112--- 2 2

16------ 21

8---=

21416------ 27

8---= 4 7

16------

Group 1 Group 2 Group 3

Longest 4·5 m 4·5 m 6·98 m

Shortest 2·1 m 0·63 m 4·75 m

Difference 2·1 m 3·87 m 2·23 m

36



10 a i Length 0·8 m ii Length 0·4 mDepth 0·15 m Depth 0·9 mHeight 0·4 m Height 0·3 m

b 500 m at Flemington210 m at Richmond4150 m at South Yarra6525 m at South Melbourne

Exercise 5H1 Shape A is 14 cm. Shape B is 16 cm.

Shape C is 29 cm. Shape D is 20 cm.

2 a 180 cm b 70 cm c 84 cm

d 18 cm e 24 cm

3 As all sides are the same length for a, b and c, the number of sides can be multiplied by the length of one side to find the perimeter.

a 42 cm b 48 cm c 85 cm d 54 mm

4 a 76 m b 169 cm

5 a 48 cm b 55 cm or 550 mm

6 Bed 1 Bed 23580 cm or 38·5 m 2140 cm or 21·4 mBed 3 Bed 44020 cm or 40·2 m 4100 cm or 41 mBed 5 Bed 67900 cm or 79 m 1600 cm or 16 m

7 a Perimeter = 3 × 10·03 cm= 30·09 cm

b Perimeter = 5 × 2·06 m= 10·30 m = 1030 cm

c Perimeter = 6 × 0·9 km= 5·4 km = 540 000 cm

d Perimeter = 9 × 154 mm= 1386 mm = 138·6 cm

e Perimeter = 2(124·06 + 60) m= 2(184·06) m = 36 812 cm

8 a 685 cm or 6·85 m b 14·1 cm or 141 mm

c 15 900 cm or 159 m d 3450 cm or 34·5 m

e 3630 cm or 36·3 m

f 1847 cm or 18·47 m or 0·018 47 km

g 0·174 km, 174 m, 17 400 cm, 174 000 mm

h 29·8 m, 2980 cm, 29 800 mm

i 0·0301 km, 31·01 m, 3101 cm, 31010 mm

Learning task 5I1 c Differences could arise due to individual

differences in body size and shape. The amount of food eaten and amount of hard manual labour could also lead to different finger thickness.

2 a Royal cubit b Hand c Digit

d Palm e Digit f Digit

Puzzles1 The life story of a car 2 He became an xray

3 A buccaneer

Applications

Coinsa The diameter of a one-dollar coin is 24 mm.

One million of these coins would reach 24 000 000 mm, 2 400 000 cm, 24 000 m or 24 km.

b The diameter of a twenty-cent coin is 28mm. One million of these coins would reach 28 000 000 mm, 2 800 000 cm, 28 000 m or 28 km.

c The diameter of a ten-cent coin is 23 mm. One million of these coins would reach 23 000 000 mm, 2 300 000 cm, 23 000 m or 23 km.

d The diameter of a five-cent coin is 19 mm. One million of these coins would reach 19 000 000 mm, 1 900 000 cm, 19 000 m or 19 km.

Enrichment1 a By measuring the relative pipe diameters it can

be seen that pipe A has a diameter that will fit most snugly into the larger pipes and allow it to be glued in place.

b 6 cm × 10 = 60 cmadd on two lots of 15 mm lengths60 + 1·5 + 1·5 = 63 cm

2 a 65 + 100 + 35 + 30 + 20 + 20 + 20 + 30 + 30 + 20 = 370 cm

b 70 + 10 + 30 + 30 + 30 + 10 + 30 + 20 + 10 + 60 + 30 + 10 = 340 cm

3 If there are 330 shapes required and twice as many hexagons as octagons, 220 hexagons and 110 octagons are required.

Each hexagon has a perimeter of 6 × 15 = 90 cm

Each octagon has a perimeter of 8 × 15 = 120 cm

The total length of wire required is 220 × 90 + 110 × 120 = 33 000 cm = 330 m

The density of the wire is 200 g per metre so 200 × 330 = 66 000 g = 66 kg of wire is required.

4 a i total length of wire = 41 sides × 14 mm = 574 mm

ii Perimeter = 22 sides × 14 mm= 308 mm

b i total length = 46 sides × 12 mm= 552 mm

ii Perimeter = 28 sides × 14 mm= 336 mm

5 a Black: length is 40 m Width is 6 + (4 × 2·5) + (2 × 3) = 22 mPerimeter is 40 + 22 + 40 + 22 = 124 m

Red: length is 40 − (2 × 3) = 34 m Width is 6 + (4 × 2·5) = 16 mPerimeter is 34 + 16 +34 + 16 = 100 m

Green: length is 40 − (4 × 3) = 28 m Width is 6 + (2 × 2·5) = 11 mPerimeter is = 28 + 11 + 28 + 11 = 78 m

Blue: length is 40 − (6 × 3) = 22 m Width is 6 mPerimeter is 22 + 6 + 22 + 6 = 56 m



b The total length of tape required:56 + 78 + 100 + 124 = 358 mThe total cost: 0·25 × 354 = $89·50

6 The perimeter of bed 1 is 2 × 1350 + 2 × 900 = 4500 cm

The perimeter of bed 2 is 2 × 1440 + 2 × 945 = 4770 cm




The total perimeter of the garden beds is 4500 + 4770 + 6480 + 2250 + 3690 = 21 690 cm

This means Linda needs to buy 21 690 ÷ 45 = 482 tiles

7 There is room for 40 cm ÷ 1·5 cm = 26·67 spaces between dark lines along the length of the paper. This means there would be 26 gaps on every page in which the pen can be used. Across each line there can be 300 mm ÷ 4 mm = 75 pen strokes.

This means that one page can contain 26 × 75 = 1950 pen strokes. As each stroke is 1·5 cm long, this is a distance of 1950 × 1·5 = 2925 cm = 29·25 m.

In total, the pen can write 10 000 m so 10 000 ÷ 29·25 = 341·88 ≈ 342 pages are needed for each pen.

Revision1 a Millimetres b Metres

c Kilometres d Centimetres

2 Door measures about 0·8 cm and plane length about 14 cm.

Door:Length (scale is 1:250)0·8 cm:14 cm200 cm:3500 cm

So, real length of plane is about 35 m.

3 Check with your ruler.

4

5 a 14 mm b 22 mm c 26 mm d 34 mm

e 56 mm f 150 mm g 200 mm

6 a 48·9 cm = 489 mm b 32·88 km = 32880 m

c 214 mm = 21·4 cm d 0·021 km = 21 m

e 8·56 cm = 0·0856 m f 514 m = 0·514 km

g 4·5 cm = 45 mm h 125 km = 1250 m

i 0·2 m = 20 cm

7 a Length = 3 × 15 cm = 45 cm = 0·45 m

b Length = 5 × 15 cm = 75 cm = 0·75 m

c Length = 20 × 15 cm = 300 cm = 3 m

d Length = 24 × 15 cm = 360 cm = 3·6 m

e Length = 38 × 15 cm = 570 cm = 5·7 m

8 a 1·8 cm = 18 mm23 mm + 18 mm = 41 mm

b 2·4 km = 2400 m4500 m − 2400 m = 2100 m

c 1·2 m = 1200 mm56 cm = 560 mm1200 mm + 560 mm − 450 mm = 1310 mm

9 a 2 m = 200 cm = 2000 mm

2000 mm − 1591 mm = 409 mmJohn is 409 mm shorter than 2 m.

2 m − 1·67 m = 0·33 mManuel is 0·33m shorter than 2 m.

2000 mm − 1365 mm = 635 mmLulu is 635 mm shorter than 2 m.

200 cm − 142 cm = 58 cmValda is 58 cm shorter than 2 m.

b 1·67 m = 1670 mm142 cm = 1420 mm

The sum of their heights is 1591 mm + 1670 mm + 1420 mm + 1365 mm= 6046 mm = 604·6 cm = 6·046 m

10 2 m = 2000 mm12 cm + 120 mm = 230 mm = 23 cm512 mm = 51·2 cm30 cm = 30·75 cm

The total length of the chains is:200 + 12 + 23 + 30·75 + 51·2 = 316·95 cm

11 a Perimeter = 4 × 2·5 cm = 10 cm

b Perimeter = 2 × 2·5 cm + 2 × 3 cm = 11 cm

c Perimeter = 5 × 1·6 cm = 8 cm

d Perimeter = 4 × 46 cm = 184 cm

Exercise 6A1 A = 4 squares, B = 6 squares, C = 7 squares,

D = 8 squares, E = 10 squares, F = 5 squaresOrder: E, D, C, B, F, A

2 From largest to smallest area (estimates):

A = 3 squares, B = 5 squares, C = 4 squares,

D = 6 squares, E = 7 squares, F = 5 squares

Order: E, D, B, F, C, A

3 A = 14 cm2 B = 11 cm2 C = 12 cm2

Exercise 6B1 a 9 cm2 b 10 cm2 c 10 cm2 d 9 cm2

e 7 cm2 f 14 cm2 g 10 cm2

2 a 20 cm2 b 14 cm2 c 15 cm2 d 18 cm2

Learning task 6C1 a 10 cm2 b 10 cm2 c 8 cm2

d 9 cm2 e 12 cm2 f 9 cm2

Exercise 6D1 a i 8 cm2 ii Area = 4 cm × 2 cm = 8 cm2

b i 12 cm2 ii Area = 4 cm × 3 cm = 12 cm2

c i 24 cm2 ii Area = 6 cm × 4 cm = 24 cm2

d i 30 cm2 ii Area = 6 cm × 5 cm = 30 cm2

2 a Area = 4 cm × 4 cm = 16 cm2

b Area = 12 cm × 3 cm = 36 cm2

c Area = 22 cm × 32 cm = 704 cm2

d Area = 15 cm × 21 cm = 315 cm2

e b f a d c

34---

Chapter 6

12--- 1

2---

12---

38



3 a Area = 13 m × 18 m = 234 m2

b Area = 3 km × 3 km = 9 km2

c Area = 14 mm × 8 mm = 112 mm2

d Area = 32 km × 18 km = 576 km2

e Area = 39 cm × 51 cm = 1989 cm2

f Area = 5 km × 2 km = 10 km2

g Area = 34 mm × 87 mm = 2958 mm2

h Area = 25 km × 47 km = 1175 km2

i Area = 160 m × 83 m = 13 280 m2

4 a Area = (18 × 21) + (2 × 3) = 384 cm2

b Area = (8 × 3) + (3 × 2) + (2 × 3) = 36 m2

c Area = (25 × 11) + (10 × 12) + (7 × 5) = 430 km2

5 a 0·12 × 100 = 12 cmArea = 12 cm × 2 cm = 24 cm2

b 0·2 × 100 = 20 cmArea = 20 cm × 352 cm = 7040 cm2

c 0·9 × 100 = 90 cmArea = 90 cm × 61 cm = 5490 cm2

6 a Area = 32 mm × 56 mm = 1792 mm2

b Area = 1·2 km × km = 1·152 km2

c Area = (30 × 10) mm × 260 mm = 78 000 mm2

d Area = 45 mm × 45 mm = 2025 mm2

7 a Area = (20 m × 16 m) − (14 m × 12 m) = 152 m2

b Area = (17 m × 23 m) − (20 m × 13 m) = 131 m2

c Area = (48 m × 37 m) − (45 m × 33 m) = 291 m2

8 a Area = (205 cm × 201 cm) − (101 cm × 122 cm) = 28 883 cm2

b Area = (57 m × 40 m) − (19 m × 33 m) − (14 m × 35 m) = 1163 m2

c Area = (31 m × 27 m) − (17 m × 23 m) − (7 m × 20 m) = 306 m2

9 a Area = (1·2 m × 5 m) + (7 m × 4·5 m) + (3·8 m × 14 m) = 90·7 m2

The total area of the garden beds is 90·7 m2.

b Area = (14 m × 20 m) − (90·7 m2) = 189·3 m2

The total are of grass is 189·3 m2.

10 Area = (25 cm × 15 cm) − (19 cm × 9 cm) = 204 cm2

The area of the margin is 204 cm2.

11 a Area + 4 × 4 = 16 cm2

b Area = 64 × 16 cm2 =1024 cm2

c Area of white squares = 1024 ÷ 2 = 512 cm2

d Chess board has 8 squares on each side. 8 × 4 = 32 cm

Border is 2 cm wide ∴ Total width of squares plus border: 32 + 2 + 2 = 36 cm

Area of border = 36 × 36 − 32 × 32 = 272 cm2

Exercise 6E1 a Area = 14 cm × 18 cm = 252 cm2

b Area = 6 m × 7 m = 42 cm2

c Area = 9 cm × 10 cm = 90 cm2

d Area = 43 km × 50 km = 2150 km2

e Area = 17 m × 19 m = 323 m2

f Area = 72 mm × 89 mm = 6408 mm2

2 a 60 ÷ 10 = 6 cmArea = 6 × 4 = 24 cm2

b 300 ÷ 10 = 30 cmArea = 30 × 30 = 900 cm2

c 28 ÷ 10 = 2·8 cmArea = 2·8 × 4 = 11·2 cm2

d 1·2 × 100 = 120 cmArea = 120 × 130 = 15 600 cm2

e 2·3 × 100 = 230 cmArea = 230 × 400 = 92 000 cm2

f 0·8 × 100 = 80 cmArea = 80 × 120 = 9600 cm2

3 a (19 × 16) − (15 × 12) = 124 mm2

b (24 × 20) − (20 × 16) = 160 m2

c (38 × 79 × 2) + (132 × 79) = 16 432 mm2

d (13 × 11) − (5 × 8) = 103 cm2

e 2 × ( × 12 × 10) = 120 cm2

or (2 × 12 × 10) = 120 cm2

f Shaded area (27 × 159 – 21 × 124) + (18 × 98)= 3453 cm2

Activity 6F1 Area increases.

2 Area decreases.

3 Height remains constant.

4 Height and base of triangle remain constant.

5 a 5 cm2

b height = 2 cm, width = 5 cm

6 a 10·5 cm2

b 10·5 cm2

c 10·5 cm2

d 10·5 cm2

Exercise 6G1 a Area = 0·5 × 6 cm × 6 cm = 18 cm2

b Area = 0·5 × 14 cm × 12 cm = 84 cm2

c Area = 0·5 × 11 m × 8 m = 44 m2

d Area = 0·5 × 15 km × 12 km = 90 km2

e Area = 0·5 × 40 mm × 61 mm = 1220 mm2

f Area = 0·5 × 65 m × 86 m = 2795 m2

g Area = 0·5 × 68 mm × 62 mm = 2108 mm2

h Area = 0·5 × 7 km × 9 km = 31·5 km2

i Area = 0·5 × 13 m × 15 m = 97·5 m2

2 a Area = 0·5 × 29 m × 28 m = 406 m2

b Area = 0·5 × 49 mm × 52 mm = 1274 mm2

c Area = 0·5 × 5 m × 12 m = 30 m2

d Area = 0·5 × 18 cm × 15 cm = 135 cm2

e 58 ÷ 10 = 5·8 cmArea = 0·5 × 5·8 cm × 6 cm = 17·4 cm2

f 46 ÷ 10 = 4·6 cmArea = 0·5 × 4·6 cm × 5 cm = 11·5 cm2

3 a Large ▲ =

Now shaded ▲ =

Shaded area = = 150

Area = (0·5 × 40 × 14) − (0·5 × 10 × 26) = 150 mm2

b Area = (0·5 × 38 × 28) − (0·5 × 20 × 15) = 382 m2

9601000------------

12---

12---

12--- 40 14××

12--- 10 26××

12--- 40 14 1

2--- 10 26××–××



c Area = (0·5 × 21 × 14) − (0·5 × 18 × 10) = 57 m2

d Area = (0·5 × 32 × 45) − (0·5 × 18 × 20) = 540 km2

e Area = (12 × 14) − (0·5 × 9 × 14) = 105 mm2

f Area = (0·5 × 28 × 24) − (12 × 14) = 168 m2

4 a Area = 0·5 × 32 × 45 − 0·5 × 18 × 45 = 315 km2

b Area = 0·5 × 28 × 42 − 0·5 × 18 × 15 = 453 m2

c Area = 0·5 × 12 × 11 − 0·5 × 8 × 10 = 26 m2

d Area = 0·5 × 24 × 28 − 0·5 × 18 × 18 = 174 mm2

e Area = 0·5 × 12 × 14 − 0·5 × 9 × 12 = 30 mm2

f Area = 0·5 × 20 × 18 − 0·5 × 12 × 14 = 96 m2

5 a Area of each triangle: = 0·5 × 6 × 6 = 18 cm2

Red: 1 × 18 = 18 cm2

Blue: 2 × 18 = 36 cm2

Orange: 3 × 18 = 54 cm2

Purple: 4 × 18 = 72 cm2

Crimson: 5 × 18 = 90 cm2

Yellow: 6 × 18 = 108 cm2

Green: 7 × 18 = 126 cm2

White: 21 × 18 = 378 cm2

b Area of each triangle: = 0·5 × 12 × 27·7 = 166·2 cm2

White: 18 × 166·2 = 2991·6 cm2

Green: 31 × 166·2 = 5152·2 cm2

c Red: = 100 cm2

Orange: = 300 cm2

Yellow: = 600 cm2

Green: = 1000 cm2

Blue: = 1500 cm2

d Pink: = 675 cm2

Light Green: = 675 cm2

Dark Green: = 675 cm2

Purple: = 675 cm2

Red: = 675 cm2

Exercise 6H1 a 64 cubes = 64 cm3

b 64 cubes = 64 cm3

c 76 cubes = 76 cm3

d 128 cubes = 128 cm3

e 448 cubes = 448 cm3

f 112 cubes = 112 cm3

g 384 cubes = 384 cm3

2 a 20 cubes = 20 cm3 b 30 cubes = 30 cm3

c 30 cubes = 30 cm3 d 35 cubes = 35 cm3

Learning task 6I

1 d

e i The area of the base for a rectangular prism is equal to the length multiplied by the width.

ii Area of base = l × w

iii The volume of the prism is equal to the area of the base multiplied by the height of the prism.

iv Volume = area of base × height of prism or V = l × w × h

3 a Volume = area of the base × number of layers or V = l × w × h

b Yes this does work for a cube, however the length, width and height will be the same.

Exercise 6J1 a Volume = 16 × 8 = 128 cubes

b Volume = 8 × 8 = 64 cubes

c Volume = 16 × 4 = 64 cubes

2 a Volume = 12 cm × 8 cm × 20 cm = 1920 cm3

b Volume = 10 cm × 4 cm × 6 cm = 240 cm3

c Volume = 7 cm × 6 cm × 14 cm = 588 cm3

d Volume = 9 cm × 10 cm × 15 cm = 1350 cm3

e Volume = 10 cm × 6 cm × 10 cm = 600 cm3

f Volume = 10 cm × 10 cm × 21 cm = 2100 cm3

g Volume = 19 cm × 4 cm × 7 cm = 532 cm3

h Volume = 23 cm × 21 cm × 38 cm = 18 354 cm3

3 a Volume = (20 × 15 × 15) + (16 × 15 × 15) + (15 × 15 × 15) = 11 475 cm3

b Volume = (20 × 30 × 15 × 2) + (30 × 30 × 15) + (15 × 30 × 15) = 38 250 cm3

4 Some suggested answers, others are possible:

a 1 cm × 1 cm × 54 cm2 cm × 1 cm × 27 cm3 cm × 2 cm × 9 cm

b 1 cm × 1 cm × 36 cm2 cm × 1 cm × 18 cm3 cm × 2 cm × 6 cm

c 1 cm × 1 cm × 48 cm2 cm × 1 cm × 24 cm3 cm × 2 cm × 8 cm

d 1 cm × 1 cm × 144 cm2 cm × 1 cm × 72 cm3 cm × 2 cm × 24 cm

5 There is a range of answers—these are some suggested answers:

a 2 cm × 2 cm × 2 cm and2 cm × 2 cm × 4 cm

b 2 cm × 3 cm × 4 cm2 cm × 2 cm × 2 cm2 cm × 1 cm × 5 cm

12--- 10 20××

12--- 20 40 100–××

12--- 30 60 300–××

12--- 40 80 600–××

12--- 50 100 1000–××

12--- 15 90××

12--- 30 90 675–××

12--- 45 90 1350–××

12--- 60 90 2025–××

12--- 75 90 2700–××

Prism Units in

length

Units in

width

Units in base (area)

Units in

height

Volume of

prism

1 3 2 6 1 6

2 3 2 6 2 12

3 3 2 6 3 18

40



Exercise 6K1 a Volume = 54 cm2 × 11 cm = 594 cm3

b Volume = 49 cm2 × 32 cm = 1568 cm3

c Volume = 98 cm2 × 73 cm = 7154 cm3

d Volume = 123 cm2 × 40 cm = 4920 cm3

2 a Volume = 54 cm2 × 12 cm = 648 cm3

b Volume = 12 cm2 × 21 cm = 252 cm3

c Volume = 35 cm2 × 21 cm = 735 cm3

d Volume = 30 cm2 × 21 cm = 630 cm3

e Volume = 42 cm2 × 12 cm = 504 cm3

f Volume = 40 cm2 × 9 cm = 360 cm3

g Volume = 51 cm2 × 18 cm = 918 cm3

h Volume = 102 cm2 × 19 cm = 1938 cm3

3 a Base area = 0·5 × 7 cm × 10 cm = 35 cm2

Volume = 35 cm2 × 17 cm = 595 cm3

b Base area = 0·5 × 9 cm × 8 cm = 36 cm2

Volume = 36 cm2 × 12 cm = 432 cm3

c Base area = 0·5 × 6 cm × 7 cm = 21 cm2

Volume = 21 cm2 × 8 cm = 168 cm3

d Base area = 0·5 × 7 cm × 16 cm = 56 cm2

Volume = 56 cm2 × 18 cm = 1008 cm3

e Base area = 0.5 × 42 × 58 = 1218 m2

Volume = 1218 m2 × 46 m = 56028 m3

f Base area = 0.5 × 20 × 26 = 260 cm2

Volume = 260 cm2 × 22 cm = 5720 cm3

Puzzles1 A rubbish bin

2 Sari sarong number

3 They made a spectacle!

Enrichment1 a Area of bed = (4 × 10) + (8 × 2) = 56 m2

Area of bed + path = (6 × 10) + (10 × 4) = 100 m2

Area of path 100 − 56 = 44 m2

b Area of bed = (22 × 10) + (5 × 10) + (5 × 14) = 340 m2

Area of bed + path = (24 × 12) + (3 × 12) + (7 × 16) = 436 m2

Area of path 436 – 340 = 96 m2

c Area of bed = (40 × 14) + (4 × 24) + (42 × 20) = 1496 m2

Area of bed + path = (42 × 16) + (2 × 26) + (44 × 22) = 1692 m2

Area of path 1692 − 1496 = 196 m2

2 a Area = (48 cm × 26 cm) + (24 cm × 26 cm) + (48 cm × 32 cm) = 3408 cm2

b Area = (26 cm × 13 cm) × 2 = 676 cm2

3 a Area = 4000 m × 4000 m =

= 1600 hectares

b Area = 24 000 m × 8000 m =

= 19 200 hectares

c Area (5000 m × 5000 m) + (9000 m × 7000 m)

= = 8800 hectares

d Area: 3200 m × 5800 m = 18560000 m2

= = 1856 hectares

e Area: 0·5 × 6200 m × 12600 m

= 39060000 m2

= = 3906 hectares

4 a Area = (40 mm × 24 mm) − (0·5 × 18 mm × 24 mm) = 744 mm2

b Area = (0·5 × 38 m × 28 m) − (20 m × 15 m) = 232 m2

c Area = (0·5 × 21 m × 14 m) − (0·5 × 18 m × 10 m) = 57 m2

5 The area of one tile is 20 cm × 10 cm = 200 cm2

a Area of wall = 2·4 m × 6·2 m = 14·88 m2

= 148 800 cm2

= 744

744 tiles are needed.

b = 37·2

He should buy 38 boxes.

c 20 tiles in a box, 10% are cracked, therefore there are 18 good tiles in a box18 × 38 boxes = 684 tiles. Need 744Need an extra 60 tiles.

= 3·3333 extra boxes needed, so buy 4 extra

boxes or 42 boxes in total.

d 42 × 18 = 756. He will have a total of 756 good tiles756 − 744 = 12. He will have 12 tiles left over

e Area of wall = (480 × 420) − (90 × 240)

= 180 000 cm2

Area of a tile = 20 × 40 = 800 cm2

= 225 tiles needed to complete

the job.

6 a (9 m × 9 m) × 6 = 486 m2

b 12 cm × 34 cm × 4 + 12 cm × 12 cm × 2 = 1920 cm2

c (0·5 × 7 m × 24 m × 2) + (15 m × 24 m) + (15 m × 7 m) + (15 m × 25 m) = 1008 m2

7 a Dimensions at:

12 noonArea = 6 mm × 8 mm = 48 mm2

2 p.m.Area = 12 mm × 16 mm = 192 mm2

4 p.m.Area = 24 mm × 32 mm = 768 mm2

6 p.m.Area = 48 mm × 64 mm = 3072 mm2

8 p.m.Area = 96 mm × 128 mm = 12 288 mm2

10 p.m.Area = 192 mm × 256 mm = 49 152 mm2

12 midnightArea = 384 mm × 512 mm = 19 6608 mm2

16 000 000 m2

10 000 m2

----------------------------------

192 000 000 m2

10 000 m2

-------------------------------------

88 000 000 m2

10 000 m2

----------------------------------

1856000010000

-------------------------

3906000010000

-------------------------

148 800 cm2

200 cm2

------------------------------

74420

---------

6018------

180 000 cm2

800 cm2

------------------------------



b Area at each time interval as a percentage of the life form’s area at noon:

12 noon

Area = × 100 = 100%

2 pm

Area = × 100 = 400%

4 pm

Area = × 100 = 1600%

6 pm

Area = × 100 = 6400%

8 pm

Area = × 100 = 25 600%

10 pm

Area = × 100 = 102 400%

12 pm

Area = × 100 = 409 600%

Hence as the dimensions double the area increases by a factor of four.

c Dimensions at:

12 noonVolume = 2 cm × 3 cm × 4 cm = 24 cm3

2 pmVolume = 4 cm × 6 cm × 8 cm = 192 cm3

4 pmVolume = 8 cm × 12 cm × 16 cm = 1536 cm3

6 pmVolume = 16 cm × 24 cm × 32 cm = 12 288 cm3



12 midnightVolume = 128 cm × 192 cm × 256 cm = 6 291 456 cm3

d Area at each time interval as a percentage of the life form’s area at noon:

12 noon

Volume = × 100 = 100%

2 pm

Volume = × 100 = 800%

4 pm

Volume = × 100 = 6400%

6 pm

Volume = × 100 = 51 200%

8 pm

Volume = × 100 = 409 600%

10 pm

Volume = × 100 = 3 276 800%

12 pm

Volume = × 100 = 26 214 400%

Hence as the dimensions double the area increases by a factor of eight.

8 a 100 seconds

b

c 704 cm3 or 704 millilitres

Revision1 Shapes in order from largest to smallest

area (estimates):

A = 6 squares, B = 4 squares, C = 7 squares,

D = 4 squares, E = 4 squares, F = 4 squares

Order C, A, B, D, E and F

2 Estimated area of shapes using a grid:

a 24 squares b 54 squares

3 a i 32 squares

ii Area = 4 cm × 8 cm = 32 cm2

b i 60 squares

ii Area = 12 cm × 5 cm = 60 cm2

c i 64 squares

ii Area = 8 cm × 8 cm = 64 cm2

d i 52 squares

ii Area = 6 cm × 10 cm – 2 cm × 4 cm= 60 cm2 – 8 cm2

= 52 cm2

4 a Area = 7 cm × 4 cm = 28 cm2

b Area = 33 cm × 42 cm = 1386 cm2

c 1·8 × 100 = 180 cmArea = 180 × 220 = 39 600 cm2 or 3·96 m2

5 a Shaded area = (48 m × 37 m) − (32 m × 27 m) = 912 m2

b Shaded area = (0·5 × 42 × 70) = 1470 cm2

6 a Area = 32 m × 21 m = 672 m2

b Area = 23 cm × 12 cm = 276 cm2

c Area = 93 km × 81 km = 7533 km2

7 a Area = (56 × 60) − (36 × 42) = 1848 cm2

b Area = (11·6 × 5·3) × 2 = 122·96 cm2

c 58 cm × 80 cm – 42 cm × 58 cm= 4640 cm2 – 2436 cm2

= 2204 cm2

d 18cm × 24 cm – 18 cm × 18 cm= 432 cm2 – 324 cm2

= 108 cm2

4848------

19248

---------

76848

---------

307248

------------

12 28848

----------------

49 15248

----------------

196 60848

-------------------

2424------

19224

---------

153624

------------

12 28824

----------------

98 30424

----------------

786 43224

-------------------

6 291 45624

-----------------------

Time (s)

Height (cm)

Volume

10 1 12 × 8 × 1 = 96 cm3

20 2 12 × 8 × 2 = 192 cm3

30 3 12 × 8 × 3 = 288 cm3

40 4 12 × 8 × 4 = 384 cm3

50 5 12 × 8 × 5 = 480 cm3

60 6 12 × 8 × 6 = 576 cm3

70 7 4 × 8 × 1 = 32576 + 32 = 608 cm3

80 8 608 + 32 = 640 cm3

90 9 640 + 32 = 672 cm3

100 10 672 + 32 = 704 cm3

12---

42



8 a Area = 0·5 × 29 cm × 38 cm = 551 cm2

b Area = 0·5 × 32 m × 21 m = 336 m2

c Area = 0·5 × 16 km × 32 km = 256 km2

d Area = 0·5 × 12 cm × 6 cm = 36 cm2

9 a 28 cubes = 28 cm3

b 96 cubes = 96 cm3

10 Volume = 20 cubes (in base) × 4 (layers) = 80 cubes

11 a Volume = 12 cm × 6 cm × 5 cm = 360 cm3

b Volume = 12 cm × 9 cm × 21 cm = 2268 cm3

c Volume = 19 mm × 18 mm × 20 mm = 6840 mm3

12 a Volume = 68 cm2 × 15 cm = 1020 cm3

b Volume = 120 m2 × 42 m = 5040 m3

c Volume = 248 mm2 × 49 mm = 12 152 mm3

13 a Volume = (0·5 × 18 m × 21 m) × 25 m = 4725 m3

b Volume = (0·5 × 9 mm × 8 mm) × 11 mm = 396 mm3

Exercise 7A

1

2

3 6:00 am Lifelong Learning (30 min)6:30 am Tennis (3 hours)9:30 am Playschool (30 min)10:00 am For the Juniors (30 min)10:30 am Le Club (15 min)10:45 am Africa’s Child (45 min)11:30 am Discovering Science (30 min)12 noon World at Noon (30 min)12:30 pm Catalyst (30 min)1:00 pm Two Years in Galapagos (1 hour)

2:00 pm The Geisha (1 hour)3:00 pm Tweenies (30 min)3:30 pm Play School (30 min)4:00 pm Bananas in Pyjamas (15 min)4:15 pm Bob the Builder (10 min)4:25 pm Little Monsters (5 min)4:30 pm Arthur (25 min)4:55 pm Zoo Olympics (5 min)5:00 pm Rugrats

4

5

6 6:00 am Digswell Dig Show6:30 am Dennis the Menace7:00 am The Magic School Bus8:00 am Totally Wild8:30 am Where on Earth is Carmen Sandiego?9:00 am Video Hits11:30 am Geisha12 noon Bright Ideas2:00 pm Motorcycle Racing4:00 pm The Making of Rugrats in Paris5:00 pm News5:30 pm Sports Tonight6:00 pm Blockbuster Entertainment6:30 pm 7th Heaven7:30 pm MOVIE: Robin Hood: Men in Tights9:40 pm MOVIE: Powder Burn11:40 pm News

Exercise 7B

1 Appropriate units to measure in for the following times:

a To toast a piece of bread seconds

b For an oak tree to fully grow from an acorn years

c From sunrise to sunset hours

d To travel from Perth to Geraldton by car hours

e To travel from Perth to Melbourne by plane hours

f To play a netball game minutes

Chapter 7

1400 1554Camembert

cheese

French fries1700

1762Sandwiches

Potato chips1853

1861Jellybeans

Margarine1870

1890Peanutbutter

Vegemite1923

2000

Hot dogs1484

1890 1900 1910 1920 1930 1940 1950 1960

1891Netballadapted

1901Code

of rules

1924First National Assoc

1960International Federation

1963Word Netaball Champs

1926 England National Assoc

1927 Aust National Assoc

1850 1860 1870 1880 1890

1859Cape Schank

1859Wilson Promontory

1862GaboIsland

1880Cape

Nelson

1884Cape Otway

1890Point Hicks

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990

1908Canberra

selected tobe thecapital

1911NorthernTerritory

transferred to Commonwealth

1932SydneyHarbourBridgeopens

1930Phar Lap

winsMelbourne

Cup

1948Holden

carproduced

in Victoria

1956MelbourneOlympicGames 1961

Tram inSydneyclose

1973SydneyOperaHouseopens

1974CycloneTracey

hitsDarwin

1985Floodlights

installedat MCG

1982Commonwealth

GamesBrisbane



g Between seeing lightning and hearing the thunder seconds

h That you spend at school each day hours

2 a 9 centuries = 9 × 100 = 900 years

b 5 centuries = 5·5 × 100 = 550 years

c 50 years = = 5 decades

d 7 decades = 7·5 × 10 = 75 years

e 28 decades = 28 × 10 = 280 years

f 45 years = = 4·5 decades

g 350 years = = 3·5 centuries

h 75 years = = 7·5 decades

i 575 years = = 5·75 centuries

j 2·5 centuries = 2·5 × 10 = 25 decades

3 a 2 years = 2 × 365 = 730 days

b 5 years = 5 × 12 = 60 months

c 35 days = = 5 weeks

d 9 weeks = 9 × 7 = 63 days

e 108 months = = 9 years

f 5 weeks = 5 × 7 = 35 days

g 2 years = 2·25 × 12 = 27 months

h 7 years = 7·5 × 52 = 390 weeks

4 a 4 days = 4 × 24 = 96 hours

b 5 hours = 5 × 60 = 300 minutes

c 36 minutes = 36 × 60 = 2160 seconds

d 420 seconds = = 7 minutes

e 120 hours = = 5 days

f 180 minutes = = 3 hours

g 3 days = 3·5 × 24 = 84 hours

h 5 hours = 5·25 × 60 = 315 minutes

i 2 minutes = 2·75 × 60 = 165 seconds

j 200 minutes = = 3 hours

5 Bert’s time = 2·5 minutes

Guido’s time = = 2·33 minutes

Therefore Bert can balance the ball the longest.

6 Time with Helen = 19 daysTime with Ian = 3 × 7 = 21 daysThey spent the most time with Ian.

7 Best Bake time = 70 minutesAussie Cookbook time = 1·5 × 60 = 90 minutesBest Bake has the shortest cooking time.

8 Samantha = 2·5 years

Sean = = 2·42 years

Samantha has been collecting stamps for longer.

9 Chris’s time = 48 minutesMatthew’s time = 45 minutesMatthew had the quickest time.

10 Sam: 6 days = 6·5 × 24 × 60 = 9360 minutes

Suzie: 150 hours = 150 × 60 = 9000 minutesQuoc: 9240 minutes

a Sam’s experiment lasts the longest.

b Suzie’s experiment lasts the shortest.

Exercise 7C1 a 19 March to 1 April = 12 + 1 = 13 days

b 19 March to 25 April = 12 + 25 = 37 days

c 19 March to 30 June = 12 + 30 + 31 + 30= 103 days

d 19 March to 1 August = 12 +30 +31 + 30 + 31+ 1 = 135 days

e 19 March to 16 August = 12 + 30 + 31 + 30 + 31+ 16 = 150 days

f 19 March to 24 Dec = 12 + 30 + 31 + 30 + 31+ 31 + 30 +31 + 30 + 24 = 280 days

2 a 17 + 10 = 27 days

b 8 + 30 + 31 + 30 + 31 + 1 = 131 days

c 16 + 30 + 31 + 30 + 24 = 131 days

d 22 + 31 + 30 + 31 + 30 + 31 + 24 = 199 days

e 21 + 31 + 30 + 31 + 30 + 31 + 24 = 198 days

f 12 + 30 + 31 + 31 + 19 = 123 days

g 1 + 31 + 31 + 1 = 64 days

h 31 + 28 + 31 + 30 + 22 = 142 days

i 29 + 31 + 30 + 31 + 30 + 8 = 159 days

j 12 + 30 + 31 + 30 + 31 + 31 + 30 + 11 = 206 days

3 Number of years the following people lived:

a Aristarchus 310 − 250 = 60 years

b Aristotle 384 − 322 = 62 yearsPlato 428 − 347 = 81 years Socrates 470 − 399 = 71 years

c Eudoxus 408 − 355 = 53 yearsDecartes 1650 − 1596 = 54 yearsArchimedes 287 − 212 = 75 yearsFermat 1665 − 1601 = 64 yearsPascal 1662 − 1623 = 39 yearsNewton 1727 − 1642 = 85 yearsLeibnitz 1716 − 1646 = 70 yearsEuler 1783 − 1707 = 76 yearsLagrange 1813 − 1736 = 77 yearsGauss 1855 − 1777 = 78 years

4 a 18 + 30 + 31 + 11 = 90 days

b 18 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 25= 287 days

c 5 + 31 + 11 = 47 days

d 18 + 24 = 42 days

12---

5010------

12---

4510------

350100---------

7510------

575100---------

357

------

10812

---------

14---

12---

42060

---------

12024

---------

18060

---------

12---

14---

34---

20060

--------- 13---

14060

---------

2912------

12---

44



e 30 + 28 + 31 + 30 + 31 + 11 = 161 days

f 23 + 24 = 47 days

5 Term 1: 28 + 31 + 7 = 66 days

Term 2: 5 + 31 + 30 = 66 days

Term 3: 15 + 31 + 22 = 68 days

Term 4: 23 + 30 + 8 = 61 daysThe students were at school for 261 days.

6 a 17 b 38 c 2 d 17

e 1 f 3 g 18 h 11

i 68 j 40 k 4 l 31

7 a 14 b 23 c 4 d 14

Exercise 7D1 a 0420 hours = 4:20 am

b 0931 hours = 9:31 am

c 0832 hours = 8:32 am

d 1204 hours = 12:04 pm

e 1600 hours = 4:00 pm

f 1912 hours = 7:12 pm

g 2121 hours = 9:21 pm

h 2302 hours = 11:02 pm

i 23 minutes past 4 pm = 4:23 pm

j quarter past 6 am = 6:15 am

k 14 minutes past 11 am = 11:14 am

l 24 minutes to 11 pm = 10:36 pm

m 12 minutes to 4 am = 3:48 am

n 4 minutes to 8 pm = 7:56 pm

2 a 0510 hours b 0751 hours

c 0511 hours d 1313 hours

e 1720 hours f 1938 hours

g 2021 hours h 2352 hours

i 16 minutes past 5 am = 5:16 am = 0516 hours

j quarter past 7 am = 7:15 am = 0715 hours

k 17 minutes past 4 am = 4:17 am = 0417 hours

l 13 minutes to 10 pm = 9:47 pm = 2147 hours

m 8 minutes to 7 pm = 6:52 pm = 1852 hours

n 17 minutes to 11 pm = 10:43 pm = 2243 hours

3 a 4:15 am = a quarter past 4 am

b 7:30 pm = half past 7 pm

c 5:10 am = 10 min past 5 am

d 9:35 am = 25 min to 10 am

e 11:21 am = 21 min past 11 am

f 0900 hours = 9 am

g 0118 hours = 18 min past 1 am

h 1310 hours = 10 min past 1 pm

i 1525 hours = 25 min past 3 pm

j 1819 hours = 19 min past 6 pm

4

5 a 3:00 am, 0300 hours

b 7:15 am, 0715 hours

c 9:30 am, 0930 hours

d 6:20 am, 0620 hours

e 11:35 am, 1135 hours

6 a 5:00 pm, 1700 hours

b 6:30 pm, 1830 hours

c 1:15 pm, 1315 hours

d 9:20 pm, 2120 hours

e 2:55 pm, 1455 hours

7 6:15 am Return of the Nerds1 hour 27 minutes or 87 minutes

7:42 am The Bouncing Bees33 minutes

8:15 am Cooking with Gas56 minutes

9:11 am Home Shopping1 hour 21 minutes or 81 minutes

10:32 am The Nerds Fight Back29 minutes

11:01 am Battling Bullants59 minutes

12 noon The Bullsons49 minutes

12:49 pm Baffling Bullherds1 hour 26 minutes or 86 minutes

2:15 pm Carpet Madness55 minutes

3:10 pm Inky Darkness55 minutes

4:05 pm Tickling the Tonsils55 minutes

5:00 pm Yell and Scream1 hour 15 minutes or 75 minutes

6:15 pm The Nerds are Everywherelength of program can’t be determined

Exercise 7E1 a 7 am to 7:35 am: 35 minutes

b 7:35 am to 8:00 am: 25 minutes

c First departure: 7 amLast arrival: 8:35 pmTime between: 13 h 35 min

d Joylene could at the latest take the 12 noon ferry from Sorrento which would still give her ample time to meet her friend and go to lunch on time. To arrive home by 5 p.m. she needs to catch the 3 pm ferry from Queenscliff.

Clock face time Digital time 24-hour time

Half past 7 in the morning

7:30 am 0730 hours

Quarter past 2 in the morning

2:15 am 0215 hours

25 min past 2 in the afternoon

2:25 pm 1425 hours

10 min past 8 in the evening

8:10 pm 2010 hours

11 min past 9 in the evening

9:11 pm 2111 hours

16 min past 5 pm 5:16 pm 1716 hours

23 min to 11 in the morning

10:37 am 1037 hours

11 min past midnight

12:11 am 0011 hours

29 min past midday 12:29 pm 1329 hours

Clock face time Digital time 24-hour time



2 a i 4:35 pm ii 1:10 pm iii 2 pm iv 4:35 pm

b 3:29 pm

c Mon–Fri: 8 h 35 minSat: 8h 40 minSun: 8h 40 min

d 30 minutes

Exercise 7F1 a 3 pm − 30 min = 2:30 pm

b 3 pm − 2 h = 1:00 pm

c Canberra is in the same time zone as Melbourne: 3 pm

d 3 pm + 2 h = 5 pm

e Launceston is in the same time zone asMelbourne: 3 pm

f Brisbane is in the same time zone as Melbourne: 3 pm

2 a 6 pm − 2 hours = 4 pm

b 6 pm − 2 hours = 4 pm

c 6 pm − 2 hours = 3:30 pm

d 6 pm − 4 hours = 2 pm

e 6 pm − 2 hours = 4 pm

f 6 pm − 2 hours = 3:30 pm

3

4 2:17 pm + 45 minutes = 3:02 pmThe plane will touch down at 3:02 pm EST.

5 Left Adelaide at 0430 hours (4:30 am)Arrived Canberra 1749 hours (5:49 pm)Time difference = 13 hours 19 minutesSubtracting time gained across zone line (0·5 hours) gives a total journey time of 12 hours 49 minutes.

6 Left Auckland 3 p.m. (NZST)3 pm + flight time 5 hours 19 minutes = 8:19 pmSubtracting 4 hours to account for time zones crossed means the plane touched down at the local time of 4:19 pm (WST).

7 Depart Melbourne 1715 hours (5:15 pm) ESTArrive Auckland 2230 hours (10:30 pm) NZST

a Quoc Tran should arrive at Melbourne airport at 4:45 pm EST (5:15 pm − 30 min).

b Quoc Tran will leave Auckland airport at 11:15 pm NZST (10:30 pm + 45 min).

c Journey length from departure to arrival = 5 hours 15 minutesSubtracting time gained in crossing the time zone (2 hours) gives a total flight time of 3 hours 15 minutes.

8 a

b If it is 5 pm in Melbourne the following will be the times in:

i Perth (−3 hours) = 2 pm

ii Canberra (same) = 5 pm

iii Alice Springs (−1·5 hours) = 3:30 pm

iv Adelaide (−0·5 hours) = 4:30 pm

v Hobart (same) = 5 pm

c If it is 11 am in Adelaide, it will be the following times in:

i Perth (−2·5 hours) = 8:30 am

ii Sydney (+0·5 hours) = 11:30 am

iii Darwin (−1 hour) = 10 am

iv Brisbane (−0·5 hours) = 10:30 am

v Canberra (+0·5 hours) = 11:30 am

Exercise 7G1 a This flow chart examines whether the dog is

hungry on two separaate occasions.

b First if you don’t want to go to bed now, watch TV for 15 minutes. This loop continues until you go to bed. Sleep well and if the alarm clock rings, get up on time, have breakfast and go to school. If the alarm clock doesn’t ring, wake up late and rush to school without having breakfast.

2 a • Woken by alarm clock• Get out of bed• Get dressed• Go to the kitchen• Eat breakfast• Get ready for school• Go to school

b • Boil water in saucepan• Get egg from fridge• Put egg into boiling water• Take egg out of boiling water after 3 minutes• Put hot egg under cold water• Break shell and eat the egg

3

Time in Perth

Time in Adelaide

Time in Melbourne

Time in Auckland

4:00 am 5:30 am 6:00 am 8:00 am

4:00 pm 5:30 pm 6:00 pm 8:00 pm

5:15 am 6:45 am 7:15 am 9:15 am

8:00 am 9:30 am 10:00 am 12 noon

12 midnight

1:30 am 2:00 am 4:00 am

12---

12---

Queensland

Tasmania

NorthernTerritory

WesternAustralia

SouthAustralia

–0·5 h

–1 hour–1·5 h

–3 h New South WalesVictoria ACT

Start

Dividenumber by 2

Is there a remainder?

The numberis EVEN

The numberis ODD

YES

NO

Finish

46



4

5 d, a, c, b

7 a F, FL b 0, FR

c 1, FL d 1, R

e 2, FL f 0, R

g 2, FR h 1, FR

i 0, FL j 2, R

k F, FR l F, R

Exercise 7H1 Best units to express the mass of the following:

a an ant miligram

b a brick kilogram

c a car tonne

d a person kilogram

e a pencil gram

f a trailer load of sand tonne

g a feather milligram

h twenty big books kilogram

i an elephant tonne

j 3000 litres of petrol tonne

k a truck tonne

l a piece of paper gram

2 a 2 tonnes = 2 × 1000 = 2000 kg

b 3·6 t = 3·6 × 1000 = 3600 kg

c 1·02 t = 1·02 × 1000 = 1020 kg

d 3090 kg = = 3·09 t

e 540 kg = = 0·54 t

f 21 500 kg = = 21·5 t

3 a 5 kg = 5 × 1000 = 5000 g

b 6·08 kg = 6·08 × 1000 = 6080 g

c 10·02 kg = 10·02 × 1000 = 10 020 g

d 7 g = 7 × 1000 = 7000 mg

e 3254 g = 3254 × 1000 = 3 254 000 mg

f 990 g = 990 × 1000 = 990 000 mg

4 a 4000 mg = = 4 g

b 8·3 g = 8300 × 1000 = 8300 mg

c 1200 mg = = 1·2 g

d 620 mg = = 0·620 g

e 5·4 g = 5400 × 1000 = 5400 mg

f 310 mg = = 0·310 g

5 a 4300 g = = 4·3 kg

b 8720 g = = 8·72 kg

c 450 g = = 0·45 kg

d 2600 kg = = 2·6 t

e 340 kg = = 0·34 t

f 9900 kg = = 9·9 t

6 a The weights in grams:450 g1 kg (× 1000) = 1000 g672 gTotal weight in grams equals 2122 g

b The weights in kilograms:

= 0·45 kg

1 kg

= 0·672 kg

Total weight in kilograms equals 2·122 kg

7 Total amount of ice cream eaten = 0·435 kg+ 0·050 kg + 1·2 kg = 1·685 kg or 1685 g

a 3000 g − 1685 g = 1315 g

b 3 kg − 1·685 kg = 1·315 kgThere was 1·315 kg or 1315 g of ice cream left.

8 Egbert originally weighed 1323·4 kg.

a His total weight loss:1·2 + 0·45 + 1·02 + 0·7 + 2·04 = 5·41 kg = 54 kg

b Final weight:1323·4 − 5·41 = 1317·99 kg1317·99 × 1000 = 1317·990 g

9 Weight of box: 4·5 × 1000 = 4500 g

For 50 g packets: 200 × 50 + 4500 = 14 500 g = 14·5 kg

For 100 g packets:200 × 100 + 4500 = 24 500 g = 24·5 kg

For 200 g packets:200 × 200 + 4500 = 44 500 g = 44·5 kg

For 250 g packets:200 × 250 + 4500 = 54 500 g = 54·5 kg

10 Total number of worms:1200 + 1500 + 580 = 3280

Total weight:3280 × 12 = 39 360 g= 39·36 kg

Start

Is the sum of the digits divisible

by 3?

Number is divisible by 6

Number is notdivisible by 6

NO

YES

YES

Finish

NOIs the

number even?

30901000------------

5401000------------

21 5001000

----------------

40001000------------

12001000------------

6201000------------

3101000------------

43001000------------

87201000------------

4501000------------

26001000------------

3401000------------

99001000------------

450 g1000-------------

672 g1000-------------



Puzzles

1

2 Because it needed a hand.

3 You get a leap year.

Enrichment

1

2 a Days in:

i 5 years in a row= 365 × 3 + 366 + 365 = 1826 daysor starting with a leap year:366 + 3 × 365 + 366 = 1827 days

ii 6 years in a row= 365 × 3 + 366 + 365+ 365= 2191 daysor starting with a leap year:366 + 3 × 365 + 366 + 365= 2192 days

iii 7 years in a row = 365 × 3 + 366 + 365 × 3= 2556 daysor starting with a leap year:366 + 3 × 365 + 366 + 2 × 365= 2557 days

b

As 1896 is divisible by four it was a leap year.

c Paris 1900 Helsinki 1952St Louis 1904 Melbourne 1956London 1908 Rome 1960Stockholm 1912 Tokyo 1964No Games 1916 Mexico City 1968Antwerp 1920 Munich 1972Paris 1924 Montreal 1976Amsterdam 1928 Moscow 1980Los Angeles 1932 Los Angeles 1984Berlin 1936 Seoul 1988No Games 1940 Barcelona 1992No Games 1944 Atlanta 1996London 1948 Sydney 2000

3

4

4 3 2 0 3 7 5

0 3 3 7

5 7 6 5 4

2 8 8 5

1 3 5 4 6

6 1 9 5 8 4 0

0 2 0 0

0 1 0 0 8 0 0

Planet Rise Set Time above Earth’s horizon

Mercury 5:08 am 6:35 pm 13 h 27 min

Venus 8:59 am 7:38 pm 10 h 39 min

Mars 11:09 pm 1:48 pm 14 h 39 min

Jupiter 12:52 pm 10:44 pm 9 h 52 min

Saturn 12:05 pm 10:19 pm 10 h 14 min

Mercuryrise

5:08 am

Venusrise

8:59 am

Saturnrise

12:05 pm

Jupiterrise

12:52 pm

Marsset

1:48 pm

Mercuryset

6:35 pm

Venusset

7:38 pm

Saturnset

10:19 pm

Marsrise

11:09 pm

Jupiterset

10:44 pm

18964

------------ 474=

State or

Territory

Vic NSW Qld SA WA Tas ACT NT

Term 1 Jan 25 to Apr 7

Jan 28 to Apr 14

Jan 31 to Apr 20

Jan 31 to Apr 14

Feb 1 to

Apr 7

Feb 15 to Jun 2

Jan 28 to Apr 14

Jan 31 to Apr 7

Term 2 Apr 26 to

Jun 23

May 1 to

Jun 30

May 2 to

Jun 30

May 1 to

Jul 7

Apr 26 to

Jun 30

Jun 19 to

Sep 14

May 1 to

Jun 30

Apr 17 to

Jun 23

Term 3 Jul 10 to

Sept 15

Jul 17 to

Sept 8

Jul 18 to

Sept 15

Jul 24 to

Sept 15

Jul 17 to

Sept 22

Oct 2 to

Dec 20

Jul 17 to

Sept 8

Jul 24 to

Sept 29

Term 4 Oct 2 to

Dec 19

Oct 3 to

Dec 19

Oct 2 to

Dec 15

Oct 3 to

Dec 15

Oct 9 to

Dec 15

Oct 3 to

Dec 19

Oct 9 to

Dec 15

Number of school

days

73 + 59 + 68 + 79

= 279 days

77 + 61 + 54 + 78

= 270 days

80 + 60 + 60 + 75

= 275

days

74 + 68 + 54 + 74

= 270

days

66 + 66 + 68 + 68

= 268

days

108 + 88 + 80

= 276

days

77 + 61 + 54 + 78

= 270

days

67 + 68 + 68 + 68

= 271

days

Stop

Moonee Ponds 5:33 am

6:13 am

6:33 am

6:45 am

6:59 am

Maribyrnong Rd 5:34 6:14 6:34 6:46 7:00

Hotham St 5:37 6:17 6:37 6:49 7:03

Maribyrnong River

5:40 6:20 6:40 6:52 7:06

Highpoint 5:46 6:26 6:44 6:58 7:06

Monash St 5:51 6:31 6:49 7:03 7:12

Western Automatics

5:52 6:32 6:50 7:04 7:17

Geelong Rd 5:55 6:35 6:53 7:07 7:21

Footscray Station

5:57 6:37 6:55 7:09 7:23

Stop

48



5

6 1 dozen bottles in crate weigh12 × 800 g + 1200 g = 10 800 g or 10·8 kg

Milk bar4 dozen bottles: 4 × 10 800 g= 43 200 g = 43·2 kg

School canteen9 dozen bottles: 9 × 10 800 g= 97 200 g = 97·2 kg

Take-away shop9 bottles: 9 × 800 g= 7200 g = 7·2 kg

Total weight on truck20 dozen bottles: 20 × 10 800 g= 216 000 g = 216 kg

Load left on truck216 000 g − 43 200 g − 97 200 g − 7200 g= 68 400 g = 68·4 kg

7 a Volume = 20 × 30 × 10 = 6000 cm3

Weight: 6000 g = 6 kg

b Volume = 80 × 28 × 28 = 62 720 g = 62·72 kg

c Volume = 3·5 m × 2·8 m × 1 m = 9 800 000 g = 9800 kg

Revision1 1911: VFL players receive payment for the

first time

1926: Speedo bathers are launched

1930: Sir Donald Bradman scores 334 runs against England

1933: Australia plays England in the ‘bodyline series’

1940: Howard Florey discovers antibiotics

1946: The Hills Hoist (clothes line) is invented

1956: Olympic Games held in Melbourne

1974: Cyclone Tracy hits Darwin

1981: Australia’s population reaches 15 million

2000: Sydney hosts the Olympic Games

2 a 5 centuries = 5 × 100 = 500 years

b 54 years = 54 ÷ 10 = 5·4 decades

c 400 years = 400 ÷ 100 = 4 centuries

d 3 years = 3 × 12 = 36 months

e 3 weeks = 3 × 7 = 21 days

f 7 days = 7 × 24 = 168 hours

g 32 minutes = 32 × 60 = 1920 seconds

h 420 seconds = = 7 minutes

3 Number of days between (not including) the following dates:

a 13 May and 4 June = 18 + 3 = 21 days

b 1 August and 1 November= 30 + 30 + 31 = 91 days

c 13 December and 1 January = 18 days

d 19 March and 19 May = 12 + 30 + 18 = 60 days

4 Number of years between and including:

a 12 BC and 2 BC = 11 years

b AD 1300 and AD 2001 = 702 years

c 230 BC and AD 540 = 230 + 540 = 770 years

d 120 BC and AD 1 = 120 + 1 = 121 years

5 a 9:30 am b 12:30 pm c 4:00 pm

d 9:42 pm e 3:15 am f 4:20 am

6 a 5:15 am b 11:31 p.m.

c 0900 hours d 1730 hours

e 1720 hours

7 Time between the following times on the same day:

a 5 hours 17 min b 8 hours 3 min

c 2 hours 24 min d 4 hours 37 min

e 4 hours 8 min f 4 hours 4 min

8 a Jill can catch the 8:28 or the 9:28 bus.

b i 37 minutes ii 33 minutes

iii 25 minutes iv 37 minutes

9 a 4 pm b 4 pm c 2 pm

d 3:30 pm e 6 pm f 4 pm

10 a 5 tonnes = 5 × 1000 = 5000 kilograms

b 6·9 t = 6·9 × 1000 = 6900 kg

c 7·06 t = 7·06 × 1000 = 7060 kg

d 9 grams = 9 × 1000 = 9000 mg

e 3298 g = 3298 × 1000 = 3 298 000 mg

f 770 g = 770 × 1000 = 770 000 mg

g 4380 mg = 4380 ÷ 1000 = 4·380 g

h 1760 mg = 1760 ÷ 1000 = 1·760 grams

i 9400 mg = 9400 ÷ 1000 = 9·400 g

j 7620 kilograms = 7620 ÷ 1000 = 7·620 t

k 780 kg = 780 ÷ 1000 = 0·78 t

l 5800 kg = 5800 ÷ 1000 = 5·8 t

Exercise 8A1 a ∠O, ∠BOC or ∠COB

b ∠S, ∠MSK or ∠KSM

c ∠G, ∠MGF or ∠FGM

d ∠P, ∠KPL or ∠LPK

2 ∠ABC, ∠CBA, ∠BCD, ∠DCB, ∠CDE, ∠EDC, ∠DEF, ∠FED, ∠EFG, ∠GFE

Start

Scalene

Are the three sides different?

NO

YES

Stop

Isosceles

Are the three sides

equal?

YES

NO

Equilateral

42060

---------

12 111210

9 348

57 6

12 111210

9 348

57 6

12 111210

9 348

57 6

12 111210

9 348

57 6

12 111210

9 348

57 6

Chapter 8



a b c

d e f

g h i

j k l

m n o

p q r

s t u

v w x

Exercise 8B1 a Acute angle b Obtuse angle

c Reflex angle d Reflex angle

e Right angle f Obtuse angle

g Full circle h Straight angle

i Acute angle j Reflex angle

k Right angle l Reflex angle

m Straight angle n Reflex angle

o Right angle

2 a Internal: acute b Internal: rightExternal: reflex External: reflex

c Internal: obtuse and acuteExternal: reflex

d Internal: obtuse e Internal: obtuse

External: reflex External: reflex

3 a Acute angles: ∠DOI, ∠IOD, ∠IOH, ∠HOI, ∠FOG, ∠GOF, ∠FOE, ∠EOF

b Right angles: ∠DOH, ∠HOD, ∠HOG, ∠GOH, ∠GOE, ∠EOG, ∠DOE, ∠EOD

c Obtuse angles: ∠IOG, ∠GOI, ∠HOF, ∠FOH, ∠DOF, ∠FOD, ∠EOI, ∠IOE

d Straight angles: ∠DOG, ∠GOD, ∠IOF, ∠FOI, ∠HOE, ∠EOH

e ∠EOI, ∠IOG, ∠FOD, ∠FOH

f ∠EOH, ∠HOE, ∠DOG, ∠GOD, ∠FOI, ∠IOF

4 a Acute angle b Right angle

c Acute angle d Obtuse angle

e Acute angle f Acute angle

Exercise 8C1 a 14° b 28° c 37° d 48°

e 57° f 62° g 109° h 123°i 137° j 143° k 152° l 167°

2 a 0° and 90° b 270° and 360°c 270° and 360° d 0° and 90°

e 270° and 360° f 0° and 90°g 90° and 180° h 180° and 270°i 270° to 360° j 270° and 360°k 90° and 180° l 0° and 90°m 90° and 180° n 0° and 80°o 90° and 180°

3 a Z = 58° M = 50° b Z = 35° M = 25°c Z = 135° M = 130° d Z = 255° M = 220°

4 a 45° b 10° c 23° d 145°e 115° f 115° g 145° h 215°i 240° j 335° k 320° l 295°m 144° n 143° o 216°

5 a 28° b 104° c 48° d 40°e 72° f 42°

6 a 60° b 90° c 150° d 180°e 240° f 330°

7 a 12:00 b 3:00 c 6:00 d 12:00

e 1:00 f 4:00 g 7:00 h 9:00

Exercise 8D

1 a b

c d

e f

g h

2 a b

c d

e f

g h

3 4

Exercise 8E1 a 90° − 70° = 20° b 90° − 12° = 78°

a = 20° a = 78°

A

CB L

K

M Q

P

R

Y

H

T

s t

r x

M

A

K

V Y

W

D

B

F A

S

C

A M R

s m y

t a

B

A

C

M

L

N P

O

Q S

R

T

M35°

d42°

X

Y Z

55° F

75°

105°h

A

BC

158°

k167°

GYA

178°

185°

M

197°d

205°

YX

ZF

214°

h224°

A

B C239°

k275°A

Y

G

315°

60°

60° 60°

70°

40°

125°

125°

50



c 90° − 25° = 65° d 90° − 53° = 37°a = 65° a = 37°

e 90° − 35° = 55° f 90° − 47° = 43°a = 55° a = 43°

g 90° − 61° = 29° h 90° − 68° = 22°a = 29° a = 22°

i 90° − 52° = 38°a = 38°

2 a 90° − 17° − 36° = 37°a = 37°

b 90° − 10° − 35° = 45°a = 45º

c 90° − 34° − 25° = 31°a = 31°

d 90° − 50° − 5° = 35°a = 35°

e 90° − 25° − 20° = 45°a = 45°

f 90° − 17° − 17° = 56°a = 56º

3 a 90° = 3a b 90° = 6a a = 30° a = 15°

c 90° = a + a + 30 d 90° = a + a + 50°2a = 60° 2a = 40°a = 30° a = 20°

e 90° = a + 10 + a + 60° f 90° = 2a + 2a + 10°= 2a + 70° 80° = 4a2a = 20° a = 20°a = 10°

g 90° = 7a + 2a h 90° = 2a + 4a 90° = 9a 90° = 6aa = 10° a = 15°

4 c and e are complementary

5 a 90° − 15° = 75°complement of 15° is 75°

b 90° − 36° = 54°Complement of 36° is 54°

c 90° − 58° = 32°Complement of 58° is 32°

d 90° − 71° = 19°Complement of 71° is 19°

e 90° − 89° = 1°Complement of 89° is 1°

6 35° + 55° = 90°Yes, they are complementary.

7 90° − 75° = 15°∠AMN = 15°

8 Two angles are complementary if they add to 90°.

9 a 5:00 b 150°c 3 o’clock, 9 o’clock

Exercise 8F1 a 180° − 125° = 55° b 180° − 143° = 37°

a = 55° a = 37°c 180° − 135° = 45° d 180° − 124° = 56°

a = 45° a = 56°e 180° − 98° = 82° f 180° − 90° = 90°

a = 82° a = 90°2 a 180° − 36° − 125° = 19°

a = 19°b 180° − 40° − 35° = 105°

a = 105°

c 180° − 20° − 25° − 35° = 100°a = 100°

d 180° − 87° − 60° = 33°a = 33°

3 a 180° − 140° = 40°40° = 2aa = 20°

b 180° − 30° = 150°150° = 3aa = 50°

c 180° − 20° − 25° − 100° = 35°a = 35°

d 180° − 60° = 120°120° = 6aa = 20°

e 180° − 90° – 53° = 37°a = 37°

f 180° − 110° = 70°70° = 2aa = 35°

g 4a = 180°a = 45°

h 180° − 90° = 90°3a = 90°a = 30°

4 A, B and D are supplementary.

5 a 180° − 15° = 165°Supplement of 15° is 165°

b 180° − 56° = 124°Supplement of 56° is 124°

c 180° − 98° = 82°Supplement of 98° is 82°

d 180° − 111° = 69°Supplement of 111° is 69°

e 180° − 159° = 21°Supplement of 159° is 21°

6 165° + 15° = 180°Yes, they are supplementary.

7 180° − 75° = 105°∠LBC = 105°

8 If two angles add up to 180° they are supplementary.

9 If three angles add up to 180° they are supplementary.

10 a 120°, 60°b 120° + 60° = 180°

11 building trusses in the roof of a house

Exercise 8G1 a 360° − 288° = 72° b 360° − 272° = 88°

x = 72° x = 88°c 360° − 289° = 71° d 360° − 144° = 216°

x = 71° x = 216°e 360° − 251° = 109° f 360° − 92° = 268°

x = 109° x = 268°2 a 360° − 133° − 136° = 91°

a = 91°b 360° − 88° − 221° = 51°

a = 51°c 360° − 180° − 127° = 53°

a = 53°d 360° − 178° − 90° = 92°

a = 92°



e 360° − 109° − 68° − 71° = 112°a = 112°

f 360° − 118° − 62° − 46° = 134°a = 134°

3 a 360° = 6k b 360° = 9kk = 60° k = 40°

c 360° = 18k d 360° – 90° = 5kk = 20° k = 54º

e 360° − 120° − 90° = 150° f 3k = 360°3k = 150° k = 120ºk = 50°

4 360° − 165° − 15° = 180∠AQP = 180º

5 360° − 75° = 285°∠AMN = 285°

6 7

a° + b° = 360° a° + b° + c° = 360°

Technology activity 8H

1

a + b = 180°

Puzzles1 To spin a world wide web

2 A cockerpoodledoo 3 Kite

Applications

Pizza anglesa 75°, 105°, 75°, 105°b 360° c They are equal.

Angles on a compass45°, 90°, 135°, 180°, 225°, 270°, 315°, 360°

Angles in polygonsa i triangle ii 60° iii 60 + 60 + 60 = 180°

b i rectangle ii 90° iii 90 + 90 + 90 + 90 = 360°

c i square ii 90° iii 90 + 90 + 90 + 90 = 360°

d i octogon ii 135°

iii 135 + 135 + 135 + 135 + 135 + 135 + 135 + 135 = 1080°

Golf anglesThe larger the number on the club the higher the ball goes.

If you want distance choose a low club number.

If you want to hit the ball over an obstacle or out of a bunker choose a high club number.

Enrichment 1 a ∠AOB, ∠BOC, ∠COD, ∠DOE, ∠EOF (others

possible)

b ∠BOD

c ∠AOD, ∠BOE, ∠COF, ∠AOE, ∠BOF (others possible)

d ∠AOF

2 a 40°, 40°, 140°, 140°b 40°, 140° are supplementary angles

3 a 24 revolutions (one for each hour)

b 1440 revolutions (60 for each hour and 24 hours in a day)

c 86 400 revolutions (60 for each minute and 1440 minutes in a day)

4 i For example: train tracks, ruler sides, boxes

ii a b

c d

e

5 i a C = 50° b O = 50°c A = 70° and 110° d X = 70°

ii Corresponding angles are equal; vertically opposite angles are equal; co-interior angles add up to 180°; alternate angles are equal.

6 a 70° (O) b 105° (C) c 120° (A)d 52° (C) e 58° (X) f 118° (X)

7 a 53° b 127° c 53° d 53° e 127°

Revision1 ∠XYZ, ∠ZYX

2 no answer

3 a Acute angle b Obtuse angle

c Reflex angle d Obtuse angle

e Right angle f Acute angle

g Straight angle h Full circle or perigon

i Right angle

4 a 28° b 135° c 325°5 162°, 165°

6 a b

c d

e f

7 The angle sum of complementary angles is 90°.

8 a 90° − 69° = 21° b 90° − 56° = 34°a = 21° a = 34°

Angle a Angle b

120° 60°

30° 150°

45° 135°

10° 170°

170° 10°

90° 90°

a°

b°

a°

c°b°

25° A 137°

312°

W

UV

98°

123°

S

165°

52



c 90° − 6° = 84° d 90° = 3a + a = 4aa = 84° a = 22·5°

e 90° = 3a + 6a = 9a f 90° = 4a + 10° + 4aa = 10° 90° = 8a + 10°

a = 10°9 The angle sum of supplementary angles is 180°.

10 a 180° = h + 139° b 180° – 37° = 143°h = 41° h = 143°

c 180° − 46° = 134° d 180° – 94° = 86°h = 134° 2h = 86°

h = 43°e 180° = h + 2h + 48° f 90° = 2h + 4h = 6h

180° = 3h + 48° h = 15°132° = 3hh = 44°

11 One revolution is 360°.

12 a 360° − 68° − 68° = 224°p = 224º

b 360° − 180° − 147° = 33°m = 33º s = 180º

c 360° − 112° − 90° = 158°n = 158°

Exercise 9A

1

An isosceles triangle has two sides of equal length and two angles of equal magnitude.

2

An equilateral triangle has three sides of equal length and three angles of equal magnitude.

3

4 a Scalene b Isosceles c Isosceles

d Isosceles e Equilateral f Isosceles

g Scalene h Scalene i Equilateral

Exercise 9B

1

2 a Acute-angled triangle

b Right-angled triangle

c Acute-angled triangle

d Obtuse-angled triangle

e Obtuse-angled triangle

f Right-angled triangle

g Right-angled triangle

h Obtuse-angled triangle

3 a Right-angled scalene triangle

b Acute-angled scalene triangles

4 a Right-angle isosceles triangles

b Obtuse-angle isosceles triangles

c Acute-angle isosceles triangles

d Obtuse-angle isosceles triangles

Exercise 9C1 a 180° − 35° − 77° = 68°

x = 68°b 180° − 25° − 84° = 71°

x = 71°c 180° − 34° − 68° = 78°

m = 78º

d 180° − 90° − 40° = 50°x = 50°

e 180° − 126° − 28° = 26°t = 26º

f 180° − 32° − 32° = 116°h = 116°

g 180° − 46° − 76° = 58°f = 58°

h 180° − 65° − 32° = 83°g = 83°

i 180° − 57° − 63° = 60°k = 60°

j 180° − 90° − 38° = 52°f = 52°

k 180° − 93° − 47° = 40°b = 40º

l 180° − 83° − 83° = 14°t = 14°

m 180° − 82° − 25° = 73°p = 73°

n 180° − 132° − 36° = 12°m = 12°

Triangle ∠L ∠M ∠N

a 120° 30° 30°

b 50° 50° 80°

c 110° 35° 35°

d 15° 15° 150°

Triangle ∠L ∠M ∠N

a 60° 60° 60°

b 60° 60° 60°

c 60°° 60° 60°

d 60° 60° 60°

Triangle Length of side Type of triangleLM MN LN

a 15 mm 15 mm 22 mm isosceles

b 19 mm 13 mm 19 mm isosceles

c 9 mm 21 mm 21 mm isosceles

d 23 mm 17 mm 17 mm isosceles

e 40 mm 26 mm 20 mm scalene

f 23 mm 20 mm 40 mm scalene

Chapter 9

Triangle Magnitude or size of angle Type of triangleAngle L Angle M Angle L

a 45° 90° 45° right angled

b 40° 70° 70° acute angled

c 77° 77° 26° acute angled

d 47° 47° 86° acute angled

e 33° 24° 123° obtuse angled

f 20° 137° 23° obtuse angled



2 a 180° − 74° = 106° b 180° − 124° = 56°106° = 2x 56° = 2xx = 53° x = 28°

c 180° − 93° − 47° = 40° d 180° − 90° = 90°b = 40° 90° = 2x

x = 45°e 180° − 126° = 54° f 180° − 32° − 32° = 116°

54° = 6t 116° = 2ht = 9° h = 58°

g 180° − 90° = 90° h 180° = 3k90° = 5y k = 60°y = 18

i 180° − 90° = 90° j 180° − 34° = 146°90° = 5t 146° = 2mt = 18° m = 73°

k 180° = 3r l 180° − 88° = 92°r = 60° 92° = 4p

p = 23°m 180° − 90° = 90° n 180° − 80° = 100°

9y = 90° 5a = 100°y = 10° a = 20°

o 180° − 60° = 120°120° = 3xx = 40°

Exercise 9Da 35° + 57° = 92° b 25° + 84° = 109°

x = 92° x = 109°c 68° + 34° = 102° d 90° + 40° = 130°

m = 102° g = 130°e 126° + 28° = 154° f 32° + 32° = 64°

t = 154° h = 64°g 46° + 76° = 122° h 63° + 57° = 120°

f = 122° k = 120°i 47° + 93° = 140° j 90° + 38° = 128°

b = 140° f = 128°k c° = 101° + 42°

c = 143°

Technology activity 9E1 a 180°2 c 180°4 The sum of the angle in a triangle is always 180°.

5 It is opposite the obtuse angle.

6 It is opposite the smallest side.

7 If two angles are equal in size, the length of the sides opposite them are equal.

8 If all three angles in the triangle are the same, all three side lengths are the same.

Exercise 9F1 a Parallelogram b Kite c Trapezium

d Rectangle e Parallelogram f Rhombus

g Trapezium h Square i Trapezium

2 a Rectangle, right-angled triangle

b Rectangle, square, isosceles triangle

c Rectangle, square, parallelogram, triangle

d Trapezium, rectangle

e Rhombus, parallelogram, rectangle, triangle

f Rectangle, square, triangle, trapezium

g Rectangle, trapezium, square, isoscles triangle

h Rectangle, trapezium, square, isocles triangle

4 There are 204 squares on a checkers board:64 1 × 1, 49 2 × 2, 36 3 × 3, 25 4 × 4, 16 5 × 5, 9 6 × 6, 4 7 × 7, 1 8 × 8

Exercise 9G1 a Paralelogram b Diamond

2 a i r = s = t = u = 90°

ii r = u = 70° s = t = 110°

iii r = s = 65° t = u = 115°

iv r = s = t = u = 90°

v r = u = 120° s = t = 60°

vi r = 124° s = 92° t = 104° u = 40°

b

c The angle sum in a quadrilateral is 360°.

3 a 360° − 270° = 90°a = 90°

b 360° − 90° − 90° − 30° = 150°b = 150°

c 360° − 110° − 70° − 110° = 70°c = 70°

d 360° − 65° − 115° − 65° = 115°d = 115°

e 360° − 118° − 118° − 62° = 62°e = 62°

f 360° − 270° = 90°f = 90°

g 360° – 120° – 120° – 60°= 60°a = 60°

h 90° = 9g°g = 10°

i 360° – 130° – 90° – 90°= 50°b = 50°

4 a 360° − 35° − 47° − 134° = 144°n = 144°

b 360° − 35° − 96° − 98° = 131°m = 131°

c 360° − 103° − 36° − 129° = 92°r = 92°

d 360° − 154° − 46° − 56° = 104°f = 104°

e 360° − 47° − 88° − 92° = 133°g = 133°

f 360° − 85° − 87° − 63° = 125°h = 125°

g 360° – 105° – 125° – 78° = 52°j = 52°

h 360° − 88° − 156° − 79° = 37°k = 37°

Shape ∠r ∠s ∠t ∠u Angle sum

a 90 90 90 90 360°

b 70 110 110 70 360°

c 65 65 115 115 360°

d 90 90 90 90 360°

e 120 60 60 120 360°

f 120 95 103 42 360°

54



i 360° − 100° − 40° − 100° = 120°x = 120°

j 360° − 95° − 90° − 102° = 73°m = 73°

k 360° − 63° − 63° = 234°2x = 234°x = 117°

l 360° − 120° − 120° = 120°2y = 120°y = 60°

m a = 60°360° − 60° − 60° = 240°2b = 240°b = 120°

n c = 110°360° − 110° − 110 − 90° = d°d = 50°

o 360° − 155° = f °f = 205°e = 37°

5 a 360° − 90° = 270° b 360° = 8a5a = 270° a = 45°a = 54°

c 360° = 9a d 360° − 180° = 180°a = 40° 180° = 3a

a = 60°

e 360° = 10a f 360° = 6aa = 36° a = 60°

Exercise 9H1 a Triangle b Quadrilateral

c Pentagon d Octagon

e Rectangle f Octagon

2 a Triangle b Square

c Pentagon d Hexagon

e Heptagon f Octagon

g Nonagon h Decagon

3

Exercise 9I1 Angle sums are:

a Square 360° b Hexagon 720°c Pentagon 540° d Octagon 1080°e Heptagon 900° f Octagon 1080°g 11-agon 1620° h 13-agon 1980°

2 a 2340° b 2700° c 3780° d 5940°e 7200° f 8640° g 12960° h 26 640°

i 5580° j 1980° k 8820° l 1620°m 3240° n 5760° o 2700° p 9000°q 10620° r 12780° s 7380° t 8460°

3 a 360° − 60° − 64° − 124° = 112°m = 112°

b 720° − 115° − 105° − 135° − 123° − 116° = 126°t = 126°

c 540° − 92° − 97° − 115° − 113° = 123°r = 123°

d 1080° − 136° − 133° − 135° − 144° − 124° − 137° − 128° = 143°s = 143°

e 720° − 135° − 153° − 80° − 117° − 141° = 94°y = 94°

f 540° − 115° − 91° − 150° − 62° = 122°k = 122°

4 a 360° − 71° − 130° − 52° = 107°j = 107°

b 360° − 113° − 75° − 63° = 109°k = 109°

c 540° − 97° − 113° − 92° = 238°238° = 2rr = 119°

d 1080° − 119° − 135° − 129° − 119° − 125° = 453°453° = 3ss = 151°

e 720° = 6hh = 120°

f 540° − 76° − 136° − 132° = 196°196° = 2gg = 98°

Puzzles1 You are too tense

2 The referee called a foul

3 Protractor, compass

Enrichment 1 a (n − 2) × 180° = 540°

n − 2 = 3n = 5

b (n − 2) × 180° = 720°n − 2 = 4n = 6

c (n − 2) × 180° = 1080°n − 2 = 6n = 8

d (n − 2) × 180° = 10 800°n − 2 = 60n = 62

2 For cylinder:

a circle b ellipse

c rectangle d rectangle is a polygon

For cube:

a square b rectangle

c square d rectangle and squareare polygons

Poly

gon Name No of

sidesNo of angles

Size of int angle

Angle sum

a Equilateral triangle

3 3 60° 180°

b Square 4 4 90° 360°

c Pentagon 5 5 108° 540°

d Hexagon 6 6 120° 720°

e Heptagon 7 7 128·57° 900°

f Octagon 8 8 135° 1080°

g Nonagon 9 9 140° 1260°

h Decagon 10 10 144° 1440°



3

d Cut C in triangular based pyramid is a polygon.

4 For cone: For square based pyramid:

Size decreases as cuts made further up the pyramid but all cross–sections are the same.

5

In an n-sided polygon, there are diagonals.

6 a 5(5 − 3) ÷ 2 = 5

b 8(8 − 3) ÷ 2 = 20

c 12(12 − 3) ÷ 2 = 54

d 18(18 − 3) ÷ 2 = 135

e 200(200 − 3) ÷ 2 = 19700

7 a 14(14 − 3) ÷ 2 = 77

b 25(25 − 3) ÷ 2 = 275

c 40(40 − 3) ÷ 2 = 740

Revision1 a Right-angled triangle, scalene triangle

b Acute-angled triangle, equilateral triangle

c Acute-angled triangle, isosceles triangle

d Obtuse-angled triangle, scalene triangle

e Acute-angled triangle, equalateral triangle

f Right-angled triangle, isosceles triangle

g Acute-angled triangle, isosceles triangle

h Obtuse-angled triangle, scalene triangle

2 a 180° − 136° − 22° = 22°t = 48°

b 180° − 36° − 52° = 92°h = 92°

c 180° − 89° − 43° = 48°y = 48°

d 180° − 90° − 56° = 34°y = 34°

e 180° = 57° + 63° + kk = 60°

f 180° = a + a + a = 3aa = 60°

3 a 52° + 65° = 117° b 42° + 80° = 122°x = 117° x = 122°

c 45° + 62° = 107° d 28° + 125° = 153°x = 107° x = 153°

e 45° + 90° = 135° f 58° + 64° = 122°x = 135° x = 122°or or180° − 45° = 135° 180° − 58° = 135°x = 135° x = 122°

4 a Kite b Rhombus

c Trapezium d Parallelogram

e Rectangle f Square

g Trapezium h Kite

5 a 360° − 45° − 57° − 124° = 134°n = 134°

b 360° − 113° − 36° − 98° = 113°y = 113°

c 360° − 124° − 128° − 60° = 48°z = 48°

d 360° − 123° − 46° − 43° = 148°t = 148°

e 360° – 143° – 59° – 42° = 116°w = 116°

f 360° – 168° – 44° – 43° = 105°m = 105°

6 a Equilateral triangle b Regular hexagon

c Regular pentagon d Octagon

e Square f Isosceles triangle

7 a 360° − 89° − 107° − 84° = 80°p = 80°

b 720° − 115° − 107° − 123° − 140° − 85° = 150°p = 150°

c 540° − 113° − 95° − 125° − 92° = 115°w = 115°

d 1080° − 134° − 151° − 134° − 118° − 166° − 114° − 145° = 118°h = 118°

Exercise 10A1 a 2 across, 2 up b 4 across, 2 up

c 3 across, 4 up d 6 across, 0 up

e 1 across, 4 up f 0 across, 2 up

Name of polygon

Number of diagonals

Rule

Triangle 0

Square 2

Pentagon 5

Hexagon 9

Heptagon 14

Octagon 20

Nonagon 27

Decagon 35

A

A

B

B

C

C

45°

A

BC

A

B

C

45°

A B C A B C

3 3 3–( )2

-------------------- 0=

4 4 3–( )2

-------------------- 2=

5 5 3–( )2

-------------------- 5=

6 6 3–( )2

-------------------- 9=

7 7 3–( )2

-------------------- 14=

8 8 3–( )2

-------------------- 20=

9 9 3–( )2

-------------------- 27=

10 10 3–( )2

-------------------------- 35=

n n 3–( )2

--------------------

Chapter 10

56



2 a 5 across, 2 up b 2 across, 6 up











6 a 3 across, 1 down b 4 across, 1 down

c 5 across, 2 down d 4 across, 1 down

7

Exercise 10B

1 2

3 a C b B c H d A

e E f G g D h F

i K j I k L l J

4

Rectangle

5

Arrow

6

Star

7 START (1, 2), (11, 2), (11, 8), (8, 11), (8, 13), (7, 13), (7, 12), (6, 13), (1, 8), (1, 2) STOP

START (3, 9), (5, 9), (5, 7), (3, 7), (3, 9) STOP

START (7, 9), (9, 9), (9, 7), (7, 7), (7, 9) STOP

START (4, 2), (4, 5), (8, 5), (8, 2) STOP

8 Bridge (200, 500) Camp (0, 0)Toilet (100, 0) Dam (600, 100)Cave (500, 400) Lookout (400, 500)Obstacle course (300, 300)

9 a (4, 6) 10 a (6, 7)

b (1, 5) b (4, 1)

c (3, 4) c (2, 8)

d (4, 3) d (4, 5)

e (6, 3) e (3, 2)

f (2, 3) f (7, 3)

g (5, 1) g (6, 4)

h (2, 1) h (8, 6)

11 a b HI

12 a

6

5

4

3

2

1

10 2 3 4 5 6

Ant

Sun

Flower

Dog Moon

Bone

Up

Across

6

5

4

3

2

1

10 2 3 4 5 6

y

x

H(0, 4)

I(3, 5) C(4, 5)

F(5, 3)

B(4, 2)

E(4, 1)

G(5, 0)

A(1,2)

D(2, 3)

Up

Across

6

5

4

3

2

1

10 2 3 4 5 6

C(1, 5) D(2, 5)

E(4, 4)

G(6, 2)

F(5, 1)

H(3, 0)

B(3, 2)

I(0, 6)

6

5

4

3

2

1

10 2 3 4 5 6

y

x

A(0, 4)

H(0, 0)G(2, 0) F(4, 0) E(6, 0)

B(2, 4) C(4, 4)

D(6, 4)

6

5

4

3

2

1

10 2 3 4 5 6

y

x

C(3, 6)

D(3, 4) E(6, 4)

F(6, 2)

G(3, 2)

H(3, 0)

A(0, 3)

B(1, 4)

6

5

4

3

2

1

10 2 3 4 5 6

y

x

C(3, 6)

D(4, 4)

E(6, 3)

F(4, 2)

G(3, 0)

H(2, 2)

A(0,3)

B(2, 4)

6

7

8

9

10

5

4

3

2

1

1 2 3 4 5 6 7

y

x

B(5, 10)

A(1, 7)

G(1, 6)

D(4, 5)

F(5, 3)

E(3, 2)

C(2, 1) H(7, 2)



b

13 Check with your partner.

14 Check with your partner.

Exercise 10D1 a 1:500 b 1:250

c 1:200 d 1:300

e 1:1000 f 1:400 000 000

g 1:27 500 h 1:100 000 000

2 a 10 cm b 50 cm c 2·5 m d 1 m

e 1·5 m f 5 m g 250 m h 1 km

3 1 cm represents 10 km110 km = 11 × 10 kmDistance on map will be 11 cm

4 a i 1mm = = 45 km

ii 1 cm = = 450 km

iii 10 cm = = 4500 km

iv 26·5 cm = = 11 925 km

b i 90 km = = 2 mm

ii 900 km = = 20 mm = 2 cm

iii 2700 km = = 6 cm

iv 4050 km = = 9 cm

c i 1 cm: 450 km ii 6·9 cm: 3105 km

iii 8 cm: 3600 km iv 2·6 cm: 1170 km

d = 82 cm

e = 38 cm2

f i 34 cm2 (90%) ii 8 cm2 (20%)

5 Check with your teacher.

Exercise 10E

1

2 A 022°, N22°E B 060°, N60°E

C 135°, S45°E D 215°, S45°W

E 250°, S70°W F 280°, N80°W

G 330°, N30°W

3 Answers are given as true bearings:

a b

c d

e f

g h

4 Due north is 000°, due south is 180°, due west is 270° and due east is 090°.

5 a i 700 m ii 700 m

b i 90 m × 110 m ii 40 m × 90 m

c i 063° ii 165° iii 357°

Puzzles1 Frostbite 2 Snake pit

45 000 000 mm1000 1000×

------------------------------------

45 000 000 cm100 1000×

----------------------------------

45 000 000 10 cm×100 1000×

------------------------------------------------

26·5 45 000 000 cm×100 100×

---------------------------------------------------

90 1000 1000××45 000 000

------------------------------------------

900 1000 1000××45 000 000

---------------------------------------------

2700 1000 100××45 000 000

---------------------------------------------

4050 1000 100××45 000 000

---------------------------------------------

36 735 1000 100××45 000 000

-------------------------------------------------

7 686 850 1000 100×( )2×45 000 000( )2

----------------------------------------------------------------

Angle, as shown, from

boy to girl

True bearing

Compass bearing

a 40° 040° N40°E

b 70° 070° N70°E

c 110° 110° S70°E

d 140° 140° S40°E

e 160° 160° S20°E

f 180° 180° S

g 200° 200° S20°W

h 305° 305° N55°W

i 90° 090° E or N90°E

j 235° 235° S55°W

k 270° 270° W or S90°W

l 306° 306° N54°W

N

E

25°

025°

N

E

15°

S15°W

N

E

35°

N35°E

N

E166°

166°

N

E

78°

S78°E

N

E235°

235°

N

E85°

N85°W

N

E315°

315°

58



Applications

Orienteering

1 a

b Scale 6 mm:100 m i 500 m ii 800 m iii 900 m

c 600 m

Enrichment and Extension

1 a

b 045°c i 045° ii 022° iii 117°

2 a

b 285°c i 308° ii 135° iii 243°

Revision Questions1 a 3 across and 1 up b 3 across and 5 up

c 4 across and 2 up d 5 across and 1 up

e 2 across and 4 up f 0 across and 5 up

2

3 a (5, 0) b (2, 1) c (0, 3)

d (3, 4) e (2, 5) f (6, 1)

4 a (9, 11) b (12, 11) c (9, 3)

d (2, 3) e (11, 8) f (4, 1)

g (8, 6) h (2, 6) i (3, 8)

5 a 1:500 b 1:500 000

c 1:250 d 1:400 000

6 a 10 m b 5 m c 80 cm d 100 m

7 a b

c d

e f

g h

8 a 1 cm = 25 m or 1:2500

b It is about 50 m × 75 m.

c It is about 40 m × 45 m.

Exercise 11A1 a + 4 b − 3

c ÷ 4 = d 5

e or ÷ 5 f 5 ÷

g h 5 − 3

i 3 + 2 j − 4 + 3

2 a 5n + 4 b − 2 c 3y + 6

d + 30 e f

g h i

3 a l + l + l + l + l = 4l

b a + a + a = 3a

c x + a + x + b = 2x + a + b

4 a + is the number of students

b + 3 is the number of boys

c − 2 is the number of girls

d ( + 3) + ( − 2) = + + 1

is the total number of students

600

700

800

500

400

300

200

100

1000 200 300 400 500 600 700

y

x

Lookout

Cave

Dam

Toilet block

Obstacle course

Bridge

y

x–5–6 –4 –3 –2 –1 1 2 3 4 5 6

–6

–5

–4

–3

–1

1

2

–2

3

4

5

6F(2, 6)

D(4, 5)

B(3, 4)

E(0, 1)

A(1, 2)

C(2, 3) G(4, 2)

H(6, 1)

y

x–5–6 –4 –3 –2 –1 1 2 3 4 5 6

–6

–5

–4

–3

–1

1

2

–2

3

4

5

6

A(2, 4)

B(–2, 5)

D(–6, 4)

G(–4, 2)

H(–6, 1)

E(0, –1)

F(2, –3)

C(4, –4)

6

5

4

3

2

1

10 2 3 4 5 6

y

x

I(0, 6)

C(1, 5)

D(2, 5) E(4, 4)

G(6, 2)B(3, 2)

H(3, 0)

F(5, 1)

N

75°

075°

E

N

205°

205°

E

N

345°

345°E

N

126°

126°

E

N

71°

S71°E

E

N

35°

S35°W

E

N

63°

N63°W

EW

N

39°

N39°E

E

Chapter 11

14---

•

•

• ••

•••

•••

•

15---

•

•

• ••

•••

•••

•

x3---

p2--- q 2+

y------------ x 3+

4------------

4y 10– 3x5

------ x2 7+



5 a 5d b c

d 2d + p e d + 2p

6 a 2d + f b 10d + f

c nd + f d

7 a 4x + 3y b 3x + 4y c mx + ny

8 a f + r + s b 2f

c r − 3 d

9 a Current number of dives = n – m

b Number of dives p ago = n − m − p

Exercise 11B1 a 3 bobcats + 2 gorillas + 4 zebras

b 5 apples + 2 bananas + 2 cherries + orange

c eraser + 5 pens + 4 pencils + scissors

d 6 cars + caravan + 2 scooters + 3 trucks

2 a 3 and 10 , 4 and 10 , 2 and 3 ,

5 and 6

3 8f and 2f, 10ab and 3ba8kz and 5kz, 3pq and 12qp9jg and 2gj, 6b and b

4 a + + + = 4

b + = 2

c 2 + 3 − 2 = 3

d 4 + 4 − 2 + = 7

e 10 + 10 + 10 = 20 + 10

f 3 + 4 + 2 = 5 + 4

g 4▲ + 3▲ − ▲ + ■ = 6▲ + ■

h 6■ + 4● − 2■ = 4■ + 4●

i 3♥ + ♥ + ▲ + 2▲ = 4♥ + 3▲

j 5 + 6 − ● + = 12 − ●

k 4■ − ▲ + 4▲ = 4■ + 3▲

l 6♥ − 3♥ + 2● = 3♥ + 2●

m 2 + 5 + 3▲ + 2▲= 7 + 5▲

n 5■ − 2■ + 3▲ − 2■ = 3■ + ▲

5 a m + m + m = 3m b x + x + x + x = 4x

c x + x + x + y + y = 3x + 2y

d a + b + a + a + b + a = 4a + 2b

e 10x + 5x = 15x f 5a + 2a = 7a

g 12x − 7x = 5x h 15y − 8y = 7y

i 27t + 18t = 45t j 25p − 17p = 8p

k 9x − 8x = x l 8y − 8y = 0

6 a 2xy + 6xy = 8xy b 7xy + 9yx = 16xy

c 12ab − 5ab = 7ab d 18ab − 6ba = 12ab

e 5pq + 8pq + 9pq = 22pq

f 7pq + 2pq + 4qp = 13pq

g 18mn + 16mn − 28mn = 6mn

h 15mn + 17nm − 5nm = 27mn

i 23xy − 15xy − 6xy = 2xy

j 28xy − 16xy − 9xy = 3xy

k 13wx − 12wx = wx

l 6rs + 2rs − 8rs = 0

7 a 4x + 5x + y = 9x + y

b 5m − 2m + 3n = 3n + 3m

c 6xy + 2xy + zy = 8xy + zy

d 6pq − 3q + 2np = 8pq − 3q

e 2x + 3y + 4x + 5y = 6x + 8y

f 3x + 2 + 4x + 5 = 7x + 7

g a + 5 + 2a – 2 = 3a + 3

h 4 + 3x − 2 − x = 2x + 2

i 6x + 3y + 2 + 4x + 5y + 1 = 10x + 8y + 3

j 8x + 2y − 3 − 6x + y + 7 = 2x + 3y + 4

8 a 2a + 3b − c − a + b + 2c + 3a − b + c = 4a + 3b + 2c

b 6ab + 3bc − ca − 2ab + 4bc − ab + ca = 3ab + 7bc

c 7xy + 5yz − 2zy + 3zx + 4xy − 3yz + 6zx = 11xy + 9zx

9

10

Exercise 11C

1 a 2 × G = 2G b 5 × G = 5G

c G ÷ 2 = or G d G ÷ 3 = or G

e G ÷ 6 or or G f 2G – 4

g 3G + 5

2 a 4 × y = 4y b 5 × y = 5y

c a × 10 = 10a d b × 6 = 6b

e a × b = ab f m × n = mn

g 12 × z × y = 12yz h m × n × 9 = 9mn

i a × b × c = abc j y × 6 × 5 = 30y

k y × 8 × 6 = 48y l 4 × 7 × p = 28p

m 3 × a × 7 × b = 21ab n 3 × z × 8 × y = 24yz

o a × b × b = ab2 p 8 × z × 9 × z = 72z2

q 4 × y2 × z × 9 = 36y2z r 3 × m × n × m = 3m2n

3 a 5 × 2x = 10x b 6 × 8y = 48y

c 3a × 7 = 21a d y × 5x = 5xy

e m2 × 6n = 6m2n f 7c × 5b = 35bc

g 5z × 6y = 30yz h 7p × 9q = 63pq

i 6z × 6x = 36z2 j 4y × 5y = 20y2

k 2a × 4b × 7 = 56ab l 6m × 2n × 9p = 108mnp

m 3p × 5q × 2r = 30pqr n 3a × 6b × 7c = 126abc

o 4y × 3z × 5y = 60y2z

4 a x ÷ 3 = b m ÷ 6 =

c p ÷ 10 = d 5 ÷ x =

d2--- 3d

2------

nd f+4

----------------

s2---

★ ★ ★ ★

★ ★ ★

★ ★ ★

+ 3 5y 2x 5xy

2 5 5y + 2 2x + 2 5xy + 2

3y 3y + 3 8y 2x + 3y 5xy + 3y

4x 4x + 3 4x + 5y 6x 5xy + 4x

2xy 2xy + 3 2xy + 5y 2xy + 2x 7xy

− 6 8a 10b 7ab

4 2 8a − 4 10b − 4 7ab − 4

3a 6 − 3a 5a 10b − 3a 7ab − 3a

5b 6 − 5b 8a − 5b 5b 7ab − 5b

2ab 6 − 2ab 8a − 2ab 10b − 2ab 5ab

G2---- 1

2--- G

3---- 1

3---

G6---- 1

6---

x3--- m

6----

p10------ 5

x---

60



e 7 ÷ 2x = f 3x ÷ 5y =

5 a b c

d e f

g h i

j k l

m n o

6

7

Exercise 11D1 a 4 × (7 + 3) b 4 × 7 + 4 × 3

= 4 × 10 = 28 + 12= 40 = 40

c 8 × (12 − 4) d 8 × 12 − 8 × 4= 8 × 8 = 96 − 32= 64 = 64

2 a 3(x + y) b 7(a + b)= 3x + 3y = 7a + 7b

c 7(m + n) d 9(x + 4)= 7m + 7n = 9x + 36

e 6(y + 7) f 10(p + 8)= 6y + 42 = 10p + 80

g (a + 4)8 h (c + 5)9= 8a + 32 = 9c + 45

i (b + 9)5 j (6 + p)6= 5b + 45 = 36 + 6p

k (12 + q)7 l (5 + n)8= 84 + 7q = 40 + 8n

m 3x + 15 n 7a + 7b

o 10m + 10n p 7r + 7s

3 a 5(x − y) b 7(a − b)= 5x − 5y = 7a − 7b

c 9(m − n) d 8(x − 7)= 9m − 9n = 8x − 56

e 3(x − 9) f 9(x − 12)= 3x − 27 = 9x − 108

g 2(13 − m) h 8(7 − q)= 26 − 2m = 56 − 8q

i 4(9 − p) j (7 − x)8= 36 − 4p = 56 − 8x

k (18 − b)3 l (15 − m)4= 54 − 3b = 60 − 4m

4 a x(y + z) b m(p + q)= xy + xz = mp + mq

c a(b + c) d r(s − t)= ab + ac = rs − rt

e p(q − r) f l(m − n)= pq − pr = lm − ln

g m(n − 8) h a(b − 12)= mn − 8m = ab − 12a

i z(y − 8) j c(9 − b)= yz − 8z = 9c − bc

k p(14 − q) l m(9 − n)= 14p − pq = 9m − mn

5 a 8(3x + 2) b 5(4y + 6)= 24x + 16 = 20y + 30

c 7(9b + 4) d 5(7q − 6)= 63b + 28 = 35q − 30

e 9(6p − 12) f 8(3s − 7)= 54p − 108 = 24s − 56

g 4(2x + 5y) h 5(6m + 9n)= 8x + 20y = 30m + 45n

i 7(8a + 12b) j (3a − 7b)6= 56a + 84b = 18a − 42b

k (8m − 6n)11 l (2m − 3n)9= 88m − 66n = 18m − 27n

6 a 3(2x + 6) + 9= 6x + 18 + 9= 6x + 27

b 7(7y − 1) + 10= 49y − 7 + 10= 49y + 3

c 4 + 5(3m + 6)= 4 + 15m + 30= 15m + 34

d 30 + 9(b − 2)= 30 + 9b − 18= 9b + 12

e 4(2a + 3b + 4c) + 5b= 8a + 12b + 16c + 5b= 8a + 17b + 16c

f 4x(3x + 2)= 12x2 + 8x

g 2x(3x + 2) + 3(3x + 2)= 6x2 + 4x + 9x + 6= 6x2 + 13x + 6

h 6y(5y − 8)= 30y2 − 48y

i 3x(2x + 5) + 4x(3x − 2)= 6x2 + 15x + 12x2 − 8x= 18x2 + 7x

j 5p(4p + 2m) − 20p2 − 8mp= 20p2 + 10mp − 20p2 − 8mp= 2mp

7 a 6(n + 3) b 7(n − 4)= 6n + 18 = 7n − 28

c 4(2n + 3) d 3(4n − 6)= 8n + 12 = 12n − 18

e 4( − 3)

= 2n − 12

8 a a + c b 3a + 1·5c

c 5(3a + 1·5c) d 15a + 7·5c

× 3 5x 2x 5xy

2 6 10y 4x 10xy

3y 9y 15y2 6xy 15xy2

4x 12x 20xy 8x2 20x2y

2xy 6xy 10xy2 4x2y 10x2y2

÷ 24 48a 72b 96ab

3 8 16a 24b 32ab

4a 12 24b

2b 36 48a

8ab 12

72x------ 3x

5y------

3a15------ a

5---= 7a

14------ a

2---= 2y

8------ y

4---=

126x------ 2

x---= 18

9y------ 2

y---= 21

7m------- 3

m----=

824 p--------- 1

3 p------= 5

20q--------- 1

4q------= 16

64xy------------ 1

4xy---------=

10x8

--------- 5x4

------= 12x10

--------- 6x5

------= 18y12

--------- 3y2

------=

3212x--------- 8x

3------= 12

30b--------- 2

5b------= 21

35w---------- 3

5w-------=

6a--- 18b

a---------

12b

------ 24ab

---------

3ab------ 6

b--- 9

a---

n2---



Exercise 11E1 a 2♣ = 2 × 4 = 8 b ♣ + 5 = 4 + 5 = 9

c ♣ ÷ 2 = 4 ÷ 2 = 2 d ♣ – 3 = 4 – 3 = 1

2 a 3 = 3 × 8 = 24 b 7 = 7 × 8 = 56

c = × 8 = 4 d + 9 = 8 + 9 = 17

3 a 6xy = 6 × 5 × 4 = 120

b 2xy − 1 = 2 × 5 × 4 − 1 = 39

c xy − 1 = × 5 × 4 − 1 = 4

d 2x + 6y = 2 × 5 + 6 × 4 = 34

e 9x − 8y = 9 × 5 − 8 × 4 = 13

f 4y + 3x = 4 × 4 + 3 × 5 = 31

4 a = 10

b = 5

c = 2

d = 3

e = 2

f = 2

g a(2c + 4) h a(b + 4)= 5(6 + 4) = 5(6 + 4)= 50 = 50

i 2c(a + b) j 5c2

= 6(5 + 6) = 5(3)2

= 66 = 45

k b2 − 2c l (2a)2

= 62 − 3 × 2 = (10)2

= 30 = 100

m 2a2 n a2 + b2

= 2 × 52 = 52 + 62

= 50 = 61

o (a + b)2 p b2 − c2

= (5 + 6)2 = 62 − 32

= 121 = 27

q (b – c)2 r (3c)3

= (6 − 3)2 = 93

= 9 = 729

5 a 3, 5, 7, 9, 11 b 3, 4, 5, 6, 7

c 7, 6, 5, 4, 3 d 1, 4, 7, 10, 13

6 a n = c + d where n is the number of discs

b n = c + d = 24 + 16 = 40

Sam has 40 discs in a collection

7 a h = m + b where h is the number of horse literatures

b h = m + b = 5 + 12 = 17

Tarli has 17 horse literatures in her collection.

8 a c = 15x + 20y where c is the cost

b c = 15 × 5 + 20 × 3 = 135

The discs would cost $135.

c The combinations of CDs and DVDs purchased could be:8 CDs and no DVDs4 CDs and 3 DVDsNo CDs and 6 DVDs

9 a c = 2x + 3y where c is the cost

b c = 2 × 3 + 3 × 4 = 18The cost would be $18.

c The combinations of popcorn and drinks purchased could be:No drinks and 12 popcorn2 drinks and 9 popcorn4 drinks and 6 popcorn6 drinks and 3 popcorn8 drinks and no popcorn

10 a c = 2·5x + 4y where c is the cost

b c = 2·5x + 4yc = 2·5 × 2 + 4 × 5c = 25The cost of the food would be $25.

c If $27 was spent, the only combination of hot dogs and hamburgers could be:6 hot dogs and 3 hamburgers

Technology Activity 11F1 a 172, 172

b Yes

2 c same

3 c same

d Yes

7 = 25 = 52

a = 5, b = 12, c = 13

Learning task 11G

1 a The next two shapes have 15 and 21 dots. nth has

dots.

b The first 10 triangular numbers have 1, 3, 6, 10, 15, 21, 28, 36, 45, and 55 dots.

c The nth term is the sum of the numbers from 1 to n.e.g. 6th term is 1 + 2 + 3 + 4 + 5 + 6 = 21

2 a The next two shapes have 25 and 36 dots.

b The first 10 square numbers have 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100 dots.

c The nth square number is equal to n2. In other words to find the number of dots in a number you multiply that number by itself.

3 a These numbers are called pentagonal as they can form patterns containing pentagons, which have 5 sides.

b 13 and 17 dots

c 1, 5, 9, 13, 17, 21, 25, 29, 33 and 37 dots

d The nth pentagonal number is equal to the previous number plus 4. In other words to find the number of dots in a number you multiply the previous number (i.e. n − 1) by 4 and add 1.

4 a By listing, 9 and 25.

b By listing, 36 belongs to both number sets.

12--- 1

2---

14---

abc

------ 5 6×3

------------=

2acb

--------- 2 5× 3×6

---------------------=

b 4+a

------------ 6 4+5

------------=

b c+c

------------ 6 3+3

------------=

2a 2+b

--------------- 2 5 2+×6

---------------------=

bc 8–a

--------------- 6 3 8–×5

---------------------=

32 42+

n2 n+2

--------------

62



Learning task 11H1 a The next three shapes have 9, 11 and 13 matches.

b 3, 5, 7, 9, 11, 13, 15, 17, 19

c Add 2 onto the previous number.

d 31 matches

2 a 13 matches

b The fourth term has 13 matches.

c To find the fourth term you add 3 matches onto the third term.

d We start with 4 matches, then add 3 matches each time.

3 a 24 matches

b The fourth term has 24 matches.

c To find the fourth term you add 3 matches onto each side of the third.

d We start with 6 matches, then add 6 matches each time.

Exercise 11I1 a P = 2x + y b P = 2x + y

P = 2 × 5 + 3 P = 2 × 8 + 4= 10 + 3 = 16 + 4= 13 cm = 20 cm

2 a A = LW b A = LW= 12 × 9 = 6 × 7= 108 cm2 = 42 m2

3 A =

= 24 cm2

4 a i P = 6g + b ii P = 6g + b= 6 × 5 + 16 = 6 × 8 + 9= 30 + 16 = 48 + 9= 46 points = 57 points

b As both teams scored 22 points it was a draw.

5 a N = 1 + 2T b N = 1 + 2T= 1 + 2 × 5 = 1 + 2 × 20= 11 = 1 + 40

= 41

c N = 1 + 2T= 1 + 2 × 33= 1 + 66= 67

6 a i 13 ii 16

b 4, 7, 10, 13, 16, 19, 21, 24, 24, 30

c N = 1 + 3R

7 a i18 ii 22

b 6, 10, 14, 18, 22, 26, 30, 34, 38, 42

c N = 2 + 4A

8 a i $55 ii $62·50 iii $75 iv 0·5n + 50

b C = 0·5n + 50

c C = 5(10) + 50= 5 + 50

C = $55 for 10 programs

d C = 0·5(150) + 50= $125

9 a i $40 ii $55 iii $70 iv 5n + 30

b A = 5n + 30

c A = 5(5) + 30 d 135 = 5n + 30= 25 + 30 5n = 105= $55 n = 21

It will take 21 weeks.

Puzzles1 Fission chips

2 Nothing it just waved

3 It spun a website

4 Answers for clues are as follows:

Across Down

1 105 1 189

3 129 2 572

4 242 3 123

6 306 5 250

8 120 7 602

9 270 8 140

Enrichment

1 a Q = or

b Q = 3P − 3 c Q = P2 − P

2

3

= n

4 a 8x + 12y b 10m + 15n= 4(2x + 3y) = 5(2m + 3n)

c 6x2 + 9x d x2 + 6xy= 3x(2x + 3) = x(x + 6y)

e 3x2 − 6x f x2 − 4xy= 3x(x − 2) = x(x − 4y)

g 5x2 − 10 h 2x2 + 8x= 5(x2 − 2) = 2x(x + 4)

5 a 14x + 21y b 16x + 20y= 7(2x + 3y) = 4(4x + 5y)

c 25a + 30b d 8a – 12b= 5(5a + 6b) = 4(2a – 3b)

e x2 + 5x f x2 – 7x= x(x + 5) = x(x – 7)

g 6x2 – 12x h 4x2 – 6x= 6x(x – 2) = 2x(2x – 3)

i 6x2 – 14xy= 2x(3x – 7y)

6 a i t = 1∴ s = 36 × 1 = 36 km/hThe speed of the parachutist after 1 second is 36 km/h.

12--- 8 6××

m 9 1 5 2 8 7 10 3 4

m + 1 10 2 6 3 9 8 11 4 5

5m 45 5 25 10 40 35 50 15 20

m2 81 1 25 4 64 49 100 9 16

4 2 1 4 3 5 1 2

3m + 1 28 4 16 7 25 22 31 10 13

2m2 162 2 50 8 128 98 200 18 32

(2m)2 324 4 100 16 256 196 400 36 64

17 − m 8 16 12 15 9 10 7 14 13

m3 729 1 125 8 512 343 1000 27 64

P 2+2

------------- P2--- 1+

m2---- 1

2--- 1

2--- 1

2--- 1

2--- 1

2---

5 2n 3+( ) 15–10

------------------------------------

10n 15 15–+10

---------------------------------=

10n10

---------=



ii t = 2∴ s = 36 × 2 = 72 km/hThe speed of the parachutist after 2 seconds is 72 km/h.

b

c

e

7 a

b

d

e

f i It takes the parachutist 4 seconds to fall 80 m.

ii It takes the parachutist 10·5 seconds to fall 400 m.

iii It takes the parachutist 14·5 seconds to fall 600 m.

g Terminal velocity is 50 metres/second.

Revision1 a ♣ + 9 b − 12 c ♥

d 3 e f +

2 a The sum of c and 10

b Eight times the value of a

c One ninth of the value of y

d The sum of x and 2 is divided by 3.

e Four is multiplied by b and the product is divided by 3.

f The sum of x and 6 is multiplied by 3.

3 a 8 + 9 = 17 b 6♥ + 5♥ = 11♥c 13 − 5 = 8 d 19 − 4 = 15

e 7 + 2 = 9 f + + = 3

g 7 + 3 + 2■ + 4■ = 10 + 6■

h 4 + 3 + 6★ + 2★ = 7 + 8★

i 5 − 2 + 8■ − 6■ = 3 + 2■

4 a 8a + 4b − c − 2a + 3b + 5c + 3a − b + c= 9a + 6b + 5c

b 4x + 3y – 2x – y + 1= 2x + 2y + 4

c 7ab + 5bc − ca − 3ab + 4bc – ab + 2ac= 3ab + 9bc + ac

d 5x + 4y + 7 – 2x + y – 3= 3x + 5y + 4

e 8xy + 9yz − 2zy + 3zx + 4xy − 3yz + 5zx= 12xy + 4zy + 8xz

f 9a + 7b + 6c – 6a – 6b – 5c= 3a + b + c

5 a 7 × a = 7a b 9 × y = 9y

c a × 15 = 15a d b × 8 = 8b

e a × c = ac f m × p = mp

g 16 × y × z = 16yz h m × n × 6 = 6mn

i a × p × q = apq j p × 8 × 9 = 72p

k y × 4 × 2 = 8y l 8 × 7 × p = 56p

6 a x ÷ 5 = b m ÷ 9 =

c p ÷ 12 = d 5 × y ÷ z =

e 9 × y ÷ 4x = f 5x ÷ 7y =

g = h =

i =

7 a 4(x + y) b 9(a + b)= 4x + 4y = 9a + 9b

c 6(m + n) d y(x + 4)= 6m + 6n = xy + 4y

e y(y + 7) f p(p + 8)= y2 + 7y = p2 + 8p

g (a − 4)5 h (c + 5)4= 5a − 20 = 4c + 20

i (b − 9)5 j (6 + p)p= 5b − 45 = 6p + p2

k (12 − q)3q l (5 − n)8n= 36q − 3q2 = 40n − 8n2

m x(x + 1) n x(x – 3)= x2 + x = x2 – 3x

o x(2x + 5) p 6y(5y – 2)= 2x2 + 5x 30y2 – 12y

q 5q(2q – 4) r 2x(x + 1) + x(x + 1)= 10q2 – 20q 3x2 + 3x

s x(2x–1) + 2x(x + 1) t 3x(x + 5) – 3x2

= 2x2 – x + 2x2 + 2x = 3x2 + 15x – 3x2

= 4x2 + x = 15x

u mp(m – p)= m2p – mp2

8 a P = 2x + yP = 2 × 7 + 4P = 18 cm

The perimeter of the triangle is 18 cm.

b P = 2x + yP = 2 × 4 + 3P = 11 cm

The perimeter of the triangle is 11 cm.

t (seconds) 0 1 2 3 4 5

s (km/h) 0 36 72 108 144 180

t (seconds) 0 1 2 3 4 5

p (metres) 0 5 20 45 80 125

t (seconds) 5 6 7 8 9 10

d (metres) 125 175 225 275 325 375

t (seconds)

s (k

m/h

)

0

50

100

150

200

1 2 3 4 5 6

s = 36t

t (seconds)

s (k

m/h

)

0

50

100

150

200

1 2 3 4 5 6 7 8 9 10

t (seconds)

p (m

)

0

20

1 2 3 4 5

40

60

80

100

120

140

t (seconds)

p (m

)

0

100

200

300

400

1 2 3 4 5 6 7 8 9 10

15---

17---

x5--- m

9----

p12------ 5y

z------

9y4x------ 5x

7y------

5x15------ x

3--- 16

32x--------- 1

2x------

2835w---------- 4

5w-------

64



c P = 2x + y13 = 2x + (x + 1)13 = 3x + 113 = 3 × 4 + 1so x = 4, and thus y = 5

The sides of the triangle are 5 cm and 4 cm.

9 a 8xy b 5xy − 1= 8 × 6 × 8 = 5 × 6 × 8 − 1= 384 = 239

c xy − 2 d 6x + 2y

= × 6 × 8 − 2 = 6 × 6 + 2 × 8

= 10 = 52

e 10x − 7y f 4x + 3y= 10 × 6 − 7 × 8 = 4 × 6 + 3 × 8= 4 = 48

g 5(2x + 1) + y h 3(2x − 1) + 2y= 5(13) + 8 = 3(11) + 2(8)= 73 = 49

i 2(2x − 4) + 3y j 6 + y2

= 2(8) + 3(8) = 6 + 82

= 40 = 70

k 2y2 + 3y + 3 l 2x2 ÷ y= 2(8)2 + 3(8) + 3 = 2(6)2 ÷ 8= 155 = 9

10 a 3x + 2y b 3(3) + 2(5)= 9 + 10= $19

c $24 = 3x + 2y

11 a

b 1, 8, 21, 40, 65, 96, 133, 176, 225, 280

c Start with 1, then add 7, then add 7 + 6. Increase the amount you add by 6 each time.3n2 − 2n works out nth term

12 a A = LW b A = LWA = 12 × 8 = 16 × 4

= 96 cm2 = 64 m2

c P = 2(l + w) d A = LW= 2(12 + 8) = 8 × 2= 40 cm = 16 cm2

This is one quarter of the previous area.

Exercise 12A1 a a + 15 = 20 b b − 9 = 8

5 + 15 = 20 17 − 9 = 8so a = 5 so b = 17

c c − 10 = 26 d d + 21 = 3036 − 10 = 26 9 + 21 = 30so c = 36 so d = 9

e e − 2 = 19 f f + 37 = 5021 − 2 = 19 13 + 37 = 50so e = 21 so f = 13

g g + 154 = 181 h h − 57 = 2627 + 154 = 181 83 − 57 = 26so g = 27 so h = 83

i i + 219 = 30283 + 219 = 302so i = 83

2 a k + k + k = 213k = 21k = 7

b m + m + m + m = 364m = 36m = 9

c p + p + p + p + p = 105p = 10p = 2

d r + r + r + r + r = 555r = 55r = 11

e t + t + t + t + t = 605t = 60t = 12

f v + v + v + v + v+ v = 426v = 42v = 7

g 3x = 21x = 7

h 5y = 30y = 6

i 5m = 25m = 5

3 a x + 5 = 11 b y + 12 = 216 + 5 = 11 9 + 12 = 21so x = 6 so y = 9

c 7 + m = 13 d 9 + a = 177 + 6 = 13 9 + 8 = 17so m = 6 so a = 8

e r + 12 = 17 f t + 5 = 95 + 12 = 17 4 + 5 = 9so r = 5 so t = 4

g 10 + q = 18 h 22 + p = 3010 + 8 = 18 22 + 8 = 30so q = 8 so p = 8

i x + 7 = 19 j s + 6 = 1112 + 7 = 19 5 + 6 = 11so x = 12 so s = 5

k b + 2 = 8 l y + 13 = 176 + 2 = 8 4 + 13 = 17so b = 6 so y = 4

m m + 3 = 16 n a + 80 = 22013 + 3 = 16 140 + 80 = 220so m = 13 so a = 140

o e + 45 = 156 p f + 9 = 110111 + 45 = 156 101 + 9 = 110so e = 111 so f = 101

q x + 19 = 35 r y + 16 = 3116 + 19 = 35 15 + 16 = 31so x = 16 so y = 15

s p + 21 = 45 t 25 + x = 4624 + 21 = 45 25 + 21 = 46p = 24 so x = 21

4 a x − 7 = 9 b s − 8 = 1116 − 7 = 9 19 − 8 = 11so x = 16 so s = 19

Popcorn 0 2 4 6 8

Drinks 12 9 6 3 0

14---

14---

Chapter 12



c b − 5 = 8 d y − 13 = 713 − 5 = 8 20 − 13 = 7so b = 13 so y = 20

e m − 13 = 14 f a − 18 = 2027 − 13 = 14 38 − 18 = 20so m = 27 so a = 38

g e − 24 = 6 h f − 9 = 1130 − 24 = 6 20 − 9 = 11so e = 30 so f = 20

i 10 − b = 8 j 13 − c = 610 − 2 = 8 13 − 7 = 6so b = 2 so c = 7

k 9 − d = 7 l 20 − a = 149 − 2 = 7 20 − 6 = 14so d = 2 so a = 6

m 39 − m = 19 n 45 − n = 2239 − 20 = 19 45 − 23 = 22so m = 20 so n = 23

o 33 − p = 8 p 50 − q = 3233 − 25 = 8 50 − 18 = 32so p = 25 so q = 18

5 a 6x = 12 b 9y = 276 × 2 = 12 9 × 3 = 27so x = 2 so y = 3

c 8a = 32 d h × 5 = 308 × 4 = 32 6 × 5 = 30so a = 4 so h = 6

e 12 × m = 60 f 8 × n = 5612 × 5 = 60 8 × 7 = 56so m = 5 so n = 7

g p × 4 = 12 h q × 15 = 453 × 4 = 12 3 × 15 = 45so p = 3 so q = 3

i 17x = 34 j 65s = 19517 × 2 = 34 65 × 3 = 195so x = 2 so s = 3

k 2b = 88 l 13y = 522 × 44 = 88 13 × 4 = 52so b = 44 so y = 4

m 30 × m = 900 n 7 × p = 28030 × 30 = 900 7 × 40 = 280so m = 30 so p = 40

o e × 45 = 135 p f × 19 = 1143 × 45 = 135 6 × 19 = 114so e = 3 so f = 6

6 a x ÷ 3 = 12 b y ÷ 2 = 2636 ÷ 3 = 12 52 ÷ 2 = 26so x = 36 so y = 52

c a ÷ 9 = 12 d h ÷ 12 = 30108 ÷ 9 = 12 360 ÷ 12 = 30so a = 108 so h = 360

e 12 ÷ m = 6 f z ÷ 12 = 712 ÷ 2 = 6 84 ÷ 12 = 7so m = 2 so z = 84

g 135 ÷ p = 27 h 77 ÷ q = 7135 ÷ 5 = 27 77 ÷ 11 = 7so p = 5 so q = 11

i = 3 j = 2

18 ÷ 6 = 3 14 ÷ 7 = 2so y = 18 so x = 14

k = 2 l = 7

20 ÷ 10 = 2 56 ÷ 8 = 7so m = 20 so n = 56

m = 4 n = 3

20 ÷ 5 = 4 27 ÷ 9 = 3so p = 20 so q = 27

o = 4 p = 6

44 ÷ 11 = 4 72 ÷ 12 = 6so r = 44 so t = 72

7 a x + 12 = 20 b y + 16 = 308 + 12 = 20 14 + 16 = 30so x = 8 so y = 14

c a − 8 = 6 d b − 18 = 1514 − 8 = 6 33 − 18 = 15so a = 14 so b = 33

8 a x + 6 = 8 b x − 11 = 202 + 6 = 8 31 − 11 = 20so x = 2 so x = 31

c = 50 d 4x + 8 = 20

100 ÷ 2 = 50 4x = 12so x = 100 4 × 3 = 12

so x = 3

e 3x − 5 = 16 f √x =53x = 21 √25 = 53 × 7 = 21 so x = 25so x = 7

9 a Incorrect b Incorrect c Incorrect

d Correct e Correct f Incorrect

g Correct h Incorrect i Correct

j Incorrect k Correct l Correct

Exercise 12B

1

The solution is then x = 7.

2

The solution is then y = 24.

3

The solution is then x = 12.

4 a

p = 11

y6--- x

7---

m10------ n

8---

x × 9 9x

=

7 ÷ 9 63

y ÷ 8

=

24 × 8 3

x × 4 4x + 9 4x + 9

= =

12 ÷ 4 48 − 9 57

p + 8 p + 8

=

11 − 8 19

p5--- q

9---

r11------ t

12------

x2---

y8---

66



b

a = 16

c

x = 7

d

y = 16

e

r = 22

f

a = 12

g

b = 24

h

m = 15

5 a

x = 3

b

y = 5

c

m = 9

d

a = 6

e

b = 5

f

c = 4

g

p = 28

h

q = 27

i

r = 60

j

m = 36

k

n = 39

a + 10 a + 10

=

16 − 10 26

x + 10 x + 10

=

7 − 10 17

y + 15 y + 15

=

16 − 15 31

r − 9 r − 9

=

22 + 9 13

a + 8 a + 8

=

12 − 8 20

b − 14 b − 14

=

24 + 14 10

m − 6 m − 6

=

15 + 6 9

x × 6 6x

=

3 ÷ 6 18

y × 8 8y

=

5 ÷ 8 40

m × 12 12m

=

9 ÷ 12 108

a × 9 9a

=

6 ÷ 9 54

b × 7 7b

=

5 ÷ 7 35

c × 8 8c

=

4 ÷ 8 32

p ÷ 7

=

28 × 7 4

q ÷ 9

=

27 × 9 3

r ÷ 12

=

60 × 12 5

m ÷ 9

=

36 × 9 4

n ÷ 3

=

39 × 3 13

p7---

q9---

r12------

m9----

n3---



l

p = 96

m

c = 12

n

a = 55

o

p = 91

6 a

x = 3

b

y = 6

c

a = 9

d

m = 6

e

n = 11

f

p = 4

g

x = 3

h

y = −3

i

a = 2

j

m = 2

k

n = 11

l

p = 4

m

x = 1

n

y = 10

p ÷ 8

=

96 × 8 12

c ÷ 4

=

12 × 4 3

a ÷ 5

=

55 × 5 11

p ÷ 7

=

91 × 7 13

x × 2 2x + 9 2x + 9

= =

3 ÷ 2 6 − 9 15

y × 4 4y + 6 4y + 6

= =

6 ÷ 4 24 − 6 30

a × 7 7a + 4 7a + 4

= =

9 ÷ 7 63 − 4 67

m × 3 3m − 5 3m − 5

= =

6 ÷ 3 18 + 5 13

n × 8 8n − 10 8n − 10

= =

11 ÷ 8 88 + 10 78

p8---

c4---

a5---

p7---

p × 9 9p − 8 9p − 8

= =

4 ÷ 9 36 + 8 28

x × 2 2x + 4 2x + 4

= =

3 ÷ 2 6 − 4 10

y × 2 2y + 6 2y + 6

= =

−3 ÷ 2 −6 − 6 0

a × 6 6a + 5 6a + 5

= =

2 ÷ 6 12 − 5 17

m × 5 5m + 1 5m + 1

= =

2 ÷ 5 10 − 1 11

n × 2 2n − 10 2n − 10

= =

11 ÷ 2 22 + 10 12

p × 9 9p − 2 9p − 2

= =

4 ÷ 9 36 + 2 34

x × 2 2x + 5 2x + 5

= =

1 ÷ 2 2 − 5 7

y × 4 4y + 6 4y + 6

= =

10 ÷ 4 40 − 6 46

68



o

a = 5

7 a 5x = 20 b = 6

x = 4 y = 48

c 8n + 5 = 37 d 9q − 8 = 55n = 4 q = 7

e 6m − 2 = 40 f 9s − 1 = 80m = 7 s = 9

g = 2 h = 11

x = 25 x = 8

Exercise 12C1 a x + 4 = 16 b y + 13 = 24

x = 16 − 4 y = 24 − 13x = 12 y = 11

c m − 7 = 15 d n − 19 = 6m = 15 + 7 n = 6 + 19m = 22 n = 25

e 18 = p − 5 f p − =

p = 18 + 5 p =

p = 23 p =

g q + 2·5 = 4·75 h t − 3·25 = 1·75q = 4·75 − 2·5 t = 1·75 + 3·25q = 2·25 t = 5

i = j =

m = q =

m = q =

k = l = 8·75

x = p =

x = 5 p = 5·25

m = 3·75 n = 6·75

s = t =

s = 1·5 t = 3·25

2 a 4x = 12 b 6y = 72x = 12 ÷ 4 y = 72 ÷ 6x = 3 y = 12

c 9n = 45 d 3g = 33n = 45 ÷ 9 g = 33 ÷ 3n = 5 g = 11

e 11p = 44 f 5m = 60p = 44 ÷ 11 m = 60 ÷ 5p = 4 m = 12

g 2r = 5 h 3s = 7

r = s =

i 7t = 11 j 4z = 10

t = z =

k 8q = 44 l 6h = 22

q = h =

m 10x = 5 n 12y = 8

x = y =

o 24z = 18 p 6m = 15

z = m = =

q 2n = 1·8 r 3t = 2·7

n = = 0·9 t = = 0·9

s 5a = 2·5 t 0·5x = 1·5

a = 0·5 x = = 3

3 a = 8 b = 3

x = 8 × 9 a = 3 × 13x = 72 a = 39

c = 12 d = 16

b = 12 × 7 p = 16 × 6b = 84 p = 96

e = 7 f = 3

q = 7 × 15 r = 3 × 18q = 105 r = 54

g h = 1·5

m = 2·5 × 4 n = 1·5 × 3m = 10 n = 4·5

i

p = 2·75 × 4p = 11

4 a 6p = 19·50p = 19·50 ÷ 6p = 3·25Each popcorn costs $3·25.

b c = 50 − 19·50c = 30·50The change was $30·50.

5 = 1·05

P = 11 × 1·05P = 11·55The cost of a movie ticket is $11·55.

6 a P = 6x = 216 b P = 2x + 8 = 38x = 216 ÷ 6 2x = 38 − 8 = 30x = 36 x = 30 ÷ 2

x = 15

Exercise 12D1 a 3x + 4 = 31 b 8y − 9 = 31

3x = 31 − 4 = 27 8y = 31 + 9 = 40x = 27 ÷ 3 y = 40 ÷ 8x = 9 y = 5

a × 7 7a + 4 7a + 4

= =

5 ÷ 7 35 − 4 39

y8---

x5--- 3– 3x

4------ 5+

12--- 31

4---

314--- 1

2---+

334---

m 34---+ 11

2--- q 21

2---– 13

4---

112--- 3

4---– 13

4--- 21

2---+

34--- 41

4---

x 123---– 31

3--- p 3·5+

313--- 12

3---+ 8·75 3·5–

s 2·25+ t 3·5+

3·75 2·25– 6·75 3·5–

212--- 21

3---

147--- 21

2---

512--- 32

3---

12--- 2

3---

34--- 15

6------ 21

2---

1·82

------- 2·73

-------

1·50·5-------

x9--- a

13------

b7--- p

6---

q15------ r

18------

m4---- 21

2---= n

3---

p4--- 23

4---=

P11------



c 9m − 3 = 60 d 7 + 3n = 199m = 60 + 3 = 63 3n = 19 − 7 = 12m = 63 ÷ 9 n = 12 ÷ 3m = 7 n = 4

e 10 + 5q = 35 f 15 + 12a = 395q = 35 − 10 = 25 12a = 39 − 15 = 24q = 25 ÷ 5 a = 24 ÷ 12q = 5 a = 2

g 18 + 6b = 36 h 45 + 5c = 806b = 36 − 18 = 18 5c = 80 − 45 = 35b = 18 ÷ 6 c = 35 ÷ 5b = 3 c = 7

i 5x − 7 = 33 j 2r + 3 = 45x = 33 + 7 = 40 2r = 4 − 3 = 1x = 40 ÷ 5 r = 1 ÷ 2

x = 8 r =

k 6s + 5 = 14 l 7a − 6 = 146s = 14 − 5 = 9 7a = 14 + 6 = 20s = 9 ÷ 6 a = 20 ÷ 7

s = a =

2 a = 10 b = 9

5x = 10 × 4 = 40 3y = 9 × 4 = 36x = 40 ÷ 5 y = 36 ÷ 3x = 8 y = 12

c = 4 d a = 6

2z = 4 × 3 = 12 3a = 6 × 5 = 30z = 12 ÷ 2 a = 30 ÷ 3y = 6 a = 10

e b = 8 f c = 10

2b = 8 × 9 = 72 5c = 10 × 2 = 20b = 72 ÷ 2 c = 20 ÷ 5b = 36 c = 4

g m = 5 h n = 2

2m = 5 × 3 = 15 4n = 2 × 5 = 10m = 15 ÷ 2 n = 10 ÷ 4

m = n =

i = 4

3p = 4 × 2 = 8p = 8 ÷ 3

p =

3 a + 5 = 7 b + 9 = 12

= 7 − 5 = 2 = 12 − 9 = 3

x = 2 × 6 y = 3 × 7x = 12 y = 21

c − 6 = 8 d m + 7 = 9

= 8 + 6 = 14 m = 9 − 7 = 2

z = 14 × 2 m = 2 × 8z = 28 m = 16

e n − 2 = 4 f p − 1 = 5

n = 4 + 2 = 6 p = 5 + 1 = 6

n = 6 × 4 p = 6 × 12n = 24 p = 72

g h

i

s = 5

4 a b

2x = 4 × 3 = 12 3a = 6 × 4 = 24x = 12 ÷ 2 a = 24 ÷ 3x = 6 a = 8

c d

4n = 12 × 3 = 36 5n = 10 × 3 = 30n = 36 ÷ 4 n = 30 ÷ 5n = 9 n = 6

e f

4p = 8 × 5 = 40 2q = 4 × 7 = 28p = 40 ÷ 4 q = 28 ÷ 2p = 10 q = 14

g h

5m = 10 × 6 = 60 2z = 6 × 5 = 30m = 60 ÷ 5 z = 30 ÷ 2m = 12 z = 15

i

3t = 6 × 8 = 48t = 48 ÷ 3t = 16

5 a b

12---

112--- 26

7---

5x4

------ 3y4

------

2z3----- 3

5---

29--- 5

2---

23--- 4

5---

712--- 21

2---

3 p2

------

223---

x6--- y

7---

x6--- y

7---

z2--- 1

8---

z2--- 1

8---

14--- 1

12------

14--- 1

12------

q2--- 3

4---+ 2= 1

4---r 1

2---– 1=

q2--- 2 3

4---– 5

4---= = 1

4---r 1 1

2---+ 3

2---= =

q 54--- 2×= r 3

2--- 4×=

q 212---= r 6=

13---s 2+ 32

3---=

13---s 32

3--- 2– 5

3---= =

s 53--- 3×=

2x3

------ 1+ 5= 3a4

------ 2+ 8=

2x3

------ 5 1– 4= = 3a4

------ 8 2– 6= =

4n3

------ 3+ 15= 5n3

------ 1– 9=

4n3

------ 15 3– 12= = 5n3

------ 9 1+ 10= =

4 p5

------ 1+ 9= 2q7

------ 3– 1=

4 p5

------ 9 1– 8= = 2q7

------ 1 3+ 4= =

56---m 7– 3= 2

5---z 4+ 10=

56---m 3 7+ 10= = 2

5---z 10 4– 6= =

38--- t 4– 2=

38--- t 2 4+ 6= =

5x − 15 = 505x = 50 + 15 = 65x = 65 ÷ 5x = 13

4x = 8 × 5 = 40x = 40 ÷ 4 = 10

4x5

------ 8=

70



c d

y = 5 ÷ 5 = 25 3y = 9 × 53y = 45y = 15

6 10d − 75 = 37510d = 375 + 75 = 450d = 450 ÷ 10d = 45

The regular price for each ski pass is $45.The students paid $37·50 for each of their tickets.

7 4p + 3 = 84p = 8 − 3 = 5p = 5 ÷ 4p = 1·25

Each doughnut costs $1·25.

8 P = 126

3P = 126 × 4 = 504P = 504 ÷ 3P = 168

The standard price for the ski lodge is $168.

9 20 − 12t + 15t = 7120 + 3t = 713t = 71 − 20 = 51t = 51 ÷ 3t = 17

It will take 17 minutes for the queue to grow to 71 people.

Exercise 12E1 a 15 + 12 > 2 × 5 b 3 × 6 < 40 ÷ 2

c 4 + 8 = 6 × 2 d 16 − 5 > 24 ÷ 3

e 4 × 0·5 = 20 ÷ 10 f 36 + 27 > 6 × 7

g 9 × 12 = 216 ÷ 2 h 42 + 1 < 20 − 2

i 52 + 122 = 132 j (2 + 3)2 > 22 + 32

2 a

b

c

d

3 a x ≥ 1 b x < 2 c −2 < x ≤ 1

d 0 ≤ x ≤ 3 e 0 < x < 3 f −1 ≥ x > 2

4 a x < 10

b y > 8

c z ≤ 5

d m ≥ 7

e 3 < x < 6

f 4 < x < 8

g 7 ≤ x < 10

h 5 < y ≤ 11

i 128 ≤ p ≤ 148

j a ≥ 17

k 13 < a ≤ 20

l 20 ≤ t ≤ 30

m 0 ≤ s ≤ 35

n 0 < s ≤ 50

o 5 ≤ d ≤ 10

5 a x + 5 < 9 b y − 8 > 10x < 9 − 5 y > 10 + 8x < 4 y > 18

c z − 15 ≥16 d m + 7 ≤ 12z ≥ 16 + 15 m ≤ 12 − 7z ≥ 31 m ≤ 5

e n + 19 < 21 f p − 17 ≤ 3n < 21 − 19 p ≤ 3 + 17n < 2 p ≤ 20

g 4x ≥ 20 h 12y > 72x ≥ 20 ÷ 4 y > 72 ÷ 12x ≥ 5 y > 6

i 6z < 33 jz < 33 ÷ 6

z <

k l 10q > 55q > 55 ÷ 10

q >

m ≥ 5 n ≤ 4

x ≥ 5 × 7 y ≤ 4 × 13x ≥ 35 y ≤ 52

o > 4 p m < 6

z > 4 × 15 m < 6 × 4z > 60 m < 24

y5--- 7+ 12= 3y

9------ 3– 2=

y5--- 12 7– 5= = 3y

9------ 2 3+ 5= =

34---

0 1 2 3 4 5x

–1–2 0 1 2x

2 3 4 5 6 7 8x

–2 –1 0 1 2 3 4 5x

0 1 2 3 4 5 6 7 8 9 10x

y0 1 2 3 4 5 6 7 8 9 10

z0–1 1 2 3 4 5 6 7 8

m0 1 2 3 4 5 6 7 8 9 10

x0 1 2 3 4 5 6 7 8 9

x0 1 2 3 4 5 6 7 8 9

x0 1 2 3 4 5 6 7 8 9 10

y4 5 6 7 8 9 10 11

p9089 91 92 93 94 95 96 97 98

a15 16 17 18 19 20

a12 13 14 15 16 17 18 19 20

t10 15 20 25 30

s–5 0 5 10 15 20 25 30 35 40

s–10 0 10 20 30 40 50 60

d0 1 2 3 4 5 6 7 8 9 10

9m ≤ 36m ≤ 36 ÷ 9m ≤ 4

512---

5p < 45p < 45 ÷ 5p < 9

512---

x7--- y

13------

z15------ 1

4---



q n ≥ 9 r p < 8

n ≥ 9 × 2 p < 8 × 3n ≥ 18 p < 24

s ≤ 12 t > 10

2x ≤ 12 × 3 3y > 10 × 5x ≤ 36 ÷ 2 y > 50 ÷ 3

x ≤ 18

u < 8 v ≤ 4

4z < 8 × 3 2a ≤ 4 × 5z < 24 ÷ 4 a ≤ 20 ÷ 2z < 6 a ≤ 10

w < 14 x ≥ 6

7b < 14 × 6 3c ≥ 6 × 4b < 84 ÷ 7 c ≥ 24 ÷ 3b < 12 c ≥ 8

6 a 4x + 2 ≥ 8 b4x ≥ 8 − 2x ≥ 6 ÷ 4

x ≥

c d 2a + 5 < 122a < 12 − 5a < 7 ÷ 2

a <

e 10b + 9 ≥ 24 f 5c − 8 < 1510b ≥ 24 − 9 5c < 15 + 8b ≥ 15 ÷ 10 c < 23 ÷ 5

b ≥ c <

g + 5 ≥ 8 h − 9 < 2

≥ 8 − 5 < 2 + 9

m ≥ 3 × 7 n < 11 × 6m ≥ 21 n < 66

i − 3 ≥ 2 j + 2 < 3

≥ 2 + 3 < 3 − 2

p ≥ 5 × 15 x < 1 × 4p ≥ 75 x < 4

k − 9 ≥ 1 l − 5 ≤ 4

≥ 1 + 9 ≤ 4 + 5

y ≥ 10 × 8 z ≤ 9 × 10y ≥ 80 z ≤ 90

m + 4 ≤ 14 n − 2 > 7

≤ 14 − 4 > 7 + 2

2x ≤ 10 × 3 3y > 9 × 5x ≤ 30 ÷ 2 y > 45 ÷ 3x ≤ 15 y > 15

o − 7 < 5 p + 3 ≤ 5

< 5 + 7 ≤ 5 − 3

4z < 12 × 3 2a ≤ 2 × 5z < 36 ÷ 4 a ≤ 10 ÷ 2z < 9 a ≤ 5

q − 2 < 12 r − 9 ≥ 3

< 12 + 2 ≥ 3 + 9

7b < 14 × 6 3c ≥ 12 × 4b < 84 ÷ 7 c ≥ 18 ÷ 3b < 12 c ≥ 16

7 a 5x − 12 > 185x > 18 + 12x > 30 ÷ 5x > 6

b < 16

4x < 16 × 5x < 80 ÷ 4x < 20

c + 7 ≥ 9

≥ 9 − 7

y ≥ 2 × 4y ≥ 8

d − 1 > 8

> 8 + 1

3y > 9 × 4y > 36 ÷ 3y > 12

8 b − 100 > 175b > 175 + 100b > 275

The original balance was greater than $275.

9 d + (d + 6) < 162d < 16 − 6d < 10 ÷ 2d < 5

The amount d is less than $5.

10 15 < t ≤ 25

11 15 > a ≥ 60

12--- 1

3---

2x3

------ 3y5

------

y 1623--->

4z3----- 2

5---a

76---b 3

4---c

5 + 2y < 132y < 13 − 5y < 8 ÷ 2y < 4

112---

6z − 2 ≤ 226z ≤ 22 + 24z ≤ 24 ÷ 6z ≤ 4

312---

112--- 43

5---

m7---- n

6---

m7---- n

6---

p15------ 1

4---x

p15------ 1

4---x

18---y 1

10------z

18---y 1

10------z

2x3

------ 3y5

------

2x3

------ 3y5

------

4z3----- 2

5---a

4z3----- 2

5---a

76---b 3

4---c

76---b 3

4---c

54 6 7 8x

4x5

------

1918 20 21 22x

y4---

y4---

87 9 10y

3y4

------

3y4

------

1110 12 13y

15 25t

15 60a

72



Learning task 12F

1

2

Puzzles1 If they flew over the bay they would be bagels

2 Take me to your weeder

3 a i 3rd row: 23, 20 ii 2nd row: 11, 19, 114th row: 43 3rd row: 30, 30

4th row: 60

b i Heart = 3 ii Heart = 3

Applications1 a n = 6 b n = 4 c x = 9

d y = 4 e x = 7 f n = 3

2 a 3x + 4 = 22 b 2n + 3 = 173x = 18 2n = 14x = 6 n = 7

c 6n + 4 = 16 d 5 + 2n = 116n = 12 2n = 6n = 2 n = 3

e 9 + 4x = 13 f 10 + 5n = 204x = 4 5n = 10x = 1 n = 2

3 2n + 6 = 4n + 22n + 4 = 4n4 = 2nn = 2

4 a n + 6 = 3n + 2 b 2n + 1 = n + 5n + 4 = 3n n + 1 = 54 = 2n n = 4n = 2

c 2n + 6 = 3n +2 d 4n + 6 = 2n + 122n + 4 = 3n 4n = 2n + 6n = 4 2n = 6

n = 3

e 4n + 8 = 6n f 6n = 5n + 68 = 2n n = 6n = 4

5 a x + 10 = 3x b x + 8 = 5x2x = 10 8 = 4xx = 5 x = 2

c 7n + 5 = 8n + 2 d 6x + 5 = 3x + 177n + 3 = 8n 6x = 3x + 12n = 3 3x = 12

x = 4

e 3x + 6 = x + 10 f 5x + 9 = 3x + 172x = 4 2x = 8x = 2 x = 4

Enrichment1 The equation is 26 – 2x = 10.

x = 8.

2 The equation is = 12.

x = 3.

3 a

The solution is a = 14.Check by substitution: 34 – 14 = 20

b

The solution is b = 13.Check by substitution: 23 – 13 = 10

x

y

x

y

x × 2 2xsubtract from 26

26 – 2x

=

8 ÷ 2 16subtractfrom 26

10


8 – 2xdivideinto 24

=


2divideinto 24

12

248 2x–---------------

248 2x–---------------

a subtract from 34 34 – a

=

14 subtract from 34 20

b subtract from 23 23 – b

=




c

The solution is m = 7.Check by substitution: 16 – 7 = 9

d

The solution is x = 2.Check by substitution: 10 – 3 × 2 = 10 – 6 = 4

e

The solution is y = 18.Check by substitution: 45 – 2 × 18 = 45 – 36 = 9

f

The solution is m = 5.Check by substitution: 52 – 8 × 5 = 52 – 40 = 12

g

The solution is n = = .

Check by substitution: 45 – 4 × = 45 – 10 = 35

h

The solution is p = = .

Check by substitution: 29 – 6p = 29 – 14 = 15

i

The solution is q = .

Check by substitution: 125 – 12 ×

= 125 – 51 = 74

4 a

The solution is x = 4.

Check by substitution: = 9

b

The solution is y = 3.


c

The solution is z = 16.


d


Check by substitution: = = 2

e



m subtract from 16 16

=



10 – 3x

=


4

y × 2 2ysubtract from 45

45 – 2y

=


9

m × 8 8msubtract from 52

52 – 8m

=


12

n × 4 4nsubtract from 45

45 – 4n

=

÷ 4 10subtractfrom 45

35212---

52--- 21

2---

52---

p × 6 6psubtract from 29

29 – 6p

=


15

q × 12 12qsubtract

from 125125 – 12q

=

÷ 12 51subtract

from 12574

x divide into 36

=

4 divide into 36 9

y divide into 81

=

3 divide into 81 27

z divide into 64

=

16 divide into 64 4

213---

73--- 21

3---

414---

414---

414---

36x

------

364

------

81y

------

813

------

64z

------

6416------


20 – 3xdivideinto 16

=


8divideinto 16

2

ysubtract from 12

12 – ydivideinto 18

=

6subtractfrom 12

6divideinto 18

3

1620 3x–------------------

1620 3 4×–------------------------ 16

8------

1812 y–--------------

1812 y–-------------- 18

6------

74



f

The solution is z = .


g

The solution is p = 3.

Check by substitution: = = = 6

h

The solution is q = 3.

Check by substitution: = = = 9

i

The solution is m = .

Check by substitution: = = = 17 – 5 = 12

5 a 50 – 7x = 8


b 18 – 4y = 10


c 25 – 6p = 7

The solution is p = 3.

z × 2 2zsubtract from 33

33 – 2zdivideinto 44

=


22divideinto 44

2


12 – 3pdivideinto 18

=


3divideinto 18

6

q × 5 5qsubtract from 18

18 – 5qdivideinto 27

=


3divideinto 27

9


15 – 2mdivideinto 50

subtract from 17

=


10divideinto 50

5subtractfrom 17

12


50 – 7x

=


8


18 – 4y

=


10


25 – 6p

=


7

4433 2z–-----------------

512---

512---

44

33 2 512---×–

---------------------------- 4433 11–------------------

1812 3 p–------------------

1812 3 3×–------------------------ 18

12 9–--------------- 18

3------

2718 5q–------------------

2718 5 3×–------------------------ 27

18 15–------------------ 27

3------

5015 2m–------------------- 17 50

15 2m–-------------------–

212---

212---

17 5015 2m–-------------------– 17 50

15 5–---------------– 17 50

10------–



d = 4


e = 2

The solution is q = 4.

f =1·5

The solution is m = 2·5.

Revision

1 a x + 6 = 13 b 9 + y = 14x = 7 y = 5

c z − 7 = 11 d m − 9 = 21z = 18 m = 30

e 16 − q = 10 f 20 − p = 12q = 6 p = 8

g 7m = 56 h n × 5 = 45m = 8 n = 9

i = 3 j = 8

p = 12 q = 56

k = 3 l = 4

r = 12 s = 7

2 a b

3 a m + 6 = 11 b p − 13 = 7m = 11 − 6 p = 7 + 13m = 5 p = 20

c d

e 4q + 3 = 19 f 6p − 7 = 414q = 19 − 3 = 16 6p = 41 + 7 = 48q = 16 ÷ 4 p = 48 ÷ 6q = 4 p = 8

4 a x + 12 = 21 b y − 17 = 18x = 21 − 12 y = 18 + 17x = 9 y = 35

c d

e f

5 a 6x + 2 = 50 b 20 + 3y = 326x = 50 − 2 = 48 3y = 32 − 20 = 12x = 48 ÷ 6 = 8 y = 12 ÷ 3 = 4

c d

e = 6 f = 6

2y = 6 × 3 = 18 3q = 6 × 4 = 24y = 18 ÷ 2 = 9 q = 24 ÷ 3 = 8

g + 5 = 7 h + 7 = 9

= 7 − 5 = 2 = 9 − 7 = 2

z = 2 × 3 = 6 m = 2 × 5 = 10

i − 1 = 3 j + 8 = 14

= 3 + 1 = 4 = 14 − 8 = 6

n = 4 × 4 = 16 3p = 6 × 5 = 30p = 30 ÷ 3 =10


20 – 7ydivideinto 24

=


6divideinto 24

4

q × 3 3qsubtract from 19

19 – 3qdivideinto 14

=


7divideinto 14

2


18 – 4mdivideinto 12

=

2·5 ÷ 4 10subtractfrom 18

8divideinto 12

1·5

2420 7y–------------------

2420 7y–------------------

1419 3q–------------------

1419 3q–------------------

1218 4m–-------------------

1218 4m–-------------------

p4--- q

7---

36r

------ 28s

------

3(5) − 4 = 1111 = 11Correct

+ 5 = 10

10 = 10Correct

204

------

8r = 48r = 48 ÷ 8r = 6

= 3

t = 3 × 7t = 21

t7---

9z = 72z = 72 ÷ 9z = 8

8m = 44m = 44 ÷ 8

m = 512---

= 4

m = 5 × 4m = 20

m5---- =

n = × 8

n8--- 1

2---

12---

8z − 4 = 688z = 68 + 4 = 72z = 72 ÷ 8 = 9

= 10

5x = 10 × 2 = 20x = 20 ÷ 5 = 4

5x2

------

2y3

------ 34---q

z3--- 1

5---m

z3--- 1

5---m

14---n 3 p

5------

14---n 3 p

5------

76



k + 5 = 13 l − 2 = 4

= 13 − 5 = 8 = 4 + 2 = 6

4q = 8 × 5 = 40 3r = 6 × 7 = 42q = 40 ÷ 4 = 10 r = 42 ÷ 3 = 14

6 a b

c + 5 = 14 d − 3 = 12

= 14 − 5 = 9 = 12 + 3 = 15

y = 9 × 2 = 18 3n = 15 × 2 = 30n = 30 ÷ 3 = 10

e = 1

= 6

3q = 24q = 8

7 Let p be the price of an individual undiscounted ice cream

10p − 20 = 2510p = 25 + 20 = 45p = 45 ÷ 10 = 4·5

Each ice cream usually costs $4·50

8 a 16 + 13 > 4 × 6 b 4 × 5 < 80 ÷ 2

c 12 × 6 = 144 ÷ 2 d 52 − 4 < 6 × 4

9 a x < 13

b z > 8

c 10 ≤ y < 15

d 20 < m < 30

e 5 < x < 8

f x < 4, x > 10

10 a 5 ≤ g ≤ 8 b 60 < m ≤ 100

c 11 ≤ x ≤ 13 d x < 15, x > 70

11 a x + 9 < 12 b z − 13 ≤ 8x < 12 − 9 z ≤ 8 + 13x < 3 z ≤ 21

c 5z > 15 d 7m > 42z > 15 ÷ 5 m > 42 ÷ 7z > 3 m > 6

e ≥ 4 f ≤ 11

p ≥ 4 × 5 q ≤ 11 × 4p ≥ 20 q ≤ 44

g ≥ 6 h ≤ 10

3n ≥ 6 × 4 5t ≤ 10 × 3n ≥ 24 ÷ 3 t ≤ 30 ÷ 5n ≥ 8 t ≤ 6

i ≥ 4

2s ≥ 4 × 5s ≥ 20 ÷ 2s ≥ 10

12 a 3x + 2 > 17 b 5y − 7 ≤ 83x > 17 − 2 5y ≤ 8 + 73x > 15 ÷ 3 y ≤ 15 ÷ 5x > 5 y ≤ 3

c − 4 ≥ 0 d + 3 > 9

≥ 0 + 4 > 9 − 3

z ≥ 4 × 5 m > 6 × 4z ≥ 20 m > 24

e + 9 < 13 f − 8 ≤ 7

< 13 − 9 ≤ 7 + 8

2p < 4 × 5 3q ≤ 15 × 4p < 20 ÷ 2 q ≤ 60 ÷ 3p < 10 q ≤ 20

13 a 6n + 2 > 506n > 50 − 2n > 48 ÷ 6n > 8

b > 3

4y > 3 × 12y > 36 ÷ 4y > 9

c + 8 ≥ 10

≥ 10 − 8

y ≥ 2 × 9y ≥ 18

d − 1 ≤ 1

≤ 1 + 1

2p ≤ 2 × 8p ≤ 16 ÷ 2p ≤ 8

45---q 3

7---r

45---q 3

7---r

7x + 4 = 607x = 60 − 4 = 56x = 56 ÷ 7 = 8

= 6

3y = 6 × 4 = 24y = 24 ÷ 3 = 8

3y4

------

y2--- 3n

2------

y2--- 3n

2------

3q4

------ 5–

3q4

------

x1110 12 13 14

z76 8 9 10 11

109 11 12 13 14 15 16y

20 25 30 m

5 6 7 8 9 10 x

2 3 4 5 6 7 8 9 10 11 12 x

p5--- 1

4---q

3n4

------ 53--- t

25---s

z5--- 1

4---m

z5--- 1

4---m

2 p5

------ 34---q

2 p5

------ 34---q

n76 8 9 10

4y12------

y8 9 10 11 12

y9---

y9---

q16 17 18 19 20

2 p8

------

2 p8

------

p76 8 9 10



14 125 < 100 + d < 14825 < d < 48

Between $25 and $48 was added to bank account.

Exercise 13A1 Unlikely, likely, definite, even chance, probably,

possible, impossible, certain, maybe

2 Impossible, unlikely, maybe, possible, even chance, likely, probably, definite, certain

3 a C b C c D d C e C

f D g I h C i C j D

4 i c ii g

5 An impossible event is that you will grow a third arm overnight.An event that will definitely happen is that you will breathe.

6 It is possible that it will rain on New Year’s Day next year.It is unlikely that we will ever meet Martians.There is an even chance your first child will be female.

7 a It is likely a woman will become the Australian Prime Minister in your lifetime.

b It is highly likely it will rain at least once in Melbourne during the month of April.

c It is possible Fremantle will win the next AFL premiership.

d It possible Australia will become a republic within a decade.

e It is unlikely Australia will win the soccer World Cup.

f It is definite the Sun will set in Melbourne tonight.

8

9 a Impossible: Fitzroy will win the next AFL premiership (they are no longer a team).

b Maybe: That you will leave class early.

c Certain: That the Sun will rise tomorrow.

d Possible: That you will marry.

e More than likely: That prices will rise.

10 There is a small chance of throwing a five or a six.Three boys are unlikely.You are likely to throw different numbers.There is an even chance of selecting a red card.It is almost certain you will select a red lolly.There is more than half a chance of selecting a girl.There is negligible chance of winning lotto.

Exercise 13B1 There are 6 possible outcomes from rolling a die:

1, 2, 3, 4, 5, and 6.

a There is 1 positive outcome which is a 6.The probability of throwing a six = .

b There are 5 positive outcomes: 1, 2, 3, 4, and 5.The probability of not throwing a six = .

c There are 3 positive outcomes: 2, 4, and 6.The probability of throwing an even number

= = .

d There are 3 positive outcomes: 1, 2, and 3.The probability of throwing a number less

than 4 is = = .

2 There are 10 possible outcomes from selecting the cards.

a There is 1 positive outcome which is the card 7.

The probability of choosing seven = .

b There are 3 positive outcomes: 1, 2, and 3.The probability of choosing a card with a

number below four = .

c There are 7 positive outcomes: 4, 5, 6, 7, 8, 9, and 10.

The probability of choosing a card with a

number above three = .

d There are 5 positive outcomes: 2, 4, 6, 8, and 10.The probability of choosing a card with an

even number = = .

e There are 3 positive outcomes: 3, 6, and 9.The probability of choosing a card divisible

by three = .

f There are 7 positive outcomes: 1, 2, 4, 5, 7, 8, and 10.The probability of choosing a card not

divisible by three = .

3

4 a Of 12 possible outcomes, there are 6 outcomes in which a yellow is chosen. There are only 3 outcomes for both red and black, so the most likely colour is yellow.

b There are 6 outcomes where a yellow is chosen.The probability of randomly choosing a yellow lolly = = .

c There are 3 outcomes where a black is chosen.The probability of randomly choosing a

yellow lolly = = .

d There are 9 outcomes where a red is not chosen.The probability of randomly choosing a lolly

that is not red = = .

e There are no green lollies so there are 12 outcomes where a green is not chosen.The probability of randomly choosing a lolly

that is not green = = 1.

d25 48

Chapter 13

0 0·5 1·0

a f c d e b

16---

56---

36--- 1

2---

36--- 1

2---

110------

310------

710------

510------ 1

2---

310------

710------

0 0·5 1·0

0·1 0·3 0·5 0·7

612------ 1

2---

312------ 1

4---

912------ 3

4---

1212------

78



5

6 a Of 30 possible outcomes, there are 18 outcomes in which a girl is chosen. There are only 12 outcomes in which a boy is chosen, so a girl is more likely to be chosen.

b Each child has a chance of being chosen

whatever their gender.

c There are 18 outcomes in which a girl is voted in.The probability of randomly choosing a girl

= = .

d There are 12 outcomes in which a boy is chosen.The probability of randomly choosing a boy

= = .

7 a There are 5 possible outcomes and 1 positive outcome in which an E is chosen.The probability of randomly choosing the

letter E = .

b There are 8 possible outcomes and 1 positive outcome in which an E is chosen.The probability of randomly choosing the

letter E = .

c There are 6 possible outcomes and 0 positive outcome in which an E is chosen.The probability of randomly choosing the letter E = 0.

d There are 9 possible outcomes and 2 positive outcomes in which an E is chosen.The probability of randomly choosing the

letter E = .

e There are 6 possible outcomes and 1 positive outcome in which an E is chosen.The probability of randomly choosing the

letter E = .

f There are 8 possible outcomes and 1 positive outcome in which an E is chosen.The probability of randomly choosing the

letter E = .

8 a There are 5 possible outcomes and 1 positive outcome in which an R is chosen.The probability of randomly choosing the

letter R = .

b There are 8 possible outcomes and 1 positive outcome in which an R is chosen.The probability of randomly choosing the

letter R = .

c There are 6 possible outcomes and 1 positive outcome in which an R is chosen.The probability of randomly choosing the

letter R = .

d There are 9 possible outcomes and 1 positive outcomes in which an R is chosen.The probability of randomly choosing the

letter R = .

e There are 6 possible outcomes and 0 positive outcome in which an R is chosen.The probability of randomly choosing the letter R = 0.

f There are 8 possible outcomes and 2 positive outcome in which an R is chosen.The probability of randomly choosing the

letter R = .

9 The probability of choosing a boy from the first

class = = = 0·6. The probability of choosing

a boy from the second class = = = 0·58. So

choosing a boy from the first class is more likely.

10 The probability a randomly selected card is not a

heart is = .

11 There are 5 possible outcomes and 2 positive outcomes.

The probability of choosing a person with a hat is .

Learning task 13C1 a If you throw a coin 50 times you expect it to land

on tails 25 times.

f You would expect to get 0 heads 25% of the time, 1 head 50% of the time and 2 heads 25% of the time.

2 d You would expect to get a red counter in about one quarter of the trials.

e You would expect to get the other colour in about three quarters of the trials.

g You would expect to get a red counter in about one quarter of the trials.

h It is unlikely that a red counter will be chosen.

3 f There is an almost even chance of choosing a prime number.

g There is about a 40% chance of getting a prime number.

Learning task 13D

1 b The spinner will land on the yellow edge

approximately 13 out of 100 spins. Pr(Y) =

2 b The spinner will land on the red section

approximately 40 out of 100 spins. Pr(R) =

Learning task 13E

1 a There are 4 possible outcomes: two heads, head and tail, tail and head and two tails. Therefore the chance heads will occur is 1 out of 4.

d The probability a person who bets on heads will

win = .

0 0·5 1·0

0·25 0·5 0·75 1·0

130------

1830------ 3

5---

1230------ 2

5---

15---

18---

29---

16---

18---

15---

18---

16---

19---

14---

1220------ 3

5---

1424------ 7

12------

1 14---– 3

4---

25---

18---

25---

14---



Learning task 13F

1 a 13 b 13 c 13 d 13 e 26

f 26 g 4 h 4 i 12 j 40

2 a b 1

3 a b 25 times

4 a b c d e

f g h i

5 a b 51 c 12 d

e

f

g

Exercise 13G

1 There are 24 sections in the Wheel of Fortune spinner.

a i 9 sections are labelled with CD player

ii 2 sections are labelled with car

iii 0 sections are labelled with fridge

iv 4 sections are labelled with computer

b i Probability of winning a CD player

= =

ii Probability of winning a car = =

iii Probability of winning a fridge is 0

iv Probability of winning a computer

2 a There are 8 possible outcomes and 3 successes.

The probability of landing on a red edge =

which is possible.

b There are 6 possible outcomes and 5 successes.

The probability of landing on a red edge =

which is highly likely.

c There are 12 possible outcomes and 8 successes.

The probability of landing on a red edge = =

which is likely.

d There are 10 possible outcomes and 6 successes.

The probability of landing on a red edge = =

which is likely.

3 a b

c d

4

5 a There are 6 possible outcomes and 1 success.

The probability of landing on blue = .

b There are 8 possible outcomes and 3 successes.

The probability of landing on blue .

c There are 20 possible outcomes and 3 successes.


d There are 12 possible outcomes and 1 success.


6 a b c

7 a 10 red and 40 green b 4 red and 12 green

c 60 red and 40 green d 40 red and 20 green

e 10 red and 15 green f 30 red and 60 green

Technology Activity 13H

4 = 20 times

5

6 =

7 a 153

c

Exercise 13I

1

2 a b c

3 a b

c d

4 a Brisbane b Perth c Brisbane

d e f Melbourne g Canberra

5 a i ii iii iv

b Footscray CarltonWest Coast GeelongRichmond HawthornN. Melbourne Adelaide

152------

12---

14--- 1

4--- 1

4--- 1

4--- 1

2---

12--- 1

13------ 3

13------ 10

13------

14--- 4

17------

14--- 4

17------× 11

50------× 11

850---------=

14--- 4

17------× 11

50------× 10

49------× 11

4165------------=

14--- 4

17------× 11

50------× 10

49------× 3

16------× 33

66 640----------------=

924------ 3

8---

224------ 1

12------

16---

38---

56---

812------ 2

3---

610------ 3

5---

No. 1 2 3 4

Weight

16---

38---

320------

112------

15--- 100×

1 2 3 4 5

17

33

13--- 500× 1662

3---

13--- 1

6--- 1

6--- 1

3---

732------

524------ 1

6--- 3

8---

644 7002 435 100----------------------- 0·26= 38 200

2 435 100----------------------- 0·16=

1 823 3002 435 100----------------------- 0·75= 1 294 700

2 435 100----------------------- 0·53=

731------ 3

5---

411------ 5

11------ 3

11------ 13

22------

80



Puzzles

1

2 Because they lost all their matches.

3 He wanted to grow mashed potatoes.

Enrichment

1 a ABCD, ABDC, ACBD, ACDB, ADBC, ADCB,BACD, BADC, BCAD, BCDA, BDAC, BDCA,CABD, CADB, CBAD, CBDA, CDAB, CDBA,DABC, DACB, DBAC, DBCA, DCAB, DCBA

b 12 arrangements have Caroline sitting next to David.

There are 24 arrangements, so the probability

Caroline sits next to David = = .

c 12 arrangements have Brenton sitting next to David.

There are 24 arrangements so the probability

Brenton does not sit next to David = = .

d 4 arrangements have Amy sitting between Brenton and David.

There are 24 arrangements so the probability Amy is sitting between Brenton and David

= = .

e There are 120 arrangements with Elizabeth.

20 arrangements have Caroline sitting next to David so the probability Caroline sits next

to David = = .

20 arrangements have Brenton sitting next to David so the probability Brenton sits next

to David = = .

6 arrangements have Amy sitting between Brenton and David so the probability Amy is sitting between Brenton and David

= = .

f There are 6 arrangements in a circle.

4 arrangements have Caroline sitting next to David so the probability Caroline sits next

to David = = .

4 arrangements have Brenton sitting next to David so the probability Brenton sits next

to David = = .

2 arrangements have Amy sitting between Brenton and David so the probability Amy

is sitting between Brenton and David = = .

2 a There are 6 possible outcomes: two of them with A, two with B and two with C.

Pr(A) = =

Pr(B) = =

Pr(C) = =

b There are 6 possible outcomes: one of them A, four with B and one C.

Pr(A) =

Pr(B) = =

Pr(C) =

c There are 4 possible outcomes: two of them with A, one B and one C.

Pr(A) = =

Pr(B) =

Pr(C) =

3 a b

c d

4 a b c

5 a Pumpkin Soup; Steak; Cheesecake

Pumpkin Soup; Steak; Chocolate Mousse

Pumpkin Soup; Chicken; Cheesecake

Pumpkin Soup; Chicken; Chocolate Mousse

Pumpkin Soup; Lasagne; Cheesecake

Pumpkin Soup; Lasagne; Chocolate Mousse

French Onion Soup; Steak; Cheesecake

French Onion Soup; Steak; Chocolate Mousse

French Onion Soup; Chicken; Cheesecake

French Onion Soup; Chicken; Chocolate Mousse

French Onion Soup; Lasagne; Cheesecake

French Onion Soup; Lasagne; Chocolate Mousse

b 12 arrangements are possible.

c 6 arrangements have mousse as a dessert.

C E R T A I N E R E S

E L F F A R S H E A D

L I K E L Y E V E L I

B P A M E E C I D V A

I D D I C E N N E C G

S E E R T C A E F O R

S R D P F T H V I U A

O D D S T A C E N N M

P R O B A B I L I T Y

M I T A I L S T T E P

I E A N N E V R E R O

1224------ 1

2---

1224------ 1

2---

424------ 1

6---

20120--------- 1

6---

20120--------- 1

6---

6120--------- 1

20------

46--- 2

3---

46--- 2

3---

26--- 1

3---

26--- 1

3---

26--- 1

3---

26--- 1

3---

16---

46--- 2

3---

16---

24--- 1

2---

14---

14---

666 22

1 CC

C BA

A

A B BB

BCCD A

B B

CC



d i There are 12 possible outcomes and 6 with chocolate mousse as the dessert so the probability of a person chosen at random having

chocolate mousse as a dessert = = .

ii There are 4 outcomes with steak as the main so the probability of a person chosen at random

having steak as the main = = .

iii There are 6 outcomes with pumpkin soup as the starter so the probability of a person chosen at random having pumpkin soup as

the starter = = .

iv There are 0 outcomes with cheesecake as a dessert and fish as a main so the probability of a person chosen at random having cheesecake as a dessert and fish as a main

= = 0.

v There are 8 outcomes with pumpkin soup or lasagne so the probability of a person chosen at random having pumpkin soup

or lasagne = = .

6 a Pumpkin Soup; Steak; Cheesecake

Pumpkin Soup; Steak; Chocolate Mousse

Pumpkin Soup; Steak; Strawberry Torte

Pumpkin Soup; Fish; Cheesecake

Pumpkin Soup; Fish; Chocolate Mousse

Pumpkin Soup; Fish; Strawberry Torte

Pumpkin Soup; Vegetable Lasagne; Cheesecake

Pumpkin Soup; Vegetable Lasagne; Chocolate Mousse

Pumpkin Soup; Vegetable Lasagne; Strawberry Torte

French Onion Soup; Steak; Cheesecake

French Onion Soup; Steak; Chocolate Mousse

French Onion Soup; Steak; Strawberry Torte

French Onion Soup; Fish; Cheesecake

French Onion Soup; Fish; Chocolate Mousse

French Onion Soup; Fish; Strawberry Torte

French Onion Soup; Vegetable Lasagne; Cheesecake

French Onion Soup; Vegetable Lasagne; Chocolate Mousse

French Onion Soup; Vegetable Lasagne; Strawberry Torte

b 18 arrangements are possible.

c 6 arrangements have mousse as a dessert.

d i There are 18 possible outcomes, 6 with chocolate mousse as the dessert so the probability of a person chosen at random having chocolate mousse as a dessert

= = .

ii There are 6 outcomes with steak as the main course, so the probability of a person chosen at random having steak as the

main course = = .

iii There are 9 outcomes with pumpkin soup as the starter, so the probability of a person chosen at random having pumpkin soup

as the starter = = .

iv There are 2 outcomes with cheesecake as a dessert and fish as a main so the probability of a person chosen at random having cheesecake as a dessert and fish as a

main course = = .

v There are 12 outcomes with pumpkin soup or lasagne so the probability of a person chosen at random having pumpkin soup

or lasagne = = .

Revision

1 c Unlikely e Negligible

2

3 a

b There are 32 successes out of 50 so the probability of getting a red marble is about

= or 64%.

c There are 18 successes out of 50 so the probability of getting a black marble is about

= or 36%.

d The number of marbles in the bag is 30 and the

probability of getting a red marble is about

so the number of red marbles in the bag is

about 30 × = 19·2 ≈ 19 red marbles.

4 a There are 30 possible outcomes and 10 successes so the probability of getting a

black marble = = .

b There are 30 possible outcomes and 0 successes so the probability of getting a

black marble = = 0.

c There are 30 possible outcomes and 20 successes so the probability of getting a

black marble = = .

d There are 30 possible outcomes and 20 successes so the probability of getting a

marble that is not black = = .

612------ 1

2---

412------ 1

3---

612------ 1

2---

012------

812------ 2

3---

618------ 1

3---

618------ 1

3---

Colour Number Probability as fraction

Probability as a

percentage

Red 32 64%

Black 18 36%

Total 50

918------ 1

2---

218------ 1

9---

1218------ 2

3---

0 0·5 1·0

e c

3250------

1850------

3250------ 16

25------

1850------ 9

25------

1625------

1625------

1030------ 1

3---

030------

2030------ 2

3---

2030------ 2

3---

82



5 There are 6 possible outcomes: 1, 2, 3, 4, 5, and 6.There are 3 positive outcomes: 1, 3 and 5.So the probability an odd number shows is

= .

6 There are 20 possible outcomes and 8 outcomes where a girl is chosen.So the probability that a girl is randomly selected

from the group = = .

7 There are 12 possible outcomes from selecting the cards.

a There are 5 positive outcomes: 2, 3, 5, 7 and 11.The probability of choosing a card with a

prime number = .

b There are 7 positive outcomes: 1, 4, 6, 8, 9, 10 and 12.The probability of choosing a card without a

prime number = .

8 All probabilities add to 1 so the probability a three-child family does not have three boys

= 1 − = .

9 a There are 25 possible outcomes and 8 outcomes with blue eyes.The probability of a person having blue eyes

= .

b There are 25 possible outcomes and 11 outcomes without brown eyes.The probability of a person not having brown

eyes = .

10 a Half of the number of spins are red, almost a quarter are white and another quarter blue so you could expect the spinner to be half red, a quarter white and a quarter blue.

b

11 a There are 8 possible outcomes and 5 successes.

The probability of landing on a red edge = .

b There are 4 possible outcomes and 1 success.

The probability of landing on a red edge = .

12

A registered vehicle is most likely to be involved in an accident in the Northern Territory.

Exercise 14A

1 a Shoe size, number of matches in a box, number of cars in a parking lot

b Height, length, time

2 a Discrete b Continuous

c Discrete d Discrete

e Continuous f Discrete

g Discrete h Discrete

i Discrete j Continuous

3 a Popcorn b Soft drink c 19

d 36 e 57

4 a

b 8 students walk to school.

c Car and bus were the most frequently used means of getting to school, each used by 9 students.

5 a

b The home team scored 7 goals in the second quarter.

c The visitors won by 2 goals, 25 to 27.

d The home team GS scored the highest with 17 goals.

6 a 52 cars travelling south are turning right.

b 121 cars are travelling south and continuing straight ahead.

c 67 cars are travelling north and continuing straight ahead.

d Although most cars travelling south go straight through the 52 cars travelling right will struggle to turn between the 67 going north.

State Probability

NSW

Vic

Qld

SA

WA

Tas

36--- 1

2---

820------ 2

5---

512------

712------

18--- 7

8---

825------

1125------

58---

14---

5633 332 500----------------------- 0·0169%=

3712 869 900----------------------- 0·0129%=

4082 012 900----------------------- 0·0203%=

163962 800------------------- 0·0169%=

1941 175 500----------------------- 0·0165%=

53319 900------------------- 0·0166%=

NT

ACT

Transport Tally Frequency

Car 9

Bus 9

Walk 8

Skateboard 1

Bike 3

Qtr Home team Total Visitors Total

1 GS 2 GS 6

GA 2 GA 4

2 GS 6 GS 6

GA 1 GA 3

3 GS 3 GS 0

GA 3 GA 2

4 GS 6 GS 1

GA 2 GA 5

Final score 25 Final score 27

State Probability

5690 400---------------- 0·0619%=

14183 800------------------- 0·0076%=

Chapter 14

| | | | | | | |

| | | | | | | |

| | | | | | |

|

| | |

| | | | | | |

| | | | | |

| | | | | | | | | |

| | | |

| | |

| | | | |

| | | | | |

| | | | | |



7

8 a Continuous. The data is grouped into classes.

b 7 c 11 d 26

Exercise 14B

1 a 1 b 7

c Thailand d Iran and Thailand

e Thailand f Iraq

g Iran h Bahrain and Thailand

2

3 a 2 b 3

c Leo d 4

e There are no Year 7 day students.

f Kyle, Leo and Huw are Year 8 male students.

Exercise 14C

1 a Asia

b Australia/Pacific

c About 28 cities in Europe have a population greater than 1 million.

d The Americas and Africa

e About 100 cities in The Americas and Africa have a population greater than 1 million.

2 a Catholic

b 3 000 000 people have claimed no religion.

c 500 000 people have claimed to have a non-Christian religion.

d 12 500 000 people total have claimed to have a Christian religion.

e Three religions—Anglican, Catholic and Other Christian—had more than 3 million followers.

3

4

5 a The washing is most likely to be done by a woman.

b Home maintenance is most likely to be done by a man.

c In about 42 families out of 100, the women do the gardening.

d In about 39 families out of 100, the men do the shopping.

6 a USA won the most gold medals.

b Russia won the most silver medals.

c USA won the most bronze medals.

d USA won the most medals in total.

e Cuba won the same number of bronze and silver medals.

f Britain won about 9 silver medals.

g Germany won more gold medals than any other type.

Exercise 14D

1 a The horizontal axis represents the first eleven days in February.

b The vertical axis represents the US cents per Australian dollar.

c 56·6 US cents could be purchased by one Australian dollar on 4 February.

d 2 February = 57·79 February = 55·5

Difference = 57·7 – 55·5= 2·2

There was a 2·2 cents difference in US cents per Australian dollar between 9 February and 2 February.

e The Australian dollar was equivalent to 55·9 US cents on 6 February.

f i The overall trend in the Australian dollar for the first part of February was a decrease in value against the US dollar.

ii This trend is seen on the graph by a downwards sloping line.

Number of Fries

Frequency

31 – 40 6

49 – 50 6

51 – 60 9

61 – 70 2

71 – 80 1

Name SexFor M

Yearlevel

Boardingor day

Favouritesubject

Language Siblings Pets

Beth F 7 Boarding Maths French 2 1

Kyle M 8 Day PE Chinese 1 4

Sarah F 8 Day Music Chinese 2 3

Leo M 8 Boarding Maths Chinese 1 0

Huw M 8 Day Maths Chinese 3 3

Laura F 8 Day Art French 2 6

0 10 20 30 40 50 60

BlackBrownGreenWhiteC

olou

r

BlueRed

Frequency

Most popular colour

Country

Number of people granted citizenship

04080

120

160

Britain

China

Vietna

mIn

dia

Phili

ppin

esS

Africa Iraq

Sri L

anka

Bosni

a

Herze

govi

na

New Z

ealan

d

84



2 a The horizontal axis represents the time after Angela started exercising.

b The vertical axis represents Angela’s pulse rate.

c Angela had 80 beats per minute after two minutes.

d Total beats= 65 + 80 + 85 + 100 + 100= 430

After 5 minutes the heart had done about 430 beats altogether.

e After 4 minutes the pulse rate was at 100 beats per minute.

f i There was a large increase in the heart rate between minutes 1 and 4.

ii You can tell this by looking at the graph as there is a steep positive slope.

g i The heart rate stayed the same between minutes 4 and 5.

ii You can tell this by looking at the graph as the slope is flat.

h i The heart rate was decreasing from the 5th minute.

ii A downwards slope to the line shows that there was a decrease.

i It took 9 minutes for the pulse rate to go back to the before exercise rate.

Exercise 14E1 a NSW has the largest population at 33%.

b 8% of the population lives in South Australia.

c 33% of the population lives in NSW.

d Northern Territory has 1% of the population.

2 a

b WA is the largest state by area.

c Tasmania is the smallest state by area.

3 a Ben saves 10 − 4 − 2·50 = $3·50 each week.

b i × 100 = 40%

ii × 100 = 25%

iii × 100 = 35%

c

4 a × 100 = 20%

b Contaminants × 100% = 1·5%

Garbage × 100 = 75%

Green waste × 100% = 3·5%

c

Exercise 14F

1 a The slowest speed was 43 km/h.

b The fastest speed was 54 km/h.

c

d The mode is 49 km/h, which appears 8 times.

e 10 of the 40 cars were speeding.

2 a The highest number of goals scored in the season was 51.

b The lowest number was 45.

c

d The modal number of goals was 46.

3 a The best typing speed was 45 words per minute.

b The slowest typing speed was 28 words per minute.

c

d The modal score was 34 words per minute.

4 a The mode was 7 b

hours of homework.

d 49 km/h e 10

5 a

b The mode was 2 goals per game.

c

6 a

b

c The test results were much higher for the second test.

7 a This is discrete data as the data hasdefinite values.

b 4 students estimated correctly.

Percentage areaNSW

NT

QLDSA

TASVIC

WA

410------

2·510-------

3·510-------

Ben s pocket money

LolliesMagazineSave

420------

0·320-------

1520------

0·720-------

Goals kicked Tally Frequency

1 6

2 13

3 8

4 4

5 2

Waste types

GarbageRecyclablesContaminantsGreen Waste

54 5551 52 5348 49 5045 46 4742 43 44Speeds

45 46 47 48 49 50 51Goals

40 42 4434 36 3828 30 32Typing speeds

9 1076 8Hours of homework

| | | | |

| | | | | | | | | | |

| | | | | | |

| | | |

| |

3 4 50 1 2 Goals

9 106 7 83 4 50 1 21st test scores

9 106 7 83 4 50 1 22nd test scores



c

d 11 students gave estimates that were too short.

e The modal estimate was 13 cm.

f The data suggests that most students have a good perception of length.

8 a This is discrete data as the data has definite values.

b

c There were 6 months with at least 10 koalas.

d There were 4 months with fewer than 8 koalas.

e The mode was 10 koalas.

9 a The mode was 4 koalas

b There were 3 months with at least 10 koalas.

d There were fewer koalas than in the previous year. There were 6 months in the previous year in which there were at least 10 koalas.

Exercise 14G

1 The total of the results is 1956.

The mean = = 48·9 km/h

2 The total of the results is 294·5.

The mean = ≅ 12·3 cm

3 a The total of the results is 1498.

The mean = = 74·9

b 11 scores were above the mean.

c 9 scores were below the mean.

4 The total of the results is 1052.

The mean = ≅ 35 wpm

5 The total of these results is 82.

The mean = ≅ 2·5 children

6 The total of these results is 4847.

The mean = ≅ 161·6 cm

7 a The total of these results is 240.

The mean = = $12

b 11 students received less than the average per week.

c i $50

ii Without this data point, the new mean is

= $10

iii The second value is a better estimate of the real mean as the first was distorted by an outlier. This can be a problem when using the mean of data.

8 a i The total is 113. The mean for the first test

is ≅ 4·2.

ii The total is 217. The mean for the second

test is ≅ 8·0.

b The difference in the means indicates that the scores were much higher across the board in the second test.

9 Edwin wants an average of 40 words over 10 tests, so a total of 40 × 10 = 400. He already has 38·5 × 9 = 346·5 so he must get 400 − 346·5 = 53·5 on the tenth test.

10 Jane needs an average of 24 over 12 games, so a total of 24 × 12 = 288 goals. She already has 227 goals, so she must get 288 − 227 = 61 goals in the 12th game to retain her place in the team.

11 a City 1: The total of these results is 160.

The mean number of dogs is = 16.

City 2: The total of these results is 180.

The mean number of dogs is = 18.

b On average, City 2 had more dogs in each council than City 1.

c The last result for City 2 should be 10. This would give the same average.

Exercise 14H

1 The median of the results is 49. The range is 54 − 43 = 11.

2 a i The median is 265.

The mean is = 271.

The range is 323 − 230 = 93.

ii The median is 265.

The mean is = 249.

The range is 323 − 100 = 223.

iii The median is 265.

The mean is = 298.

The range is 487 − 230 = 257.

iv The median is 265.

The mean is = 277.

The range is 487 − 100 = 387

b The mean of a set of data is much more affected by an outlier. Here we saw that the median did not change, although the mean (and also range) changed significantly.

3 The median number of children in each family is 2.

4 a

b The median score was 75 and the range is 80 − 72 = 8.

c 7 scores were above the median.

d 9 scores were below the median.

13 1410 11 12Centimetres

15 16 1712 13 149 10 116 7 83 4 5Number of koalas

15 1612 13 149 10 116 7 83 4 5Number of koalas

195640

------------

294·524

-------------

149820

------------

105230

------------

8233------

484730

------------

24020

---------

19019

---------

11327

---------

21727

---------

16010

---------

18010

---------

16266

------------

14966

------------

17906

------------

16606

------------

7877 8079767572 7473

86



5 a The median was 12·5 cm.

b The range was 14·5 − 10 = 4·5 cm.

6 a The median amount of pocket money was $9·75.The range of pocket money was $50 − $3·5 = $46·50.

b The mean of these results is = $12.

c i The mean is higher than the median.

ii The median is more reliable as the mean is affected by the outlier of $50.

7 The median of the dot plot is 14.

8 a The mean height for squad A is = 170 cm.

The mean height for squad B is = 170·6 cm.

b The median height for squad A is 169·5 cm.The median height for squad B is 171·5 cm.

c Team A: 200 − 152 = 48 cmTeam B: 175 − 154 = 21 cm

d There is more variation in the heights of Team A players but the mean and medians are both around 170.

Exercise 14I

1 a Median is 46, range is 48

b Median is 65, range is 48

c Median score is = 120.

Range is 37.

2 a 4 1 4 4 8 8 9 Life expectancies5 0 86 1 4 5 6 87 1 2 2 3 4 4 58

b Highest life expectancy is 75. Lowest life expectancy is 41.

c Median life expectancy is 64·5.

3 a b

1 7 Typing speeds2 4 6 8 9 93 4 5 5 6 6 8 94 1 3 5 95 4 6 7 86 2 2 2 5

7 2 4 48 1 2

c The median typing speed is .

The range is 82 − 17 = 65.

4 a

1 2 8 Number of absentees2 3 5 6 7 7 8 93 2 4 6 7 7 8 94 0 1 2 3 3 5 6 8 95 0 1 1 2 2 3 4 5 6 6 6 86 1 2 3 3 5 9

b The median number of absentees was 45.The range was 69 − 12 = 57.

Exercise 14J

1 a The number of students surveyed was17 + 20 + 10 + 3 = 50.

b 3 students didn’t like either kind of music.

c 20 students listened to both kinds of music.

2 a The number of students surveyed was93 + 24 + 40 + 23 = 180.

b 24 families owned a sedan and a wagon.

c 64 families owned a wagon.

d Those without either type of car could use public transport or another type of vehicle.

e 40 out of 180 families only owned a wagon = 22%.

3 a The total number of students is 42 + 5 + 50 + 3 = 100.

b 47 students study French.

c 5 students study two languages.

d 3 students study no language.

4 a The total number of students is12 + 7 + 21 + 8 = 48.

b 28 students play soccer.

c 7 students play both sports.

5 a

b 16 + 104 + 52 + 12 = 184 people were surveyed.

c 16 people had travelled on a plane but not a train.

d 172 people had travelled on either a plane or a train.

6 14 of the 30 students

had blond hair andblue eyes, i.e. approximately half.

8 a b 20

b 12 + x + 17 + 15 = 65, so 20 people liked both hamburgers and fish and chips.

Exercise 14K

1 a

80 students were surveyed.

b 23 students didn’t like either type of music.

c 12 students listened to both types of music.

24020

---------

13608

------------

13658

------------

114 126+2

------------------------

43 45+2

------------------ 44=

Rap Not rap Total

‘Girl’ bands 12 10 22

Not ‘Girl’ bands 35 23 58

Total 47 33 80

10416 52

12

Plane Train

146 3

7

Blond hair Blue eyes

2013 17

15

Fish andchips Hamburgers



2 a

100 families were surveyed.

b 14 families owned a sedan and a wagon.

c 10 out of 100 families owned only a wagon = 10%.

3

Kathy was wrong.

4 a

b 71 pairs of stretch jeans were sold.

c The most popular pairs were non-denim stretch jeans.

d 23 of the 120 pairs sold were stretch denim, i.e. about 19%.

5 a

b 99 people were surveyed.

c 31 people had travelled on a plane but not a train.

d 87 people had travelled on either a plane or a train last year.

6 a

b The most popular destination was Indonesia.

c 36 out of the 100 passengers had visited Indonesia, i.e. 72%.

7 a

b The most popular city was Paris.

c 53 out of the 100 passengers visited Paris so 53%.

Puzzles

1 Melbourne

2 The crew was marooned

3 It quacked up

Enrichment

1 a 56 people used whitebait only.

b No—27 people used only prawns, 23 used prawns and whitebait, 4 used prawns and octopus, and 3 used all three types. So 57 people used prawns altogether.

c The total number of people surveyed was 27 + 23 + 56 + 3 + 2 + 4 + 13 = 128.

d 27 + 4 = 31 people used prawns but not whitebait, and 56 + 2 = 58 people used whitebait but not prawns, so the total was 89.

e 13 used only octopus, 56 used only whitebait, 27 used only prawns. The total is 96.

2

a The probability that a person sampled at random will like tennis is 12 out of 20 = 0·6.

b The probability that a person sampled at random will not like tennis is 8 out of 20 = 0·4.

c The probability that a a person sampled at random will like basketball is 18 out of 20 = 0·9.

d The probability that a person sampled at random will like both sports is 10 out of 20 = 0·5.

3 a

b The difference between maximum and minimum temperatures was greatest in January and February.

c The temperature difference was smallest in June and July.

4 a

c 14 4 8 9 Height in cm15 3 3 4 6 6 7 816 0 1 1 2 2 2 3 3 4 5 6 6 7 7 8 917 0 1 4 8

If we turn the stem-and-leaf plot on its side, we can see it is the same shape as the histogram.

Sedan Not sedan

Total

Wagon 14 10 24

Not wagon 51 25 76

Total 65 35 100

Bike Not bike

Total

Computer 6 6 12

Not computer 11 7 18

Total 17 13 30

Denim Not denim

Total

Stretch 23 48 71

Not stretch 12 37 49

Total 35 85 120

Train Not train

Total

Plane 34 31 65

Not Plane 22 12 34

Total 56 43 99

Indonesia Not Indonesia

Total

Japan 24 6 30

Not Japan 12 8 20

Total 36 14 50

Paris Not Paris

Total

Moscow 21 30 51

Not Moscow 32 17 49

Total 53 47 100

Height Tally Frequency

140−<150 3

150−<160 7

160−<170 16

170−<180 4

Total 30

102 8

0

Tennis Basketball

Month

Tem

pera

ture

(¡C

)

Temperatures

05

15

10

20

2530

Jan Feb Mar AprMay Jun Jul Aug Sep Oct Nov Dec

Max tempMin temp

| | |

| | | | | |

| | | | | | | | | | | | |

| | | |

88



5 a i

ii

b Males tend to fall into the higher income brackets.

Revision 1 a Categorical

b

c The favourite fast food was pizza.

2 a 4 females strongly agree that PE should be compulsory.

b 5 males strongly agree that PE should be compulsory.

c 3 students strongly disagree that PE should be compulsory.

3 a

b The most popular subject was Art.

4 a 65% of males preferred soccer.

b 55% of females preferred soccer.

5 a The horizontal axis represents the speed at which the Commodore is travelling.

b The vertical axis represents the amount of petrol that is being consumed.

c The petrol consumption at 60 km/h is 8 L/100 km.

d 120 km/h = 12 L90 km/h = 10 L

Difference = 12 − 10= 2 L

Travelling at 120 km/h uses up 2 more litres per 100 km than travelling at 90 km/h.

e The most efficient speed at which to drive the car is 60 km/h as the petrol consumption is lowest.

f The least efficient speed at which to drive the car is 30 km/h as the petrol consumption is highest.

6

7 a 20 games were played.

b The modal number of goals scored was 3.

8 a

b The total for these results is 132 so the mean is

≅ 5.

9 a The total for the first 9 bags was 318, so the

mean is ≅ 35·3.

b The total for the first 9 bags was 318.

c If the mean number of lollies in the ten bags is 35, the total number of lollies in the bags must be 350. So the tenth bag must contain 350 − 318 = 32 lollies.

10 a 0 41 0 1 2 5 6 72 1 3 3 5 6 73 2 2 4 4 6 74 5 5 85 0 1 4 4 5 6 6 6 8 96 2 3 4 5 5 5 6 7 97 2 3 3 3 4 4 5 58 4 5 5 6 79 9

b His median score is 56.

c His range is 99 − 4 = 95.

d His mean score is ≅ 51·3.

11 a

b The number of thefts peaked in March–April, then in the following January. In general, there seem to be more thefts in the summer months.

Salary male Tally Frequency

< $20 000

$20 000–39 999

12

$40 000–59 999

22

> $60 000

11

Salary female

< $20 000

14

$20 000–39 999

20

$40 000–59 999

14

> $60 000 6

Favourite fast food

Tally Frequency

Hamburgers 5

Pizza 8

Pies 3

Chips 4

Chicken 5

Total 25 25

| | | | | | | || |

| | | | | | | || | | | | | | || |

| | | | | | | ||

| | | | | | | || | | |

| | | | | | | || | | | | | | |

| | | | | | | || | | |

| | | | |

Income bracket

Salaries

Freq

uenc

y

05

1510

2025

<20 000 20–40 000 40–60 000 >60 000

MaleFemale

| | | |

| | | | | | |

| | |

| | | |

| | | |

SubjectLOTE Maths Sci. Engl. Art SOSE

Favourite subject

Freq

uenc

y

02

64

8

14

1012

Most worrying issue

EnvironmentUnemploymentWarThe economy

0 1 2 3 4 5 6 7

6789

543N

umbe

r Abs

ent

21

Frequency

13226

---------

3189

---------

282355

------------

100806040200

Number of thefts

The

fts

J F M A M J J F M A M JJ A SMonth

O N D



c The thefts decreased in May–July, the winter months.

d The mean number of thefts for the 18 months is 1141 ÷ 18 = 63·4.

12 a

Parents mostly think that their children should have more homework but students want less.

13 The median number of goals scored is 30.The range is 72 − 18 = 54.

14 a There are 24 students in the class.

b 6 students play both netball and soccer.

c 13 students play soccer.

d 10 students don’t play netball.

15 The two-way table shows the results of the survey on windcheaters.

a

b 100 windcheaters were sold.

c The most popular windcheater is the short-sleeved one without a hood.

d 32 out of the 100 or 32% of the windcheaters sold had hoods.

Hoods No hoods

Total

Long-sleeved 15 18 33

Short-sleeved 17 50 67

Total 32 68 100

No YesStudents Teachers Parents

Do year 8 student have too much homework?

0

302010

405060

Worksheet Answers

Worksheet 1: Revision Sheet 11 a 98 456, 6380, 3438, 534, 348, 23

b 773, 763, 673, 376, 367, 337

c 555, 550, 505, 500, 55, 50, 5

2 a Three hundred and sixty

b One hundred and thirty-seven thousand, two hundred and thirty-nine

c Eighty-three

3 a 3216 b 2 422 609 c 30 546

4 a 5206 b 8363 c 24 491

d 10 498 e 694

5 a 527 b 5015 c 15122

d 332 e 3778

6 a 1548 b 66 231 c 772 250

d 15 870 e 6524

7 a 107 b 245 c 3789

8 $236 000

9 a 6600 b 120 c 800

d 4780 e 320 f 2360

10 a 8 b 21 c 52 d 3 e 8 f 7

11 a XXIV b CXXXV c CLIII

12 a 16 b 252 c 45

Worksheet 2: Revision Sheet 21 a 8, 16, 24, 32, 40, 48, 56

b 4, 8, 12, 16, 20, 24

c (6, 12, 18, 24, 30, 36, 42, 48, 54) (9, 18, 27, 36,45, 54)

d 18

e (7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84)(12, 24, 36, 48, 60, 72, 84)

f 84

2 a 1, 24, 2, 12, 3, 8, 4, 6

b 1, 36, 2, 18, 3, 12, 4, 9, 6

c 1, 2, 3, 4, 6, 12 d 12 e 36

3

4 a composite b composite c neither

d prime e prime

5 a 35 b 83 c 41

6 a 5 × 5 b 6 × 6 × 6 c 12 × 12 × 12 × 12

7 a 31 b 343 c 25

8 a 36 b 4 c 144 d 225 e 676

f 6 g 8 h 12 i 0·6 j 0·11

9 a 2 × 33 b 2 × 53

c 23 × 32 × 5 d 52 × 7 × 11

10 a even b odd c odd d even

11 a 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78

b 14, 18, 22, 26 c 11, 13, 15

Worksheet 3: Revision Sheet 3

1 a b

2 a b c d

3 a Proper b Improper

c Mixed number

4 a = = =

b = = c = =

5 a b c d

6 a b c d

7 a b c d

8 a b c d

9 km

10 a b c d

11 a b c d

12 a b c 15 d

13 of a tank

14 a 6 b 12 c 15 hours d 750 grams

15 a b c d

16 a 8 b 2 c 4 d 3

Worksheet 4: Revision Sheet 41 a Tens b Tenths

c Hundreds d Hundredths

e Ten-thousandths f Units

g Hundredths h Ten-thousandths

2 a 27·9 b 1·36 c 12·162 d 1·6

e 0·04 f 12·600 g 0·64 h 2·0

3 a 65·32 b 1892·563 c 2·05

d 202·77 e 0·68 f 0·698

4 a $363·45 b Michael c $87·60

5 a 100·8 b 2·32 e 1·85

d 75·6 e 95·04 f 1588·8

6 a 13·63 b 2·4 c 104·57

d 35·75 e 6·54 f 5·05

7 a $16·78 b $16·80 c $6·67

d The second one because it is cheaper per metre.

e 7·15 metres

8 a 423·6 b 5 678 900

2 3 4 5 8

4527 ✗ ✓ ✗ ✗ ✗

3472 ✓ ✗ ✓ ✗ ✓

120 ✓ ✓ ✓ ✓ ✓

1299 ✗ ✓ ✗ ✗ ✗

658 ✓ ✗ ✗ ✗ ✗

Revision Sheets15--- 1

3---

35--- 6

19------ 16

27------ 1

4---

34--- 7

5---

137---

27--- 4

14------ 12

42------ 16

56------

37--- 9

21------ 36

84------ 6

8--- 12

16------ 78

104---------

27--- 5

6--- 1

5--- 4

7---

157--- 21

2--- 31

7--- 41

9---

134

------ 327

------ 145

------ 299

------

79--- 119

36------ 41

8--- 343

45------

5 79126---------

1142------ 1 1

14------ 22

5--- 135

36------

310------ 16

125--------- 71

2--- 3 1

30------

23--- 2

3--- 21

2---

18---

19--- 5 1

16------ 2

5--- 41

2---

1Worksheet Answers

2

Worksheet Answers

c 367 020 d 286·2

e 15·6386 f 0·004 561 245

9 a 60% b 34% c 538% d 130%

10 a 58% b 163% c 27% d 67%

11 a 4·098, 4·589, 4·598, 4·895, 4·985

b 0·42, 46%, , 0·465, , 52%

12 a $12 b 40·5 cm c $400 d 300 cents

Worksheet 5: Revision Sheet 51 a m b cm or m c km d m

2 7 m

3 Check using your ruler.

4 3·5 cm

2·25 cm

1·2 cm

8 cm

0·3 cm

6.7 cm

5 a 5 cm (50 mm) b 6 cm (60 mm)

6 a 523 mm b 27 240 m c 21·5 cm

d 37 m e 0·0967 m f 0·617 km

g 35 mm h 2500 m i 75 cm

7 a 14 m b 35 m c 84 m

8 a 44 mm b 12 700 m c 3710 mm

9 a 126 km b 6 cm

10 a 60 mm b 48 cm c 6·85m d 34·5 m

Worksheet 6: Revision Sheet 61 a C or E b 7 square units

c 3 square units

2 A 4 square units B 4·5 square units

C 7 square units D 5·5 square units

E 7 square units F 3 square units

3 a 234 m2 b 4·32 mm2

4 a 382 m2 b 120 m2 c 124 mm2

5 a 20 cm3

6 a 16 cm3

7 a 78 cm3

8 a 168 cm3


1

2 a 600 years b 3·8 decades

c 3 centuries d 24 months

e 42 days f 120 hours

g 1080 seconds h 12 minutes

i 12 hours j 84 hours

3 a 20 days b 30 days

c 25 days d 23 days

4 a 14 years b 1011 years

c 210 years d 51 years

5 a 7:30 am b 11:50 am c 5:45 pm

d 11:10 pm e 4:15 am f 2:40 pm

g 9:55 pm h 10:37 am i 6:30 pm

6 a b c

d e

7 a 5 h 15 min b 3 h 42 min c 6 h 18 min

8 a i 6 h 50 min ii 3 h 55 min

b If the train and the taxi leave at the same time the brother in the train arrives first by 5 minutes.

c 8 h 40 min

9 a 3000 kg b 2900 kg

c 3090 kg d 2000 mg

e 4 256 000 mg f 660 000

g 5·29 g h 2·54 g

i 4·2 g j 3·33 t

10 a 18 460 g b 12·31 kg

c 1550 g d 5000 mg

Worksheet 8: Revision Sheet 81 a An acute angle is less than 90°.

b An obtuse angle is greater than 90° but less than 180°.

c A right angle is an angle 90° in size.

d A straight angle is an angle 180° in size.

e A reflex angle is greater than 180° but less than 360°.

f A revolution is an angle of 360°.

2 a 33° acute b 136° obtuse

c 320° reflex d 360° full circle

e 180° straight angle f 90° right angle

3 a b c

4

5 a 20° b 78° c 55°6 a 80° b 34° c 9° d 63°7 a 53° b 35° c 26°8 a 146° b 24° c 58° d 103°9 a 88° b 216° c 52°

Worksheet 9: Revision Sheet 91 a Obtuse-angles isosceles

b Acute-angled equilateral

c Right-angled scalene

2 a 68° b 50° c 26°3 a 92° b 109° c 132°4 a 144° b 92° c 126°5 Regular polygons have all angles the same size and all

sides the same length.

6 a Square b Hexagon c Octagon

7 a 1440° b 220°

613------ 12

24------

1600 1650 1700 1750 1800 1850 1900 1950

Cof

fee

May

onna

ise

Soda

wat

er

Fish

& c

hips

Coc

a-C

ola

Ban

ana

split

sV

egem

ite

Angle a° b° c° d° e°

Size 14° 38° 62° 115° 144°

28°

A

130°

X Y

Z

280°

d°


Worksheet Answers

Worksheet 10: Revision Sheet 101 A (3, 1) B (1, 6) C (2, 4) D (6, 4)

E (5, 3) F (5, 2) G (3, 4)

2

3 a 1:300 b 1:300 000

c 1:450 d 1:800 000

4 a 50 cm b 2 m c 70 cm d 1 km

5 a 040° b 110° c 200° d 306°

6 a b c

d e f

7 a i A (100, 800) ii B (400, 700)

iii C (0, 0) iv D (100, 300)

b i E ii G iii F

c i 500 m ii 300 m iii 400 m

d 180° 300 m e 045°


1 a ♣ + 2 b ♥ – 32 c

d 5♠ e

2 a c minus 5 b 3 times a

c y divided by 6 d 12 take away x

3 a 17♥ b 5♣c 18♦ d 6∇e 12a + 5b + 7c f ab + 10bc + 8ac

g 5xy + 7yz + 5zx

4 a 2x b 3p c 12a d 4b

e pq f ab g 16xy h 4mn

i apq j 6n k 10y l 24p

5 a b c

d e f

6 a 3a + 3b b 14a – 21 c x2 + 4x d 3x2 + 2x

7 a 11 b 4 c 18 d 1

8 a 1, 4, 8, 12 b 16 c

9 a The number of edges is 12.

b The number of edges is 9.

c v = 12 d f = 6

Worksheet 12: Revision Sheet 121 a 12 b 26 c 73 d 6 e 8

f 21 g 63 h 432 i 54

2 a 18 b 24 c 46 d 7 e 108 f 12

3 a 6 b 6 c 15 d 28 e 175 f 15

4 a 7 b 28 c 5 d 9 e –4 f

5 a Incorrect b Correct

c Incorrect d Incorrect

6 a b

c = 8

x = 12

7 a x ≥ 2 b x < 9 c y ≥ 3

d y > 12 e a ≤ 5 f b < 20

8 a x ≥ 2

b x < 3

c x > 7

Worksheet 13: Revision Sheet 131 a unlikely b likely c unlikely

d even chance e certain

2 a b c approximately 17

3 a b 0 c d

4

5 a b c

6

7 a b

c d

8 a b c

Worksheet 14: Revision Sheet 141 a Discrete numerical b Categorical

c Continuous numerical d Ordinal

6

5

4

3

2

1

1 2 3 4 5 6 7

y

x

J

H

G

I

60° S20°W

N45°E

140°

320°

N40°W

∇4----

♦3----

x2--- t

2--- x

4---

3ab

------ 7n4m------- 3x

4y------

212---

11 + x = 23x = 12

= 18

x = 10

x2--- 13+

2x3

------

1 2 x3

2 3 x4

6 7 x8

1425------ 11

25------

25--- 3

5--- 3

5---

Red

Blue White

512------ 1

6--- 1

2---

16---

A

B E

D

C

F

A

B C

B

A

C

A

B C

B

A

C

R

G G

R

R

B

15--- 3

5--- 2

5---

3Worksheet Answers

4

Worksheet Answers

2 a

b Football

3 a 85 b 55 c 25 d 5

4

5 a mean = 6·975, mode = 8·0, median = 7·05

b 5·5 c 3·7

6 a mean = 6.16 b mode = 10

c median = 6 d range = 9

7 a

b 16 c 22·875 d 32

c 46 f 21·5

8 a b c d

Worksheet 15: Chapter Test 1A

1 a

b $136 233 c $64 767

2 a Nine hundred and ninety-eight: 998

b One hundred and ninety-nine thousand, nine hundred: 199 900

c Nine thousand and fifteen: 9015

3 a 104 114 b 360 c 6785

d 90 e 43 399

4 Multiply 560 by ten and then double the answer.

5 a 2628 b 144 081 c 1 430 244

6 a $56 400 b 2425 c 1825

d $24 per ticket

7 a XXV b XV c CCL d C

8 a 2 b 4 c 11

9 a 20 eggs, 1 L of milk, 300 grams of cheese and 500 grams of mushrooms

b 25

10 a 54 b 124 c 2842

11 a 216 b 56 700 c 90

d 25 e 7 whole ones

Worksheet 16: Chapter Test 2A1 a 24 b 2 and 3 or 6 and 1

c LCM of 2 and 12 is 12

2

3 a 4 b 2 c 8

4 43, 17, 101, 5, 11

5 a 2 × 34 b 3 × 52

c 2 × 3 × 72 d 7 × 52 × 24

6 a i Odd, composite ii Odd, composite

iii Even, composite iv Odd, composite

v Odd, prime vi Odd, prime

b No. Two, an even number, is not a composite. All other even numbers are composite.

7 a 2 × 2 × 2 × 2 × 2 × 2

b 5 × 5 c 3 × 3 × 3 × 3

8 a 54 b 25 c 241

9 a 210, 215 b 81, 210

c 118, 210 d 210

10 a 16 b 4 c 5 d 1

Worksheet 17: Chapter Test 3A1 b 8

c

d = = = =

2 a Impossible, all improper fractions have their numerators bigger than their denominators and therefore are larger than 1.

b There are many possible answers.

c Impossible, all mixed numbers have a whole number and a fraction and therefore are larger than one.

d There are many possible answers.

3 a

b is larger than

4 a b c

5 a b

c d

Sport Tally Frequency

Football 9

Cricket 7

Swimming 2

Netball 2

Soccer 3

Darts 2

0 3 5 7

1 2 4 6 7

2 0 3 9

3 2 2 3 4

4 0 9

Expense Rank

Insurance 4

Loan repayment 1

Car expenses 3

Food & clothing 2

Entertainment 5

| | | | | | | |

| | | | | |

| |

| |

| | |

| |

Homework

TV

Eating Sleeping

School

3184------ 5

42------ 49

84------ 1

21------

Chapter Tests A

Groupsize

36 18 12 9 6 4 3 2 1

Numberof groups

1 2 3 4 6 9 12 18 36

824------ 2

6--- 24

72------ 32

96------ 4

12------

45--- 3

4---

614--- 83

8--- 423

36------

103

------ 133

------, 815--- 93

5---,

1 54---, 33

8--- 4 7

16------,


Worksheet Answers

6 km

7 a 80 b c $68

d e mL f

8 a 45 min b 65 min

c There are many possible answers: e.g.

d $24 e

9 a b

10

Worksheet 18: Chapter Test 4A1 a Units b Thousandths

c Thousands d Tenths

e Tens f Hundreds

2 a $157·82 b $319·58

c $172 686 d $6478·31

3 a 6·6 b 300·734

c 0·000 56 d 890·516

4 a 86·243 b 3·6

c It would become 8624.3 d 100

5 a 119 b 361·6 c 477·4 d 369·9

e 14·83 f 22·58 g 23·2 h 0·03

7

8

9 a b 76·4%

c Tom: 279, Emily: 275 d 38·75, 38·19

10 a 1·2 b 0·1024 c 0·04 d 1·5625

11 a 0·04 b 1·6 c 16·3216 d 6·5

12 a 6·078, 6·708, 6·780, 6·807

b 78·5%, , 0·82,

Worksheet 19: Chapter Test 5A1 a mm b km c mm or cm

d m e cm

2 a 3 lengths

b 1995 mm, cm, 202 cm, m

3 22 mm

1.8 cm

60 mm

0·05 m

33 mm

4 a 30·3 cm b 571 m c 1·40 m d 5·5 mm

5 a 54 m b 17·6 mm c 33 m

6 a 210 cm b 420 cm

7 36·3 km

Worksheet 20: Chapter Test 6A1 a Must have a rectangle in which

the length × width = 900 mm2

b Must have a triangle in whichhalf the base × height = 36 cm2

c Must have a prism in whichthe area of the base × height = 12 m2

2 Use the cm2 grid over the top to count the squares. Divide the shape up into rectangles and calculate the area of approximately 12 cm3.

3 a 912 cm2 b 672 m2 c 192 cm2

4 a 50 pavers b 15 whole packs

5 a 10 cm3 b 80 cm3

c Yes, V = 10 × 2 × 4 = 80 cm3

6 5·152 m3

7 40 boxes (Each dimension of the small box is such that the boxes can be stacked to cover a square of area 1m2 to a depth of 1 metre.)

8 a 48 cm3 b 70 cm3

9 The prism must have a height of 5 cm.

Worksheet 21: Chapter Test 7A1 The timeline should cover 12 to 14 years, the length

of the lives of the students.

2 a Milliseconds or seconds

Recipe for 8 scones Recipe for 4 scones

teaspoon of salt teaspoon of salt

2 cups of flour 1 cups of flour

cup of margarine cup of margarine

cup of water cup of water


teaspoon of salt 1 teaspoon of salt



1 cup of water 1 cup of water

813---

1235------

116--- 1871

2--- 13

24------

940------

15---

38--- 7

10------

12--- 1

4---

12--- 1

4---

13--- 1

6---

34--- 3

8---

34--- 1

4---

34--- 1

4---

12--- 5

6---

18--- 7

8---

0·857

0·250

0·455

0·875

14---

78---

67---

511------

66·6%

15·4%

37·5%

105%

38---

23---

213------

1 5100---------

3140------

45--- 9

10------

20012--- 21

4---

5Worksheet Answers

6

Worksheet Answers

b Hours or days c Centuries

d Minutes

3 a 6:20 pm 1820 hours

b 11:35 pm 2335 hours

4 a 240 b 5760 c 2 102 400

d 159 782 400 + 104 440 = 159 891 840 including leap years

5 a 24 hours b 75 min

c 30 months d 25 weeks

e 0·4 decades f 2000 kg

g 2500 mg h 0·450 t

6 392 minutes

7 Brickie A as Brickie B’s 50 hours working time will probably take him all week

8 6 October



10 a 6:30 pm b 10:30 am c 4:45 pm

d 10:15 pm e 12:30 am f 11:45 am

11 a 219 minutes b Show your teacher

12 a 25 packets

b The individual packets are $1·59 while those in the carton cost $2, so the individual packets are cheaper.

Worksheet 22: Chapter Test 8A1 a Angle sizes that add to give 90°

b Angle sizes that add to give 180°c An angle less than 90°d An angle greater than 90° but less than 180°e An angle greater than 180° but less than 360°f An angle 360° in size

2 a 180° b 90° c 60°3 a e° or ∠E b ∠CDE c ∠EFG

d 82° e 295°4 a 65° b 37° c 43°

d 44° e 56° f 98°

5 a b

6 a 24° b 156°c More than 66° and less than 156°

7 a 57° b 102° c 167° d 24°8 a 67° b 22° c 69° d 11°

9 a b c

Worksheet 23: Chapter Test 9A1 a 78° b 116° c 130° d 120°

2 a

b Obtuse angle is >90°, right angle is 90°, therefore sum of the angles of the triangle would be >180°.

c d

e All angles in equilateral triangles are 60°.

f

3 a 131° b 120° c 112° d 119°4 a a = 57°, b = 57°, c = 123° b 2·2 m

5 110°

6 a b 2160°

7 a All the interior angles add up to 180° which is a factor of 360°.

b Yes c No

Worksheet 24: Chapter Test 10A1 A (5, 2) B (2, 6) C (1, 2) D (4, 2) E (2, 3) F (1, 5)

2

3 a 400 m b 200 m c 180° d F

4 B 10°, C 45°, D 37°, E 52°, F 90°, G 45°5 a 270° 700 m b 400 m

c 026° for 450 m then due East for 500 m

35° 225°

H

G R

F

HG

F

G I

H

6

5

4

3

2

1

1 2 3 4 5 6

y

x

C

B

D

E

F

A


Worksheet Answers

6 a

NB scale 1:1000 or 1 cm = 10 m

b 70 m bearing 115°


1 a x + y b

c x + y – 2 d 2x + y – 3

2 a 4p b 18x c 16k

d 0 e 7r – 2s f 4x + 2

g 3w + 10x + 5y h 2s + 2t – u

3 a b 3p c d e f

4 a 4x b ab c 6xy

d 36m2n e 27a3 f 4x3

5 a 3a + 3b b 8x – 4y c 5x2 – x

d 10y – 2y2 e 21x + 10 f 4x2

6 a 12·56 cm b 62·8 mm c 408·2 mm

7 a Yes b No c Yes d No

Worksheet 26: Chapter Test 12A1 a 6 b 25 c 8 d 9 e 72

f 8 g 81 h 8

2 a 2 b 3 c 4 d 20 e 15

f 4 g 6

3 a x + 4 = 6 b g – 5 = 12x = 2 g = 17

c 4s + 6 = 22 d k + k – 13 = 1s = 4 k = 7

e 3f + 16 = 28f = 4

4 a x ≥ 2 b x < 1 c x ≤ 12 d x > 10

5 a x ≤ 10

b x > 2

c x ≥ 2

d x < 6

Worksheet 27: Chapter Test 13A1 Discussion should deepen student awareness of chance

events in daily life.

2 a Unlikely b Very unlikely

c Even chance d Certain

e Impossible f Very likely

3 a b c d e

4 a b c

5 Spinner B, as you would expect it would land on the shaded region about 33 times.

6 a 6 sectors Green, 3 Red, 3 Blue

b Green approximately 50, Blue approximately 25, Red approximately 25

c Green 0·5, Blue 0·25, Red 0·25


1 Mean = = 53·8 kg

Range = 75 – 40 = 35

2 I would disagree with the statements as 21 males and females strongly agree or agree that they feel safe at home, while only 9 disagree or strongly disagree that they feel safe at home.

3 a Mean 46 mode 45 median 46

b 7 c 56 matches

4

115°

10°

30°

280°

95 m

80 m

70 m

60 miii

ii

i

N

N

NN

Z

x2---

p2--- 12

t------ 2

3 f------ 3

5r----- 2t

5-----

9 10 x11

0 1 x2 3

0 1 x2 3

4 5 x6 7

12--- 1

13------ 2

13------ 3

4--- 1

52------

625------ 16

25------ 19

25------

Green

RedBlue

161330

------------

Day

Ice cream sales

Num

ber

of ic

e cr

eam

s

0 Mon

2

4

6

8

Tues Wed Thurs Fri

7Worksheet Answers

8

Worksheet Answers

b Wednesday c 4 ice creams

d The least number of ice creams were sold on Monday.

5 a

b $58 c $440

d mean 22, mode 2 and 20 e 0·1

Worksheet 29: Chapter Test 1B

1 a

b $203 744 c $98 256

2 a One thousand, nine hundred and ninety-six: 1996

b Ninety-nine thousand, eight hundred: 99 800

c Six thousand and fourteen: 6014

3 a 209 327 b 340 c 6672

d 80 e 132 298

4 Multiply 480 by ten and then double the answer.

5 a 5058 b 139 392 c 1 511 934

6 a $63 360 b 2705 c 2305

d $24 per ticket

7 a XXXXX b XX c XCCL d CD

8 a 24 b 6 c 9

9 a 30 eggs, 1·5 L of milk, 600 grams of cheese and 350 grams of mushrooms

b 35

10 a 53 b 218 c 5459

11 a 478 b 32 700 c 120

d 30 e 6 whole ones

Worksheet 30: Chapter Test 2B1 a 30 b 2 and 5 or 10 and 1

c LCM of 6 and 18 is 18

2

3 a 2 b 4 c 6

4 23, 2, 13, 19, 97

5 a 22 × 33 b 33 × 5

c 2 × 5 × 7 × 3 d 23 × 52 × 11

6 a i Even, composite ii Odd, prime

iii Odd, composite iv Odd, prime

v Odd, composite vi Odd, composite

b No. Two, an even number, is not a composite.All other even numbers are composite.

7 a 3 × 3 × 3 × 3 × 3

b 2 × 2 × 2 c 5 × 5 × 5 × 5

8 a 36 b 73 c 361

9 a 240, 155 b 240, 189

c 240, 134 d 24010 a 1 b 36 c 8 d 7

Worksheet 31: Chapter Test 3B1 b 12

c

d = = = =

2 a Impossible, all improper fractions have their numerators bigger than their denominators and therefore are larger than 1.

b There are many possible answers.

c Impossible, all mixed numbers have a whole number and a fraction and therefore are larger than one.

d There are many possible answers.

3 a

b is larger than

4 a 7 b 7 c 7

5 a , 5 b 7, 8

c , d 3 , 4

6 6 km

7 a 120 b c $75

d 3 e 112·5 mL f

8 a 48 min b 70 min

c There are many possible answers: e.g.

d $36 e

9 a b

0 1 2 2 3 5

1 0 1 6 9

2 0 0 4 5 6

3 3 5 7

4 1

5 2 8

Expense Rank

Insurance 3

Loan repayment 2

Car expenses 4

Food & clothing 1

Entertainment 5

Group size

48 24 16 12 8 6 4 3 2 1

Number of groups

1 2 3 4 6 8 12 16 24 48

Chapter Tests B

1236------ 3

9--- 36

108--------- 48

144--------- 6

18------

23--- 3

5---

14--- 11

24------ 11

36------

195

------ 23---

512------ 1

2--- 1

2--- 9

16------

23---

1128------

59--- 7

18------

1160------

14---

58--- 3

10------


Worksheet Answers

10

Worksheet 32: Chapter Test 4B1 a tens b tenths

c hundreds d units

e thousandths f thousands

2 a $154·64 b $418·48

c $262 789 d $3489·20

3 a 6·3 b 202·245

c 0·001 67 d 980·635

4 a 77·519 b 1·8

c It would become 7751·9 d 1000

5 a 348 b 170·4 c 358·2 d 963·3

e 13·49 f 46·56 g 39·7 h 0·06

6 The second one; it is 85 cents/litre while the first is 87 cents/litre.

7

8

9 a b 73·6%

c Tom: 261, Emily: 265 d 36·25, 36·81

10 a 5·046, 5·406, 5·460, 5·604

b 79·5%, , 0·85,

Worksheet 33: Chapter Test 5B1 a km b cm c m

d mm or cm e m

2 a 4 lengths

b 2 m, 208 cm, 205 cm, 1890 mm

3 31 mm

2·4 cm

50 mm

0·09 m

83 mm

0·2 cm

4 a 27·2 cm b 251 m c 2·4 m d 6·2 mm

5 a 36 m b 11·8 mm c 38 m

6 a 250 cm b 630 cm

7 39·1 km

Worksheet 34: Chapter Test 6B1 a Must have a rectangle in which

the length × width = 700 mm2

b Must have a triangle in which half the base × height = 32 cm2

c Must have a prism in which the area of the base × height = 10 m3

2 Use the cm2 grid over the top to count the squares. Divide the shape up into rectangles and calculate the area of approximately 12 cm3.

3 a 558 m2 b 1904 m2 c 308 cm2

4 a 62 pavers b 18 whole packs

5 a 12 cm3 b 96 cm3

c Yes, V = 12 × 4 × 2 = 96 cm3

6 5·886 m3

7 100 boxes (Each dimension of the small box is such that the boxes can be stacked to cover a square of area 1 m2 to a depth of 1 metre.)

8 a 66 cm3 b 36 cm3

9 The prism must have a height of 6 cm.

Worksheet 35: Chapter Test 7B1 The timeline should cover 12 to 14 years, the length

of the lives of the students.

2 a years b minutes

c days d seconds

3 a 4:10 pm 1610 hours

b 10:40 pm 2240 hours

4 a 900 b 21 600 c 7 884 000

d 599 184 000 + 410 400 = 599 594 400 including leap years

5 a 27 hours b 150 min

c 21 months d 32 weeks

e 0·3 decades f 3000 kg

g 4500 mg h 0·220 t

6 397 minutes





cup of water cup of water




cup of margarine 1 cup of margarine

1 cup of water 1 cup of water

14--- 1

8---

34--- 3

8---

12--- 1

4---

23--- 1

3---

38--- 5

8---

18--- 7

8---

34--- 1

4---

23---

0·375

0·714

0·750

0·364

34---

38---

411------

57---

111%

62·5%

33·3%

1 84·6%

13---

58---

1113------

11100---------

2940------

56--- 7

8---

15--- 1

2---

12---

9Worksheet Answers

10

Worksheet Answers

7 Brickie A as Brickie B’s 50 hours working time will probably take him all week

8 4 May



10 a 9:30 am b 11:20 pm c 7:45 am

d 8:10 pm e 10:45 am f 1:30 am

11 a 226 minutes b Show your teacher

12 a 20 packets

b The individual packets are $2·58 while those in the carton cost $2·50, so the carton is cheaper.

Worksheet 36: Chapter Test 8B1 a An angle size equal to 90°

b An angle less than 90°c An angle greater than 90° but less than 180°d An angle greater than 180° but less than 360°e Angle sizes that add to give 90°f Angle sizes that add to give 180°

2 a 90° b 180° c 150°3 a c° or ∠C b ∠EFG c ∠DEF

d 82° e 280°4 a 75° b 27° c 52°

d 21° e 48° f 105°

5 a b

6 a 24° b 156°c More than 66° and less than 156°

7 a 147° b 61° c 99° d 16°8 a 16° b 63° c 71° d 32°

9 a b c

Worksheet 37: Chapter Test 9B1 a 77° b 122° c 140° d 115°2 a All angles in equilateral triangles are 60°.

b

c Obtuse angle is >90°, right angle is 90°, therefore sum of the angles of the triangle would be >180°.

d e

f

3 a 135° b 135° c 122° d 114°4 a a = 54°, b = 54°, c = 126°

b 3·6 m

5 112°

6 a b 2520°

7 a All the interior angles add up to 180° which is a factor of 360°.

b No c Yes

Worksheet 38: Chapter Test 10B1 A (1, 1), B (4, 3), C (3, 2), D (0, 4), E (6, 3), F (3, 5)

2

3 a 300 m b 600 m c 90° d B

4 A 64°, B 90°, C 33°, D 0°, E 64°, F 78°5 a 270° 600 m b 500 m

c 31° for 585 m then due East for 300 m

55°265°

L

M

N L

NM M

L

N

6

5

4

3

2

1

1 2 3 4 5 6

y

x

E

B

D

C

F

A


Worksheet Answers

6 a

NB scale 1:1000 or 1 cm represents 10 m

b 115° bearing 70 m


1 a x + y + z b

c x + y + z − 4 d x + y + 2z – 3

2 a 6x b 23y c 19k

d 11p – 2q e 0 f 6x + 6

g 6w + 15x + 3y h 4a + 3b − 2c

3 a b 5y c

d e f

4 a 3y b mn c 12mn

d 30ab2 e 8x3 f 12y3

5 a 2a + 2b b 15x – 5y c 8x2 − 3x

d 28f – 4f 2 e 24m + 8 f 2x2

6 a 18·84 cm b 125·6 mm c 295·16 mm

7 a No b Yes c No d Yes

Worksheet 40: Chapter Test 12B1 a 7 b 27 c 7

d 7 e 56 f 6

g 80 h 6

2 a 3 b 4 c 3

d 14 e 9 f 7

g 7

3 a x – 6 = 3 b k + 7 = 15x = 9 k = 8

c 5s + 4 = 19 d g + g − 11 = 5s = 3 g = 8

e 4t + 13 = 37t = 6

4 a x > 4 b x ≤ 3 c x < 15 d x ≥ 5

5 a m < 8

b x ≥ 4

c x ≤ 1

d x < 21

Worksheet 41: Chapter Test 13B1 Discussion should deepen student awareness of chance

events in daily life.

2 a Very likely b Very unlikely

c Unlikely d Impossible

e Even chance f Certain

3 a b c

d e

4 a b c

5 Spinner C, as you would expect it would land on the shaded region about 42 times.

6 a 6 sectors Green, 4 Red, 2 Blue

b Green approximately 50,Blue approximately 17, Red approximately 33

c Green 0·5, Blue Red


1 Mean = = 54·4 kg

Range = 80 − 39 = 41

2 I would agree with the statement as 21 males and females strongly agree or agree that they feel safe at home, while only 9 disagree or strongly disagree that they feel safe at home.

115°

10°

30°

280°

95 m

80 m

70 m

60 miii

ii

i

N

N

NN

Z

y2---

m2---- 4

t---

34 f------ 7

10r-------- 4t

7-----

7 8 x9

2 3 x4 5

0 1 x2

20 21 x22

113------ 1

2--- 3

4---

152------ 3

13------

725------ 10

25------ 18

25------

Green

BlueRed

0·16̇, 0·3̇

163130

------------

11Worksheet Answers

12

Worksheet Answers

3 a Mean 47 mode 48 median 48

b 5 c 47 matches

4

b Monday

c 4 drinks

d The greatest number of drinks were sold on Monday.

5 a

b $62

c $556

d mean $27.80, mode 5 and 30

e 0·05

0 2 4 5 5

1 1 7 9

2 0 1 5 6 8

3 0 0 8

4 3

5 3 8 9

6 2

Day

Drink salesN

umbe

r of

dri

nks

0 Mon

2

4

6

8

Tues Wed Thurs Fri


MATHS DIMENSIONS 7 FOUNDATION WORKSHEETS © Pearson Education Australia (a division of Pearson Australia Group Pty Ltd) 2006.This page may be photocopied for classroom use.

Foundation Worksheet

Name: Class:

Complete each table using the operation shown.

You can practise more by choosing new numbers for the end box and repeating the sheet.

1 7 +0 1 4 3 7 2 8 6 5 9

+

2 11 −2 8 5 1 9 6 3 10 7 4

−

3 7 ×0 2 1 5 10 3 7 4 8 6 9 11

×

4 4 ×3 6 2 7 8 1 4 9 5 10 0 11

×

5 5 +4 7 3 6 0 1 5 9 8 10

+

6 9 −3 8 7 4 1 6 9 2 0 5

−

7 3 ×8 4 6 9 7 5 2 1 0 11 3 10

×

8 8 +5 6 2 4 8 0 7 3 9 1

+

9 6 ×7 2 4 10 6 8 9 3 11 1 0 5

×

10 3 +6 5 9 2 4 7 0 10 3 8

+

11 9 ×1 3 8 11 2 9 10 0 4 7 6 5

×

12 10 −9 0 6 8 3 4 1 7 10 5

−

Exercise

1D Know Your Tables



Name: Class:

Find the basic numeral for each expression.

1 a (3 + 2) × 10 b (4 + 3) × 6 c (2 + 1) × 3

d (5 + 1) × 5 e 7 × (3 + 4) f 4 × (2 + 5)

2 a (8 − 2) × 3 b (10 − 8) × 2 c (6 − 4) × 1

d 4 × (8 − 3) e (9 − 4) × 6 f 8 × (7 − 5)

3 a 10 − (4 + 3) b 8 − (4 + 2) c 9 − (3 + 1)

d 8 − (3 + 3) e 9 − (6 − 4) f 6 − (8 − 2)

Examples

1 (6 + 3) × 8= 9 × 8= 72

2 (10 − 6) × 5= 4 × 5= 20

3 7 × (9 − 3)= 7 × 6= 42

4 12 − (8 − 3)= 12 − 5= 7

Exercise

Puzzle | Which month has 28 days?Work out the answer for each part, and put the letter for that part in the box above the correct answer.

A (5 + 3) × 4 E (7 − 5) × 4 F 7 − (4 − 2) H (7 − 3) × 6

L 5 − (3 + 2) M (8 − 5) × 4 O (7 + 1) × 2 T 10 − (8 − 4)

!32 0 0 16 5 6 24 8 12

1G Grouping Symbols



Name: Class:

1H Rounding Numbers

Each digit has a place value:

6542

When rounding, look at the next digit.If it is 5 or more, round up.If it is less than 5, leave the digit.

Thousands Hundreds Tens Units6 5 4 2

Examples

1 Round off to the nearest ten.a 532 b 1678For tens, look at the units.a 532: 2 is less than 5, so leave the tens digit.

Answer is 530.b 1678: 8 is more than 5, so round up the tens digit.

Answer is 1680.

2 Round off to the nearest hundred.a 658 b 9240For hundreds, look at the tens.a 658: 5 is 5 or more, so round up the hundreds.

Answer is 700.b 9240: 4 is less than 5, so leave the hundreds digit.

Answer is 9200.

1 Round off to the nearest ten.a 368 b 79 c 35 d 136e 574 f 6077 g 591 h 8018i 43 j 882 k 62 l 207

2 Round off to the nearest hundred.a 8731 b 1234 c 309 d 484e 6550 f 938 g 2789 h 161i 528 j 9876 k 7007 l 299

Exercise



Name: Class:

2D Divisibility Tests

1 a Write the first 10 even numbers.

b Write the first 10 odd numbers.

c Write the first 7 numbers divisible by 5.These are called multiples of 5.

2 Write the first 10 multiples of the following.

a 2

b 3

c 4

d 10

e 6

f 7

g 8

h 9

3 Write the numbers below 30 that are divisible by the following.

a 2

b 3

c 10

4 a Circle the odd numbers.

15 48 116 5030 54 321

b Circle the numbers divisible by 5.

40 554 125 75 052 100 000

c Circle the numbers divisible by 3.

12 201 755 5333 54 321 12 345

d Circle the numbers divisible by both 2 and 3.

24 8 1216 42 66 888

• An even number is divisible by 2 and ends in 0, 2, 4, 6 or 8.

• An odd number ends with an odd digit: 1, 3, 5, 7 or 9.

• A number is divisible by 3 if the total of its digits is divisible by 3: 7320 → 7 + 3 + 2 + 0 = 12 which is divisible by 3.

• A number is divisible by 5 if it ends in a 0 or 5.

Exercise



Name: Class:

2F Powers of Numbers

1 Write the simplest answer for each.

a 4 × 4 b 8 × 8 c 3 × 3 d 1 × 1 e 9 × 9

f 2 × 2 g 5 × 5 h 10 × 10 i 7 × 7 j 6 × 6

k 2 × 2 × 2 l 1 × 1 × 1 m 5 × 5 × 5 n 3 × 3 × 3 o 10 × 10 × 10

2 Write the simplest answer for each.a 72 b 102 c 52 d 82 e 22

f 12 g 62 h 42 i 32 j 92 k 33 l 23 m 43 n 103 o 63

3 Write each as a power.a 10 × 10 × 10 b 6 × 6 c 2 × 2 × 2 × 2 × 2 × 2d 7 × 7 e 5 × 5 × 5 × 5 f 9 × 9 × 9 × 9 × 9g 8 × 8 × 8 × 8 h 4 × 4 × 4 i 10 × 10 × 10 × 10 × 10

Exercise

Puzzle | Why did the chicken cross over the road?Work out the answer to each part and put the letter for that part in the box above the correct answer.A 3 × 4 B 7 × 2 C 9 × 3 D 5 × 6 E 4 × 6H 5 × 7 I 8 × 4 L 2 × 10 N 3 × 7 O 9 × 2R 12 S 22 T 32 U 42

14 24 27 12 16 4 24 35 24 27 18 16 20 30

21 18 9 27 1 18 4 4 16 21 30 24 1 32 9

The 6 is used 4 times in the product. This is 6 to the power of 4.

Examples

1 Write the answer.7 × 7 × 7= 49 × 7= 343

2 Write the answer.53 = 5 × 5 × 5

= 25 × 5= 125

3 Write as a power.6 × 6 × 6 × 6 = 64



Name: Class:

2G Square and Cube Roots

1 a If 4 × 4 = 16, then = b If 2 × 2 = 4, then =

c If 5 × 5 = 25, then = d If 9 × 9 = 81, then =

e 121 = 11 × 11, so = f 400 = 20 × 20, so =

2 a If 72 = 49, = b If 82 = 64, then =

c 100 = 102, so = d 144 = 122, so =

e If 12 = 1, then = f If 152 = 225, then =

3 a If 5 × 5 × 5 = 125, then = b If 3 × 3 × 3 = 27, then =

c If 4 × 4 × 4 = 64, then = d If 729 = 9 × 9 × 9, then =

4 a If 63 = 216, then = b If 23 = 8, then =

c Since 512 = 83, = d Since 27 000 = 303, =

Exercise

16 4

25 81

121 400

49 64

100 144

1 225

1253 273

643 7293

2163 83

5123 27 0003

Examples

The square root of a number is squared to give that number.

Similarly, a cube root is cubed to give the number.

3 7 × 7 × 7 = 343

∴ = 7

4 If 1000 = 10 × 10 × 10, then = 10

3433

10003

1 9 = 3 × 3

∴ = 39

2 6 × 6 = 36

∴ = 636Write 6 × 6 = 62, for short, and say ‘6 squared’.

Write 7 × 7 × 7 = 73, and say ‘7 cubed’.


Name: Class:


3F Addition and Subtraction of Fractions

Use the diagrams to calculate the following.1 a b

+ +

2 a b

+ +

3 a b

− −

4 Write the simplest answer.a + b − c − d + e −

f + g − h + i + j +

k + l + m − n + o −

p − q − r + s + t +

u + v − w + x − y −

Exercise

210------ 3

10------ 4

11------ 5

11------

10 48-- 1

8---1 2

12------10 3

12------ 16

12------ 9

12------

38--- 2

8--- 7

12------ 1

12------

35--- 1

5--- 7

9--- 3

9---

28--- 1

8--- 7

8--- 6

8--- 7

10------ 4

10------ 13

20------ 6

20------ 3

5--- 1

5---

715------ 4

15------ 9

11------ 2

11------ 23

100--------- 4

100--------- 1

5--- 2

5--- 1

8--- 6

8---

313------ 7

13------ 8

25------ 9

25------ 16

25------ 2

25------ 9

20------ 2

20------ 9

10------ 2

10------

815------ 6

15------ 57

100--------- 20

100--------- 19

40------ 10

40------ 4

12------ 7

12------ 70

100--------- 13

100---------

310------ 2

10------ 9

16------ 5

16------ 1

12------ 3

12------ 7

20------ 2

20------ 7

8--- 1

8---

Puzzle | Brother: ‘Did you just take a shower?’Simplify each fraction by dividing top and bottom. Match the letters with the answers below.

E G H I M N O R S T W Y

: ‘ , ?’

24--- 2

12------ 4

10------ 5

20------ 2

20------ 6

8--- 8

12------ 20

100--------- 10

18------ 3

9--- 6

20------ 15

25------

59--- 1

4--- 5

9--- 1

3--- 1

2--- 1

5--- 3

10------ 2

5--- 3

5--- 1

4--- 5

9--- 2

3--- 3

4--- 1

2--- 1

10------ 1

4--- 5

9--- 5

9--- 1

4--- 3

4--- 1

6---

1 + = 2 − =

3 + = 4 − =

=

310------ 4

10------ 7

10------ 9

13------ 4

13------ 5

13------

27--- 1

7--- 3

7--- 8

15------ 3

15------ 5

15------ Simplify

by ÷513---

Examples Add or subtract the numerators (tops) of fractions that have the same denominator (bottoms).


Name: Class:


3G Addition and Subtractionof Mixed Numbers

1 a 1 + b 5 + c + 2 d 7 + e 3 +

f + 4 g 10 + h 6 + i + 1 j + 5

2 a 2 + 1 b 2 + 3 c 7 + 2 d 4 + 2 e 5 + 3

f 6 + 4 g 8 + 1 h 5 + 3 i 1 + 1 j 3 + 2

3 a 1 − b 2 − c 3 − d 4 − e 2 −

f 3 − g 1 − h 4 − i 3 − j 10 −

4 a 3 − 1 b 4 − 2 c 3 − 2 d 6 − 4 e 5 − 3

f 2 − 1 g 5 − 4 h 7 − 3 i 1 − 1 j 2 − 2

Exercise34--- 1

10------ 5

9--- 13

20------ 7

8---

1112------ 4

5--- 12

25------ 11

100--------- 5

6---

12--- 1

4--- 5

8( )------- 3

10------ 1

9---

25--- 17

20------ 7

12------ 8

15------ 3

10------

12--- 1

4--- 1

6--- 3

8--- 3

10------

512------ 3

20------ 2

9--- 13

16------ 4

5---

12--- 3

4--- 2

3--- 7

8--- 1

5---

1720------ 8

15------ 15

16------ 47

100--------- 8

9---

Puzzle | What type of music do mummies prefer?Simplify each fraction by cancelling down. Match the letters with the answer below.

A C I M P R S U W

!

714------ 4

12------ 2

10------ 6

24------ 4

6--- 9

12------ 20

25------ 15

50------ 6

16------

38--- 3

4--- 1

2--- 2

3--- 1

4--- 3

10------ 4

5--- 1

5--- 1

3---

Examples

1 2 +

= 2

78---

78---

2 3 + 2

= 3 + 2 +

= 5

14---

14---

14---

3 5 − 2

= 5 − 2 +

= 3

35---

35---

35---

4 1 −

= −

=

920------

2020------ 9

20------

1120------

5 4 −

= 3 + 1 −

= 3 + −

= 3

715------

715------

1515------ 7

15------

815------

When adding and subtracting mixed numbers, it is usually simplest to do the whole numbers and fractions separately.

Be careful when you subtract a fraction from a whole number.



Name: Class:

3I Multiplication of Fractions

1 a 2 × b × c 5 × d × e × 3

f 4 × g 5 × h × 10 i 4 × j 10 ×

k 2 × l × 3 m 6 × n × 4 o 7 ×

2 a × b × c × d × e ×

f × g × h × i × j ×

k × l × m × n × o ×

3 a × b × c × d × e ×

f × g × h × i × j ×

Exercise14--- 2

1--- 1

4--- 11

100--------- 5

1--- 11

100--------- 2

9---

116------ 3

20------ 7

100--------- 5

24------ 7

80------

1940------ 8

27------ 1

30------ 13

60------ 8

77------

12--- 4

8--- 1

2--- 12

15------ 1

2--- 10

20------ 1

2--- 6

10------ 1

4--- 8

11------

13--- 9

10------ 1

6--- 12

20------ 1

5--- 15

16------ 1

10------ 40

45------ 1

3--- 15

18------

1824------ 1

2--- 8

16------ 1

4--- 1

8--- 24

25------ 1

5--- 20

31------ 1

4--- 28

100---------

12--- 1

3--- 1

4--- 1

3--- 1

10------ 1

7--- 1

2--- 1

10------ 1

3--- 1

5---

116------ 1

2--- 1

10------ 1

10------ 1

4--- 1

4--- 1

6--- 1

5--- 1

4--- 1

25------

Puzzle | Teacher: ‘You missed school yesterday, didn’t you?’Match the letters with the answer below.

C × D × E 5 × H × 2 M × N ×

O × R × S × 8 T × 4 U × V × Y ×

: ‘ .’

2

15--- 10

15------ 1

3--- 3

10------ 1

30------ 3

8--- 1

6--- 18

20------ 2

9--- 1

2---

13--- 1

6--- 1

2--- 1

2--- 1

4--- 1

8--- 1

4--- 8

16------ 1

10------ 20

25------ 8

11------ 1

8---

12--- 1

8--- 1

10------ 1

6--- 1

9--- 1

2--- 1

9--- 1

18------ 1

2--- 2

25------ 1

6--- 1

4--- 1

11------ 3

20------ 1

8--- 2

15------ 3

4---

Examples

1 4 ×

= ×

=

17---

41--- 1

7---

47---

2 5 ×

= ×

=

320------

51---

1 320------

4

34---

3 ×

=

17--- 2

3---

221------

4 ×

= ×

=

16--- 18

20------

16---

1

1820------

3

320------

5 ×

= ×

=

13--- 12

16------

13---

1

1216------

4 1

4

14---

Simple rules to follow when multiplying fractions.• Write each part as a fraction.• Simplify by cancelling or dividing top and bottom.• Multiply numerators and denominators.



Name: Class:

3J Division Involving Fractions

Exercise

1

3

2a How many in

∴ ÷ =

b How many in

∴ ÷ =

112------ 8

12------?

812------ 1

12------

212------ 8

12------?

812------ 2

12------

a How many in

∴ ÷ =

b How many in

∴ ÷ =

225------ 18

25------?

1825------ 2

25------

925------ 18

25------?

1825------ 9

25------

a How many in

∴ ÷ =

b How many in

∴ ÷ =

310------ 6

10------?

610------ 3

10------

210------ 6

10------?

610------ 2

10------

4 a How many in

∴ ÷ =

b How many in

∴ ÷ =

420------ 16

20------?

1620------ 4

20------

820------ 16

20------?

1620------ 8

20------

5 is shaded.

a ÷ =

b ÷ =

1421------

1421------ 7

21------

1421------ 2

21------

6 is shaded.

a ÷ =

b ÷ =

1216------

1216------ 4

16------

1216------ 3

16------

7 a ÷ b ÷ c ÷ d ÷ e ÷

f ÷ g ÷ h ÷ i ÷ j ÷

k ÷ l ÷ m ÷ n ÷ o ÷

p ÷ q ÷ r ÷ s ÷ t ÷

69--- 2

9--- 15

17------ 3

17------ 20

27------ 10

27------ 20

27------ 4

27------ 5

8--- 1

8---

40100--------- 8

100--------- 27

100--------- 9

100--------- 21

40------ 7

40------ 7

19------ 1

19------ 4

11------ 4

11------

1825------ 6

25------ 30

31------ 10

31------ 30

47------ 5

47------ 33

40------ 3

40------ 24

35------ 12

35------

2435------ 8

35------ 18

20------ 2

20------ 13

18------ 13

18------ 44

51------ 11

51------ 50

57------ 25

57------

1 Note that is shaded.

How many in ? 4.

Then ÷ = 4.

1215------

315------ 12

15------

1215------ 3

15------

Examples

2 is shaded.

How many in ? 3.

Then ÷ = 3.

1520------

520------ 15

20------

1520------ 5

20------

3 is shaded.

How many in ? 2.

Then ÷ = 2.

1012------

512------ 10

12------

1012------ 5

12------

Divisions ask ‘how many?’• 10 ÷ 2 means how many 2s in 10.• 6 ÷ means how many s in 6.

• ÷ means how many s

in

14--- 1

4---

1520------ 3

20------ 3

20------

1520------.

When the denominators are the same, just divide the numerators.



Name: Class:

3K Fractions of Quantities

1 a of 20 min b of 6 kg c of $20 d of 90 m

e of 70 mm f of $24 g of $5000 h of 36 km

i of 66 t j of 75 kg k of 180 L l of $180

m of 44 mm n of 960 t o of 48 h p of 555 min

5 a of $20 b of 70 mm c of $24 d of $5000

e of 44 t f of 75 kg g of $180 h of 555 min

i of 24 cm j of 50 L k of 27 kg l of 200 h

m of 48 m n of $60 o of $75 p of 36 cm

Exercise12--- 1

2--- 1

4--- 1

3---

110------ 1

8--- 1

100--------- 1

4---

16--- 1

5--- 1

10------ 1

3---

12--- 1

8--- 1

4--- 1

5---

2 a of 40

b of 40

c of 40

14---

24---

34---

3 a of $80

b of $80

c of $80

110------

310------

710------

4 a of $30

b of $30

c of $30

15---

25---

35---

10 10

1010

8 8 8 8 8

88888

6

6

6

6

6

34--- 3

10------ 5

8--- 7

100---------

711------ 2

5--- 2

3--- 3

5---

56--- 7

10------ 5

9--- 3

50------

38--- 4

5--- 19

25------ 5

12------

Puzzle | Do you know this book?Calculate each and place each letter above its answer below.

A of 18 B of 28 E of 200 G of 48 I of 60 L of 80

M of 20 N of 60 S of 16 T of 60 U of 27 Y of 32

‘ ’ .4 6 21 20 6 8 6 12 40 7 24 16 12 14 21 24 7 15 14 14

13--- 1

4--- 1

10------ 1

6--- 1

5--- 1

20------

45--- 2

3--- 7

8--- 7

20------ 5

9--- 3

4---

Examples

1 Find of $60

of $60

= $60 ÷ 3= $20

13---

13---

2 Find of 40 m

of 40 m

= 40 m ÷ 5= 8 m

15---

15---

3 Find of 35 L

of 35 L

= 35 L ÷ 5= 7 L

∴ of 35 L

= 3 × 7 L= 21 L

35---

15---

35---

4 Find of $200

of $200

= $200 ÷ 8= $25

∴ of $200

= 5 × $25= $125

58---

18---

58---

Fractions are divisions.



Name: Class:

4C Application of Decimals

1 Round off to the nearest dollar.

a $105.56 b $89.73 c $4.08 d $91.48 e $24.84

f $66.70 g $13.41 h $3.29 i $7.15 j $39.81

2 Round off to the nearest 5 cents.

a 73c b 87c c 29c d 42c e 58c

f 12c g 64c h 23c i 96c j 7c

3 Round off to the nearest 5 cents.

a $3.98 b $4.23 c $1.71 d $5.58 e $3.08

f $7.62 g $2.93 h $3.33 i $8.11 j $2.34

Exercise

Puzzle | Have you read this book?Complete these calculations. Match the letters with the answers below.

A 0⋅7 + 0⋅3 B 1⋅5 − 0⋅8 C 0⋅25 + 0⋅65

E 3⋅7 × 0⋅2 F 6⋅4 ÷ 2 H 2⋅7 − 1⋅3I 0⋅2 × 0⋅8 L 4 − 2⋅7 N 0⋅62 + 0⋅34

O 10 × 3⋅46 R 0⋅32 × 5 S 0⋅63 × 0⋅3U 100 × 4⋅27 W 3⋅8 + 4⋅9 Y 0⋅5 × 0⋅5

‘ ’

1⋅4 427 1⋅6 1⋅6 0⋅16 0⋅9 1 0⋅96 0⋅74

0⋅7 0⋅25 1⋅6 427 3⋅2 427 0⋅189 0⋅7 1⋅3 34⋅6 8⋅7 0⋅96 34⋅6 3⋅2 3⋅2

ExamplesWhen rounding to the nearest 5 cents:• 1c or 2c are rounded down to 0• 3c or 4c are rounded up to 5• 6c or 7c are rounded down to 5• 8c or 9c are rounded up to 10.

1 51c → 50c 2 $2.32 → $2.30

3 74c → 75c 4 $1.23 → $1.25

5 36c → 35c 6 $5.47 → $5.45

7 49c → 50c 8 $4.88 → $4.90



Name: Class:

4C Rounding Off

1 Round off to the nearest cent.

a 84⋅6c b 7⋅9c c 60⋅5c d 19⋅3c e 39⋅9c f 53⋅3c

g 3⋅1c h 45⋅7c i 26⋅5c j 30⋅2c k 88⋅4c l 14⋅4c

m 9⋅5c n 40⋅2c o 70⋅7c p 17⋅5c q 59⋅8c r 5⋅5c

2 Round off to the nearest dollar.a $7.63 b $9.24 c $3.90 d $4.08 e $2.03 f $1.92

g $8.49 h $8.88 i $11.80 j $6.30 k $5.72 l $2.38

m $3.50 n $10.05 o $5.38 p $9.90 q $6.87 r $4.44

Exercise

Puzzle | Ever heard of this book?Calculate the answers. Match each letter with the answer below.A 1⋅2 + 2⋅5 B 3⋅8 ÷ 2 C 0⋅7 × 4 D 7 − 2⋅3E 0⋅64 + 0⋅7 F 5⋅3 × 0⋅3 H 2⋅48 ÷ 4 I 3⋅7 − 2⋅6N 2⋅73 + 1⋅64 R 2⋅91 × 0⋅3 U 0⋅65 ÷ 5 Y 0⋅23 × 0⋅6

‘ ’

0⋅62 3⋅7 1⋅1 0⋅873 2⋅8 3⋅7 0⋅873 1⋅34

1⋅9 0⋅138 4⋅7 3⋅7 4⋅37 4⋅7 0⋅873 0⋅13 1⋅59 1⋅59

ExamplesTo round off to the nearest whole number, check the first decimal place.If it is 5 or more, ‘round up’ (add 1 to the whole numbers). If it is less than 5, ‘round down’ (leave the whole number).

1 43⋅7c

First place is more than 5.Round up (add 1).∴ 44c

2 $3.16

First place is less than 5.Round down (leave).∴ $3

3 17⋅2c

First place is less than 5.Round down.∴ 17c

4 $8.84

First place is more than 5.Round up.∴ $9


Name: Class:


4D Addition and Subtraction of Decimals

1 a 6⋅4 b 2⋅6 c 3⋅74 d 0⋅362 e 4⋅040⋅2 6⋅3 4⋅1 3⋅504 3⋅5

f 3⋅8 g 8⋅26 h 12⋅2 i 8⋅45 j 7⋅6232⋅73 9⋅47 5⋅9 2⋅718 6⋅9

2 a 4⋅7 b 6⋅9 c 17⋅23 d 2⋅59 e 5− 1⋅1 − 2⋅7 − 5⋅1 − 0⋅32 −3⋅2

f 3⋅64 g 19⋅81 h 3⋅86 i 4⋅2 j 9⋅7− 2⋅8 − 2⋅08 − 2⋅77 − 3⋅641 − 3⋅82

3 a 3⋅2 + 0⋅1 b 7⋅2 + 2⋅3 c 5⋅9 − 2⋅3 d 18 − 2⋅32

e 18 + 2⋅32 + 3⋅6 f 9⋅5 − 6⋅375 g 8⋅13 − 6⋅4 h 15⋅6 − 4⋅78

i 14⋅2 + 8⋅64 + 1⋅65 j 3⋅1 + 6⋅26 + 9⋅5

Exercise

Puzzle | What is the cure for water on the brain?Match the letters for these sums to the answers below.

A 2⋅05 + 2⋅343 D 0⋅243 + 1⋅87 E 0⋅63 + 2⋅442 H 0⋅007 + 2⋅174

N 0⋅02 + 1⋅843 O 1⋅7 + 1⋅63 P 1⋅03 + 3⋅96 T 2⋅45 + 1⋅88

4⋅393 4⋅33 4⋅393 4⋅99 3⋅33 1⋅863 4⋅33 2⋅181 3⋅072 2⋅181 3⋅072 4⋅393 2⋅113

1 2⋅3 + 5⋅42⋅35⋅47⋅7

2 9⋅7 − 3⋅249⋅70

−3⋅24

6⋅46

3 18 + 2⋅3 + 1⋅7618⋅00

2⋅301⋅76

22⋅06

4 7⋅674 − 3⋅267⋅674

−3⋅260

4⋅414

Examples• Line up the decimal points under each other.• For whole numbers put the point at the end.• Fill in spaces with zeros.



Name: Class:

4F Multiplying a Decimal

1 a 0⋅3 b 0⋅6 c 0⋅59 d 4⋅71 e 4⋅8 f 17⋅3× 2 × 7 × 3 × 5 × 6 × 4

g 9⋅2 h 7⋅65 i 0⋅234 j 3⋅21 k 0⋅08 l 0⋅009× 10 × 8 × 100 × 7 × 4 × 7

2 a 3 × 0⋅4 b 5 × 0⋅63 c 7 × 0⋅9 d 11 × 0⋅02

e 1⋅5 × 7 f 3⋅61 × 3 g 4⋅76 × 2 h 13⋅3 × 5

i 2⋅3 × 9 j 0⋅84 × 6 k 0⋅027 × 4 l 5⋅9 × 2

3 a 0⋅6 × 10 b 5⋅2 × 10 c 0⋅4 × 100 d 0⋅07 × 10

e 10 × 3⋅54 f 100 × 3⋅7 g 16⋅6 × 100 h 0⋅42 × 100

i 1000 × 0⋅414 j 8⋅1 × 100 k 10 × 0⋅032 l 1000 × 0⋅02

Exercise

Puzzle | Comment from student to teacherComplete these products to decode the message.A 0⋅27 × 5 C 1⋅41 × 2 D 10 × 0⋅12 E 4 × 0⋅31 F 0⋅012 × 10G 0⋅05 × 100 H 0⋅5 × 100 I 0⋅115 × 10 L 1⋅3 × 3 M 2⋅12 × 2N 7 × 0⋅58 O 4 × 0⋅11 P 8 × 0⋅51 S 0⋅08 × 5 T 0⋅063 × 3

1⋅15 1⋅2 0⋅44 4⋅06 0⋅189 5 1⋅24 0⋅189 0⋅189 50 1⋅24

4⋅08 0⋅44 1⋅15 4⋅06 0⋅189 0⋅44 0⋅12 1⋅2 1⋅24 2⋅82 1⋅15 4⋅24 1⋅35 3⋅9 0⋅4

1 2⋅7 × 32⋅7

× 3

8⋅1

2 4⋅23 × 54⋅23

× 5

21⋅15

3 1⋅894 × 101⋅894

× 10

18⋅94

4 8 × 3⋅243⋅24

× 8

25⋅92

Examples• When you multiply, there are the same number of figures

after the decimal point in the question and answer.• When multiplying by 10, 100 or 1000, move the decimal

point 1, 2 or 3 places to the right.

5 18⋅9 × 10018⋅9

× 100

18 90⋅0



Name: Class:

4F Multiplying by Decimals

1 a 0⋅41 b 0⋅27 c 1⋅4 d 3⋅7 e 0⋅234 f 4⋅15× 2 × 3 × 6 × 5 × 5 × 7

g 0⋅83 h 0⋅012 i 0⋅075 j 6⋅1 k 3⋅04 l 0⋅38× 2 × 3 × 5 × 4 × 7 × 2

2 a 0⋅4 × 0⋅7 b 0⋅2 × 0⋅3 c 0⋅5 × 0⋅07 d 5 × 0⋅01

e 0⋅8 × 0⋅5 f 0⋅4 × 9 g 0⋅03 × 0⋅9 h 0⋅06 × 0⋅08

i 0⋅3 × 0⋅3 j 0⋅5 × 0⋅5 k 0⋅004 × 0⋅8 l 0⋅3 × 0⋅02

3 a 7⋅2 b 2⋅5 c 1⋅2 d 0⋅34 e 0⋅61 f 0⋅22× 0⋅3 × 0⋅5 × 0⋅6 × 0⋅4 × 0⋅7 × 0⋅3

4 g 52 h 0⋅26 i 0⋅014 j 0⋅73 k 7⋅9 l 0⋅48× 0⋅01 × 0⋅02 × 0⋅06 × 0⋅2 × 0⋅3 × 0⋅5

Exercise

Puzzle | Can a match box?Answer each question then match the letters with the answer to solve the riddle.

A 0⋅5 × 3 B 0⋅4 × 0⋅3 C 0⋅2 × 0⋅06 I 0⋅3 × 0⋅5N 0⋅03 × 0⋅5 O 0⋅6 × 2 T 0⋅04 × 0⋅03 U 0⋅03 × 0⋅05

. !0⋅015 1⋅2 0⋅12 0⋅0015 0⋅0012 1⋅5 0⋅0012 0⋅15 0⋅015 0⋅012 1⋅5 0⋅015

1 0⋅63 × 463 × 4 = 2522 figures after the point∴ 2⋅52

2 3⋅27 × 0⋅2327 × 2 = 6543 figures after the point∴ 0⋅654


Examples• Multiply the numbers ignoring the decimal point.• The number of figures after the decimal point is the

same in the answer as the total number in the question.





Name: Class:

4G Using Decimals

1 a 2 × 0⋅3 kg b 3 × $2.24 c 7⋅3 cm × 6

d 8⋅22 L × 5 e $4.06 × 4 f 0⋅9 t × 6

g 3⋅26 m × 7 h 0⋅68 g × 4 i 3 × 5⋅07 h

j 8 × $3.17 k 0⋅04 × 6 l 8⋅4 L × 9

2 a 0⋅8 m + 0⋅3 m b $1.57 + $3.24 c $7.20 − $3.40

d 1⋅7 cm + 8⋅3 cm e 14⋅4 t − 3⋅67 t f 0⋅72 kg + 0⋅255 kg

g 7⋅501 kg − 3⋅26 kg h $7.67 + $2.94 i 0⋅6 m − 0⋅34 m

j 7⋅2 mL + 2⋅66 mL k $3.74 − $1.47 l 3⋅9 m + 4⋅73 m

3 a b c

d e f

g h i

j k l

Exercise

3 1⋅8 L 5 $2.35 4 6⋅28 m

2 0⋅54 kg 9 $9.18 3 6⋅96 mL

6 0⋅246 m 7 0⋅77 t 3 6⋅93 cm

5 0⋅405 g 4 $6.88 6 4⋅8 m

Puzzle | What is grey, has four legs, a tail and a trunk?Match the calculated answers with the letters to complete the riddle.

A $3.42 × 3 D $4.26 + $5.37 E $6.20 + $2.40 G

H $12.35 − $2.60 I $5.07 × 4 L $10 − $1.55 M $7 + $2.25

N $8 − $3.80 O S 6 × $2.35 U 8 × $1.60

Y

$10.26 $9.25 $1.12 $12.80 $14.10 $8.60 $3.01 $1.12 $20.28 $4.20 $3.01

.

$1.12 $4.20 $9.75 $1.12 $8.45 $20.28 $9.63 $10.26 $2.09

5 $15.05

4 $4.48

3 $6.27

• Follow the usual rules for decimals.• Put the unit of measurement in your answers.



Name: Class:

4H Decimal Problems

1 John is given $3.50 pocket money each week. How much would he be given in 10 weeks?

2 When Jamie went shopping, he bought 2 CDs for $19.95 each, 3 blank tapes for $1.50 each and 5 videotapes for $2.20 each. How much did he spend?

3 How much change should Clive receive if he pays for a $34.50 shirt with a $100 note?

4 How many 15 mL doses of medicine could Peter get from a 500 mL bottle?

5 Calculate the cost of 8 drinks at $1.29 each. How much would I pay in cash for them?

6 Ian played 4 rounds of golf, scoring 81, 86, 92 and 85. Find his total score and his average.

7 Helen, Tina and Janet picked fruit in a local orchard. They counted and found they had 97 apples and 65 pears. They shared the fruit by each taking the same number. How many pieces of fruit did each receive?

8 The distance from the Earth to the Sun is about 150 000 000 km. If the distance for Mercury is as much, find how far it is from the Sun.

9 Kerrie wishes to buy a new saddle priced at $480. How many weeks will it take if she saves $20 a week?

10 Heather pays $70 a month for dancing lessons. What is her cost for the year?

Exercise

215------

• Read the question carefully to decide what you have to find.• Choose a method, which uses the given information.• Set out your work clearly and neatly.• Is your answer reasonable? Answer the question.



Name: Class:

4H Dividing a Decimal

1 a b c d e

f g h i j

2 a b c d e

f g h i j

3 a b c d e

f g h i j

4 a b c d e

f g h i j

Exercise

2 0⋅8 6 0⋅6 4 0⋅8 7 0⋅07 3 0⋅03

5 0⋅05 2 0⋅6 3 0⋅09 4 0⋅08 2 0⋅4

3 0⋅69 3 0⋅36 5 0⋅45 7 0⋅77 4 0⋅52

2 0⋅26 8 0⋅24 6 0⋅18 4 0⋅64 3 0⋅93

5 2⋅5 3 6⋅3 4 6⋅8 5 5⋅5 2 8⋅6

2 3⋅6 6 7⋅2 3 9⋅3 2 4⋅6 4 8⋅8

7 7⋅14 3 6⋅36 8 8⋅08 2 8⋅26 5 5⋅75

6 2⋅46 3 1⋅26 4 4⋅48 9 9⋅27 7 7⋅28

Puzzle | How is Dorothy the Dinosaur like Conan the Barbarian?Complete these divisions then match the letters with the answers.

A 2⋅62 ÷ 2 D 3⋅9 ÷ 3 E 5⋅6 ÷ 2 H 0⋅85 ÷ 5

I 4⋅08 ÷ 4 L 0⋅65 ÷ 5 M 0⋅04 ÷ 4 N 4⋅8 ÷ 2

S 8⋅22 ÷ 2 T 6⋅6 ÷ 6 V 7⋅35 ÷ 5 Y 0⋅84 ÷ 3

1⋅1 0⋅17 2⋅8 0⋅28 0⋅17 1⋅31 1⋅47 2⋅8 1⋅1 0⋅17 2⋅8 4⋅11 1⋅31 0⋅01 2⋅8

!0⋅01 1⋅02 1⋅3 1⋅3 0⋅13 2⋅8 2⋅4 1⋅31 0⋅01 2⋅8

3 5⋅2 ÷ 4

1⋅34 5⋅2

4 4⋅84 ÷ 2

2⋅422 4⋅84

ExamplesWhen dividing a decimal by a whole number, place the point in the answer above the point in the question.

5 3⋅06 ÷ 3

1⋅023 3⋅06

1 0⋅9 ÷ 3

0⋅33 0⋅9

2 0⋅48 ÷ 4

0⋅124 0⋅48



Name: Class:

4K Review of Decimals

1 Write as a decimal.

a b c d e f

g h i j k l

m n o p q r

2 Write as a fraction.

a 0⋅7 b 0⋅03 c 0⋅53 d 0⋅09 e 0⋅123 f 0⋅091

g 0⋅13 h 0⋅59 i 0⋅563 j 0⋅21 k 0⋅303 l 0⋅299

m 0⋅06 n 0⋅4 o 0⋅25 p 0⋅64 q 0⋅005 r 0⋅014

3 Which is larger?

a 0⋅7 or 0⋅08 b 0⋅67 or 0⋅71 c 0⋅09 or 0⋅3 d 0⋅83 or 0⋅115

e 0⋅51 or 0⋅099 f 0⋅12 or 0⋅104 g 0⋅63 or 0⋅5 h 0⋅3 or 0⋅007

i 0⋅413 or 0⋅43 j 0⋅6 or 0⋅92 k 0⋅402 or 0⋅68 l 0⋅40 or 0⋅5

Exercise

310------ 7

100--------- 93

100--------- 6

10------ 4

1000------------ 133

1000------------

110------ 73

100--------- 43

100--------- 24

1000------------ 92

100--------- 28

100---------

36100--------- 555

1000------------ 2

1000------------ 99

100--------- 31

1000------------ 607

1000------------

Examples

1 Write as a decimal.

a b

= 0⋅5 = 0⋅08

c d

= 0⋅17 = 0⋅273

510------ 8

100---------

17100--------- 273

1000------------

2 Write as a fraction.a 0⋅9 b 0⋅01 c 0⋅42 d 0⋅015

= = = =

= =

910------ 1

100--------- 42

100--------- 15

1000------------

2150------ 3

200---------

3 Which is larger?

a 0⋅6 or 0⋅027 b 0⋅37 or 0⋅5 c 0⋅154 or 0⋅540⋅600 or 0⋅027 0⋅37 or 0⋅50 0⋅154 or 0⋅540∴ 0⋅600 = 0⋅6 ∴ 0⋅50 = 0⋅5 ∴ 0⋅540 = 0⋅54

• 1st decimal place is tenths 2nd decimal place is hundredths3rd decimal place is thousandths.

• Fill in empty spaces with zero.• Simplify fractions.

Write each decimal with the same number of places.

÷ 2÷ 2( ) ÷ 5

÷ 5( )


Name: Class:


4M Changing Fractions and Decimals to Percentages

1 Write as percentages.

a b c d e

f g h i j

k l m n o

p q r s t

u v w x y

2 Write as percentages.a 0⋅14 b 0⋅07 c 0⋅64 d 0⋅99 e 0⋅02f 0⋅31 g 0⋅30 h 0⋅85 i 0⋅80 j 0⋅18k 0⋅44 l 0⋅4 m 0⋅53 n 0⋅23 o 0⋅01p 0⋅29 q 0⋅71 r 0⋅9 s 0⋅25 t 0⋅58

Exercise

15100--------- 2

100--------- 47

100--------- 93

100--------- 72

100---------

350------ 1

4--- 1

5--- 1

100--------- 33

100---------

120------ 84

100--------- 9

10------ 9

20------ 6

25------

12--- 11

50------ 3

4--- 12

25------ 1

10------

77100--------- 41

50------ 7

10------ 19

20------ 19

100---------

Puzzle | Have you heard of this book?Place these in order from largest (1st) to smallest (11th). Match the letters with the order below to complete the title.

A 0⋅74 B D E 0⋅7 G 0⋅08 H 0⋅8 I M 0⋅88 N T 40% Y 85%

‘ ’10th 4th 8th 9th 6th 11th 9th 7th 3rd 11th

.9th 2nd 5th 6th 3rd 7th 4th 1st 6th 10th 8th

41100--------- 78

100--------- 3

4--- 41

50------

Examples

1 = ×

= 27%

27100--------- 27

100---------

1

1001

---------%1

To change to a percentage, multiply by 100.

• For a fraction this means × .

• For a decimal, move the point 2 places to the right.

1001

---------

2 0⋅42= 0⋅42 × 100%

= 42%

3 = ×

= 60%

35--- 3

5---

1

1001

---------%20

4 0⋅03= 0⋅03 × 100%

= 3%

5 0⋅7= 0⋅7 × 100%

= 70%



Name: Class:

4M Review of Percentages

3 Write as a fraction and as a decimal.a 3% b 17% c 63% d 99% e 27% f 20% g 5%h 6% i 15% j 44% k 25% l 50% m 18% n 62%o 55% p 36% q 83% r 46% s 77% t 1%

4 Write as a percentage.

a b 0⋅07 c d e 0⋅52 f 0⋅20

g h 0⋅75 i j k 0⋅35 l 0⋅45

m 0⋅02 n o 0⋅50 p q 0⋅61 r

Exercise1 a What percentage

is coloured?b What percentage

is not coloured?c What fraction is

coloured?d What fraction is

not coloured?

2 a What percentage is coloured?

b What percentage is not coloured?

c What fraction is coloured?

d What fraction is not coloured?

7100--------- 23

100--------- 78

100---------

39100--------- 90

100--------- 16

100---------

58100--------- 47

100--------- 28

100---------

Puzzle | Do you know this book?Write each as a simplified fraction. Match each letter with the answer below.A 10% B 19% D 40% E 75% H 30% I 16%L 35% O 42% R 51% S 50% T 4% Y 85%

‘ ’

.

310------ 21

50------ 7

20------ 4

25------ 2

5--- 1

10------ 17

20------ 1

25------ 51

100--------- 3

4--- 1

10------ 1

25------

19100--------- 17

20------ 51

100--------- 3

10------ 21

50------ 2

5--- 1

10------ 3

10------ 21

50------ 51

100--------- 1

2--- 3

4---

Examples

A percentage is a fraction over 100 or a decimal with 2 places.

1 9% = 2 73% = 3 60% = = 4 45% = =

= 0⋅09 = 0⋅73 = 0⋅60 = 0⋅6 = 0⋅45

9100--------- 73

100--------- 60

100--------- 3

5--- 45

100--------- 9

20------

If possible simplify fractions by cancelling.


Name: Class:


4N Finding a Percentage of a Quantity

1 a 50% of $30 b 10% of 80 g c 25% of 40 kg d 50% of 60 m

e 25% of 16 f 25% of 36 L g 10% of $200 h 10% of 150 cm

i 50% of 28 t j 25% of 48 g k 10% of 90 l 25% of 88 m

m 50% of 50 h n 50% of 422 t o 25% of 120 kg p 10% of $450

2 a 20% of $20 b 70% of $50 c 3% of 600 t d 5% of 700 kg

e 40% of 400 m f 6% of 900 g g 30% of 200 h 20% of 120 s

i 80% of $50 j 2% of 1200 km k 60% of 90 d l 90% of $20

m 8% of 3000 m n 30% of 180 cm o 20% of 800 g p 4% of $5000

q 11% of 300 t r 40% of $70 s 60% of 500 L t 15% of 200

Exercise

Puzzle | Teacher: ‘What came after the Stone Age and the Bronze Age?’Change each decimal to a percentage. Match the letters with the answers below.A 0⋅05 D 0⋅35 E 0⋅3 G 0⋅53 H 0⋅50N 0⋅01 S 0⋅15 T 0⋅1 U 0⋅26

:15% 10% 26% 35% 30% 1% 10%

‘ - .’10% 50% 30% 15% 5% 26% 15% 5% 53% 30%

Examples

1 4% of 200 kg 2 60% of $700 3 10% of 40 4 50% of 148 L 5 25% of 64 t

= 0⋅04 × 200 kg = 0⋅6 × $700 = × 40 = of 148 L = of 64 t

= 8 kg = $42 = 4 = 74 L = 16 t

110------ 1

2--- 1

4---

Change the percentage to a decimal or fraction and multiply. Usually it is easier to change to a decimal, but there are some fractions that are easier than decimals.



Name: Class:

5E Measuring Length

1 Measure these lengths correct to the nearest centimetre.

2 Measure these lengths in millimetres.

Exercise

a b c d

e

f

i j

g h

a b c d

e f

g h

Puzzle | What’s the easiest way to get a day off school?Put these lengths in order from shortest to longest in the boxes below to find thecode. (Change to mm first.) Use the code to solve the riddle.

1 19 mm 2 3 cm 3 28 mm 4 6⋅2 cm 5 6⋅7 cm 6 59 mm

7 1 cm 8 39 mm 9 5 cm 10 42 mm 11 4 mm

(shortest) 11 (longest)

A D I L N R S T U W Y

A A A !4 11 1 9 6 2 9 1 3 10 11 9 6 8 7 11 5

Examples• Measuring is rounding off.• Write the measurement it is closest to.

1

This measures 3 cm to the nearest cm, since it is only a bit more than 3 cm long.

1cm

2 3 4 502

This measures 37 mm to the nearest mm, since the ruler is marked in mm. (It would measure 4 cm to the nearest cm.)

— AW W09.003 —1

mm2 3 4 50



Name: Class:

5F Units of Length

1 Write down the length of each interval to the nearest centimetre.

2 a 8 cm = . . . mm b 300 cm = . . . m c 90 mm = . . . cm d 8000 mm = . . . me 7 km = . . . m f 9 m = . . . cm g 3 m = . . . mm h 12 cm = . . . mmi 5000 m = . . . km j 1500 cm = . . . m k 2 km = . . . m l 11 m = . . . mmm 50 mm = . . . cm n 10 km = . . . m o 8000 m = . . . km p 600 cm = . . . mq 12 000 mm = . . . m r 20 cm = . . . mm s 62 000 m = . . . km t 6 m = . . . mm

3 a 3 min = . . . s b 2 h = . . . min c 120 s = . . . min d 600 min = . . . he 5 min = . . . s f 480 s = . . . min g 24 h = . . . min h 300 min = . . . hi 20 min = . . . s j 30 min = . . . h k 900 s = . . . min l 7 h = . . . minm 12 h = . . . min n 10 min = . . . s o 4 h = . . . min p 15 min = . . . h

Exercise

1cm

2 3 4 5 6 7 8 9 10 11 120

ab

cd

e f

Puzzle | What do bees do if they want to catch public transport?Fill in the gaps for each question. Match the letters with the answers below.A 75 cm = . . . mm B 5 m = . . . mm I 5 m = . . . cmO 500 cm = . . . m P 570 mm = . . . cm S 7 m = . . . mmT 7 cm = . . . mm U 70 mm = . . . cm W 75 m = . . . cm Z 5 cm = . . . mm

.7500 750 500 70 750 70 750 5000 7 50 50 7000 70 5 57

Examples

10 mm = 1 cm100 cm = 1 m

1000 mm = 1 m1000 m = 1 km

1 5 m = . . . cmm is larger unit,

multiply by 1005 × 100 = 500 cm

1 h = 60 min, 1 min = 60 s

2 80 mm = . . . cmmm is smaller unit, divide by 1080 ÷ 10 = 8 cm

• When converting or changing to a smaller unit, multiply.• When converting to a larger unit, divide.

3 2 min = . . . s 4 360 min = . . . hmin is larger unit, min is smaller unit, 2 × 60 = 120 s 360 ÷ 60 = 6 h



Name: Class:

5H Perimeter

1 Calculate each perimeter.

2 Find the perimeter of the following shapes.a a square of side length 10 cmb a rectangle with a length of 16 m and a breadth of 5 mc a square with a side length of 50 md a rectangle with a length of 1⋅9 cm and a width of 1⋅1 cme a rectangle with length 37 mm and breadth 30 mmf a square with sides 3⋅6 cm longg a square with each side length 110 mh a rectangle with length 2·5 cm and breadth 1⋅7 cmi a triangle with sides 17 cm, 24 cm and 36 cmj a quadrilateral with sides of length 9⋅3 m, 14 m, 16⋅2 m and 20⋅7 m

Exercise

a b c d

e f g h

i j k l

m n o p

6 cm

8 cm

10 cm4 cm

3 cm

2 cm

8 cm

12 cm

5 cm 6 cm

20 cm

23 cm

10 cm

11 cm

15 m

19 m

20 m8 m

9 m

8 m

12 m 8 m

3 m

7 m

5 m

3·9 cm

7·3 cm

5·2 cm

12·1 m

7·3 m15·4 m

13·7 m

8 mm16 m

15 cm

10 cm7·5 mm

3·2 m

8·1 m

18 cm

8 cm

Examples

1

P = (7 + 13 + 16) cm= 36 cm

13 cm

16 cm7 cm

2

P = 2 × 20 + 2 × 10 m= 60 m

20 m

10 m

3

P = 4 + 8 + 3 + 6 + 5 m= 26 m

3m

4 m8 m

5 m

6 m

4

P = 4 × 11 mm= 44 mm

11 mm

• Perimeter is the total length around a shape.• The same marking on sides mean they have the

same length.• For a square, P = 4 × side.

For a rectangle, P = 2 × length + 2 × breadth.



Name: Class:

6B The Definition of Area

1 These shapes are drawn on centimetre grid paper. Find their areas.

2 a On your own grid paper draw 3 different shapes with an area of 6 cm2.b Draw shapes with areas of 3 cm2, 5 cm2, 7 cm2, 10 cm2.

Exercise

a b c

d e f

g h i

j

Examples

Find the area of each shape by counting square centimetres.

Area = 5 cm2 Area = 8 cm2 Area = 7 cm2

1 2 3

The area of a figure is measured by counting the number of square units it covers.



Name: Class:

6D Area of a Rectangle

1 Find the area in square units.

2 Find the area in square units.

3 Calculate the area of these rectangles.a length 10 cm, breadth 4 cm b length 14 cm, breadth 2 cmc length and breadth both 10 cm d length 8 cm, breadth 4 cme length 5 cm, breadth 9 cm f length 3 cm, breadth 11 cmg length and breadth both 6 cm h length and breadth both 8 cmi length 20 cm, breadth 5 cm j length 15 cm, breadth 2 cm

Exercise

a b c d

e f g h

a b c d

e f g h

i

Examples

Find the area of each figure.1 2 3 4

Area = 8 unit2 (by counting)

Area = 12 unit2 (3 squares across by 4 squares down)

Area = 9 unit2 (3 squares across by 3 squares down)

Area = 20 unit2 (5 across by 4 down)

For rectangles, multiply squares across by squares down: area = length × breadth.



Name: Class:

6G Area of a Triangle

1 Use the centimetre grid to find the area of each triangle.

2 Calculate the area of each triangle.

Exercise

a

b

c d

a b c d

e f g h

i j k l

2 cm

6 cm

4 cm

4 cm8 cm

6 cm

5 cm

6 cm

4 cm

7 cm

8 cm

8 cm 10 cm

5 cm 10 cm

14 cm

10 cm

7 cm

7 cm

6 cm

20 cm

12 cm 15 cm

6 cm

Examples

Find the area of these triangles.These two areas total 1 square.

These two areas total 1 square.

1 3

These two areas total 1 square.

The triangle is half the

6 by 4 rectangle.

∴ Area = × (6 × 4) cm2

= 12 cm2

12---

These two areas give 1 square.

Area = 4 cm2 Area = 3 cm2

Easier than counting is to say each triangle is half the rectangle.Area = × (4 × 2) cm2 Area = × (3 × 2) cm2

= 4 cm2 = 3 cm2

12--- 1

2---

The triangle is half the

3 by 6 rectangle.

∴ Area = × (3 × 6) cm2

= 9 cm2

12---

4

2

4 cm

6 cm

3 cm

6 cm

1 1 1



Name: Class:

6J Volume of a Rectangular Prism

1 Find the volume in cm3.

2 Find the volume of each prism in cm3.

Exercise

a b c d

a b c

d e f

g h i

2 cm

2 cm

8 cm6 cm

4 cm

2 cm

3 cm

4 cm

6 cm

5 cm

4 cm

4 cm

5 cm

2 cm

1 cm

6 cm

3 cm

2 cm

3 cm

4 cm

7 cm 8 cm

4 cm

2 cm

6 cm

10 cm

3 cm

Examples

1 2 3

This prism has 2 layers each with 3 × 3 cubes.∴ Volume = (3 × 3) × 2

= 18 cm3

This prism has 2 layers each with 4 × 2 cubes.∴ Volume = (4 × 2) × 2

= 16 cm3

This prism has 3 layers with 4 × 5 cubes.∴ Volume = 4 × 5 × 3

= 60 cm3

To find the volume of a rectangular prism, count (or imagine) the number of cubes in the box. Assume each cube has a volume of 1 cm3.



Name: Class:

7B Clocks and Times

12 12

3

4567

8

9

101112 1

2

3

4567

8

9

1011

1 How many minutes in the following lengths of time?a 1 hour b 2 hours c 10 hours d 24 hours e hour f 1 hours

g 5 hours h 5 hours i hour j 2 hours k 11 hours l 7 hours

2 Write each time as ‘minutes to’ or ‘minutes past’.

Exercise

12--- 1

2---

12--- 1

4--- 1

4---

12 12

3

4567

8

9

1011 12 1

2

3

4567

8

9

1011 12 1

2

3

4567

8

9

1011 12 1

2

3

4567

8

9

1011 12 1

2

3

4567

8

9

1011 12 1

2

3

4567

8

9

1011

12 12

3

4567

8

9

1011 12 1

2

3

4567

8

9

1011 12 1

2

3

4567

8

9

1011 12 1

2

3

4567

8

9

1011

g h i j k l

a b c d e f

12 12

3

4567

8

9

101112 1

2

3

4567

8

9

1011

Puzzle | Why is a belt like a garbage truck?Fill in the blanks below, then use the letters to answer the riddle.A 3 h = . . . min B 2 days = . . . h C 5 min = . . . s D 660 min = . . . hE 30 min = . . . s G 300 min = . . . h H 10 min = . . . s I 7 d = . . . hN 180 s = . . . min O 30 s = . . . m R day = . . . h S 6 h = . . . min

T 120 s = . . . min U 24 h = . . . day W h = . . . min

48 1800 300 180 1 360 1800 168 2 5 1800 360 180 12 1 3 11

.180 3 11 5 180 2 600 1800 12 360 2 600 1800 45 180 168 360 2

12---

34---

12--- 1

2---

Examples

2 Read the times in ‘minutes to’ or ‘minutes past’.

1 How many minutes in the following times?

b 2 hours

2 × 60

= 150 min

12---

12---

a 4 hours4 × 60= 240 min

25 minutes past 3 10 minutes to 6

a

There are 5 minutes between numbers.

b



Name: Class:

7C The Calendar and Dates

1 a How many days in 2 weeks? b How many years in 36 months?c How many days in 3 years? d How many fortnights in 16 weeks?e How many days in 4 fortnights? f How many months in 4 years?g How many days in 10 weeks? h How many weeks in 84 days?i How many (full) weeks in a year? j How many months in 10 years?k How many weeks in 280 days? l How many years in 72 months?

2 How many days from:a 13 to 20 June? b 1 to 24 April?c 22 October to 13 November? d 30 March to 21 April?e 16 February to 16 March? f 7 April to 7 July?g 20 October to Christmas Day? h 3 August to the end of the month?i 10 August to 10 October? j 15 January to 9 February?

Exercise

Puzzle | What is bigger when it is upside down?Put each day in order as it comes during the year. The first one has been done for you.

B Christmas Day E April Fool’s Day H Fathers’ Day

I New Year’s Day M Australia Day N Anzac Day

R Mothers’ Day S Boxing Day T New Year’s Eve

U Halloween (31 October) X Valentine’s Day (14 February)

Use the letters to complete the riddle.

.11 7 4 5 8 2 9 4 6 10 1 3

1

Examples2 weeks = 1 fortnight

12 months = 1 year

4 How many days from 8 to 20 September?20 − 8 = 12 days

1 How many days in 3 weeks?3 × 7 = 21 days

3 How many days in 2 years?2 × 365 = 730 days

5 How many days from 8 June to 14 July?8 to 30 June = 22+ 14 in July = 14

Total = 36 days

6 How many days from 28 April to 17 June?28 to 30 April = 2

+ May = 31+ June = 17

Total = 50 days

2 How many years in 60 months?60 ÷ 12 = 5 years

365 days = 1 year7 days = 1 week



Name: Class:

7D Operating with Time

1 a 2 h + 5 h 30 min b 1 h 20 min + 6 h c 4 h 15 min + 2 h 20 mind 3 h 25 min + 2 h 15 min e 2 h 55 min + 8 h f 10 h + 4 h 5 ming 6 h 25 min + 7 h 5 min h 1 h 17 min + 3 h 36 min i 8 h 7 min + 2 h 19 minj 4 h 15 min + 27 min k 34 min + 2 h 12 min l 3 h 5 min + 2 h 9 min

2 What is the difference between the following times (on the same day)?a 10 am and 1 pm b 7 pm and 11 pm c 4 am and 10 amd 8 am and 3 pm e 1 am and noon f 3 am and 2 pmg 11 am and 6 pm h noon and 5 pm i noon and midnightj 3 pm and 8 pm k 6 am and 6 pm l 7 am and 4 pm

3 How long is it between the following times?a 5:35 to 5:50 b 1:20 to 1:42 c 11:10 to 11:40d 7:05 to 7:30 e 3:10 to 4:30 f 10:15 to 11:35g 9:05 to 11:35 h 6:30 to 9:45 i 2:16 to 2:50j 4:30 to 6:50 k 3:25 to 4:30 l 8:27 to 8:50

Exercise

Puzzle | My sister went on a crash diet.Put these times in order from the earliest to the latest in the day (1st to 13th).Then use the letters to complete the punchline below.A 2:30 pm C noon E 7:20 am H 6:45 pm I 4 amK 9:16 pm L 11:52 am O 1 am R 3:05 pm S 5:55 amT 9 pm W 12:30 am Y 11:10 pm

3rd 4th 11th 10th 8th 11th 1st 10th 13th 4th 10th 5th

?6th 2nd 2nd 12th 4th 8th 1st 9th 5th 7th 12th

Examples

2 Find the difference between 9 am and 8 pm.9 am to 12 noon = 3 h

noon to 8 pm = 8 h∴ difference = 11 h

1 Find 3 h 10 min plus 4 h 20 min.3 h 10 min4 h 20 min

7 h 30 min

b 3:30 to 5:45?5 h 45 min

−3 h 30 min

2 h 15 min

a 8:15 to 8:55?55 min

−15 min

40 min

3 How long is it from



Name: Class:

7D Measuring Instruments

1 Measure each length in centimetres.a b c

d e

f g

h i

2 What time is shown?

Exercise

a b c d

e f g h

i j k l

12 12

3

4567

8

9

1011 12 1

2

3

4567

8

9

1011

12 12

3

4567

8

9

1011 12 1

2

3

4567

8

9

1011

12 12

3

4567

8

9

101112 1

2

3

4567

8

9

1011

PM 11:02

AM 1:2910:10AM

5:00

AM 3:20PM 7:01

Puzzle | Dad: ‘How did you find your maths test?’Put these times in order, left to right, from earliest to latest in the day, in the boxes below to find the code. Some have been done for you. Use the code to answer the question.

1 8 pm 2 10:15 am 3 7 o’clock at night 4 noon5 quarter to seven in the morning 6 1:30 pm 7 6:15 am8 half past three in the afternoon 9 ten minutes past midnight

10 quarter past nine at night 11 4:36 am12 two in the afternoon 13 twenty past six in the evening

9 11 4 8 10

A E F I L N O R S T U W Y

S N : ‘ N N A E Y

8 6 4 3 4 7 6 12 13 3 4 9 13 11 2 10

A S N S !’5 13 1 9 8 4 13 2 6 8 13

(earliest) (latest)



Name: Class:

9G Finding the Size of an Angle

Find the value of each pronumeral.

Exercise

a b c d

e f g h

i j k l

m n o p

q r s t

140°a°b°

30° 120° 32°

c°74°

85°

d°

e°235°

152°85°

f °

40°

g° 62° 37°h°

i° 65°

111°124° 62°j°

40°

80°

k° 73°l°

m°

137°

160°50°60°

n°

128°

16°

x°

p°

102°

t°

122°

68°s°

70°

70° r°

80°

70°

130°

q°

Examples

Find the value of each pronumeral.

1 A right angle = 90°.

x = 90 − 67 = 23

67°x°

2 A straight angle = 180°. 3 A revolution = 360°.

y = 180 − 134 = 46

134° y°

a = 360 − 90 − 60 = 210

60°a°

4 The angle sum of a triangle is 180°.

x = 180 − 134 − 18 = 28

18°

134°

x°

5 The angles in a quadrilateral total 360°.

x = 360 − 80 − 116 − 65 = 99

80°

116°

65°

x°


Name: Class:


11B Simplifying Algebraic Expressions

1 Simplify the following.a b c d e

2 Simplify the following by counting on or counting back.a 2x + 3x b 7a − 3a c 10p + 4p d 8f − 2f e 12k − kf 4m + 5m g y + y h 6y + y i 4x − 3x j 6t + 10tk 20w − 5w l x + 4x m 13d − 6d n 3m − 3m o 11p + 3pp 7y − y q f + f r 26c − 4c s 15c + 9c t 8ab + 4ab

3 Simplify the following by counting like terms.a 5a + 3 + 4 b 2x + 3y + 4x c 2a + 5a + 6b d 7 + 8 + 4he 7c − 3c + 1 f 10t + 8 − 3 g 6m + 7 + 3m h 10 + 3c + ci 6 + 5x − 3x j 3x − x + 4y k 10m − 3m + 2n l 15 − 4 + 7am 5x + 10x + 3y n 12x + 2y + x o 4b + 3b + 5c p 4b + 3c + 5bq 10t − 5t + 6u r 4w + 7w + 9 s 8x − x + 4 t 8 + 3y + 4

Exercise

x x a a x x

x x

x y

y ya

Puzzle | Which band member is really great at algebra?Simplify each expression, then match its letter with the answers below.A 3a + 4a B 7a + a C 6b − b D 9b − 3bE 2b + b G 13c − 10c H 5c + 2d + 3d I 6a − 2a + 5cL 2c + 12a − 8a M 6d − 4d + 12 R 3 + 9d + 2 S 2a + 3a + 4aT 3a + 5b + 5a U 7d + 3c − 2c W 3d + 9 + 8d Y 7 − 2 + 7b

. ’

8a +

5b

5c +

5d

3b 6b

9d +

5

c +

7d

2d +

12

2d +

12

3b

9d +

5

5c +

5d

3b 9a

!

3c

9d +

5

3b 7a

8a +

5b

11d

+ 9

4a +

5c

8a +

5b

5c +

5d

5b

7b +

5

2d +

12

8a 7a

4a +

2c

9a

Examples

1 4c + 3c = 7c because 4 + 3 = 7

2 10x − x = 9x as ‘x’ means ‘1x’ and 10 − 1 = 9

3 3a + 7a + 4 + 5 = 10a + 9 because 3a + 7a = 10aand 4 + 5 = 9

4 3m + 4n + 5m= 8m + 4n because 3m + 5m = 8m

A lot of algebra is just counting letters.



Name: Class:

11C Making Sense of Algebra

1 Write the number of counters in each case.a b c d e

f g h i j

2 a b c d e

f g h i j

k l m n o

Exercise

x y x x x a

y y

y y

xx

y a

aa

y y

y

y

y

y y x

y

x x y x

y

x

y

x a b

b

b

x

x

bb

aab

xxx

x

x

y

y

x

x

x y y

y

y

x y x

b

a

b b

a a

b

a

b

x

y ym n

Puzzle | What’s the difference between a night-watchman and a butcher?Each expression can be written in a shorter form. Match the letters to the abbreviations.A 6 × a D a × 3 E 1 × a G a × a H a ÷ 2 I a × b K y × xN x ÷ 4 O x × 3 R y ÷ 4 S m × m T m × 2 W y × 1 Y m ÷ 10

3x a m2 2m 6a m2 6a y 6a xy a

6a 3a 2m a 3x 2m a

!

y a ab a2 m2 6a m2 2m a 6a xy

x4--- m

10------

x4--- a

2--- a

2--- y

4---

a2---

Examples

1

x + 4

x

Imagine is a box containing an unknown number of counters .

x

2

y + 2

y 3

2a + 2

a a 4

2a + 3b

a a

b b b

How many counters are here?



Name: Class:

11D Grouping Symbols

1 Remove grouping symbols.

a 2(x + 3) b 5(a − 4) c 3(p + 2) d 8(c − 1)

e 10(m + 5) f 4(y + 8) g 7(2 − h) h 2(4 + d)

i 5(x + 6) j 9(4 − b) k 6(3 − x) l 4(y + 5)

m 7(3 + t) n 11(c − 3) o 20(a + 5) p 2(10 − x)

q 1(y + 8) r 10(x − 7) s 3(c − 4) t 6(f + 9)

2 Expand.

a 3(5m − 1) b 2(2x + 5) c 7(3 + 2x) d 4(3x + 1)

e 10(2p + 9) f 1(7x − 8) g 5(4x − 7) h 6(2x + 1)

i 8(2 − 7a) j 2(3 − 7x) k 3(8c − 5) l 11(1 − 4c)

m 9(2y + 3) n 4(9 + 5t) o 4(3d + 1) p 6(7y + 4)

q 3(7 − 5x) r 5(3x + 10) s 2(11p − 2) t 8(2x − 6)

Exercise

Puzzle | What is the best cure for dandruff?Expand each of these. Match each letter to the answers below.

A 5(3x + 2) B 2(7x + 3) D 3(5x + 4) E 8(2x + 1)

L 6(3x + 2) N 4(4x + 3) S 3(6x + 5)

14x + 6 15x + 10 18x + 12 15x + 12 16x + 12 16x + 8 18x + 15 18x + 15

Examples

1 4(a − 7) = 4 × a − 4 × 7= 4a − 28

2 3(x + 5) = 3 × x + 3 × 5= 3x + 15

3 10(2y − 3) = 10 × 2y − 10 × 3= 20y − 30

4 6(4y − 1) = 6 × 4y − 6 × 1= 24y − 6

5 5(4 − 3y) = 5 × 4 − 5 × 3y= 20 − 15y

To expand or remove grouping symbols, multiply each term inside the bracket by the term outside.



Name: Class:

11E Substitution

1 Find the value of each expression.a 3x, if x = 12 b 2y, if y = 20 c a + 3, if a = 8 d k − 10, if k = 13e m2, if m = 3 f t + 11, if t = 4 g d − 2, if d = 2 h 7p, if p = 9i 18 − c, if c = 10 j 9x, if x = 4 k 10 + w, if w = 7 l 8d, if d = 3

m v2, if v = 1 n r + 6, if r = 0 o if x = 12 p if a = 50

2 Given that x = 12 and y = 4, find the value of each expression.

a b x − y c 5y d y2 e y − 7 f 20 − x g 2x − 5

h x + 2y i j x2 − 20 k y2 + 8 l xy m y − x n x − 5y

o + 5 p 3x + 4y q − 7 r 2x − 3y s 10y − x t 3x − 6 u 15 − 3y

Exercise

x3--- , a

10------ ,

x6---

xy--

y2--- x

3---

Puzzle | What’s the difference between a monster and a biscuit?Simplify the following. Match the letters to the answers.A 6 × a D 12 × b E 3 × 4 × a I 3 × 8 × a K 10 × 6 × bM 20b + 6b N 6 × 8a O a × b R b × 5 S 4 × 2 × aT 2 × 3b U 5 × 7b V 8 × 2 × b Y 2 × a × b

12a 16b 12a 5b 6b 5b 24a 12a 12b 6b ab 12b 35b 48a 60b 6a

?26b ab 48a 8a 6b 12a 5b 24a 48a 2ab ab 35b 5b 6b 12a 6a

Examples

2 Given that x = 8 and y = 5, find the value of these.

1 Find the value of the pronumeral.b m − 6 if m = 4

m − 6 = 4 − 6= −2

a 5a, if a = 65a = 5 × a

= 5 × 6= 30

b

= x ÷ 2

= 8 ÷ 2= 4

x2---

x2---

a x + yx + y = 8 + 5

= 13

c 4x + 74x + 7 = 4 × x + 7

= 4 × 8 + 7= 39

d y2 − 10y2 − 10 = 52 − 10

= 25 − 10= 15

To substitute, put a number in place of a letter, then calculate.



Name: Class:

11I Patterns and Rules

1 Complete these patterns.

a 5, 10, 15, . . . , . . . b 4, 6, 8, . . . , . . . c 20, 18, 16, . . . , . . .

d 3, 6, 12, . . . , . . . e 20, 30, 40, . . . , . . . f 2, 4, 8, . . . , . . .

2 Complete these tables.

3 Complete the rule used in each table below.

Bottom = top + . . . Bottom = top + . . . Bottom = top × . . .

Bottom = top × . . . Bottom = top − . . . Bottom = . . . + top

4 Write the rule for each table in question 2.

a Bottom = . . . × top b Bottom = . . . + top c Bottom = top × . . .

d Bottom = top + . . . e Bottom = f Bottom =

a Top 1 2 3 4 b Top 1 2 3 4 c Top 1 2 3 4

Bottom 2 4 6 Bottom 11 12 13 Bottom 5 10 15

d Top 0 1 2 3 e Top 3 4 5 6 f Top 1 2 3 4

Bottom 4 5 6 Bottom 9 12 15 Bottom 4 5 6

a Top 1 2 3 4 b Top 3 4 5 6 c Top 0 1 2 3

Bottom 7 8 9 10 Bottom 4 5 6 7 Bottom 0 7 14 21

d Top 1 2 3 4 e Top 10 9 8 7 f Top 1 2 3 4

Bottom 10 20 30 40 Bottom 4 3 2 1 Bottom 2 3 4 5

Exercise

1 Complete this pattern.6, 12, 18, . . . , . . .The rule is ‘add 6’, so the pattern becomes 6, 12, 18, 24, 30

2 Complete the table.

The bottom is 4 times the top number, so the missing number is 4 × 4 = 16

Top 1 2 3 4

Bottom 4 8 12

3 Complete the rule.

Bottom = top + . . . 8 is added each time, so bottom = top + 8

Top 0 1 2 3

Bottom 8 9 10 11

Examples



Name: Class:

12A Algebraic Sentences

Find the number that makes the equation true.

1 a + 3 = 10 b 4 × = 20 c + 9 = 11 d × 3 = 12 e 10 × = 70

f 5 + x = 11 g x + 8 = 12 h 8x = 40 i 2a = 18 j 4 + a = 13

k 6m = 18 l y + 11 = 18 m 6k = 6 n 7w = 56 o x + 9 = 30

p p + 11 = 33 q b + 5 = 32 r 7t = 42 s 4y = 36 t 20 + h = 21

2 a x − 2 = 7 b a ÷ 2 = 9 c = 12 d y − 9 = 10 e m − 13 = 18

f h − 5 = 6 g = 2 h x − 12 = 3 i a − 7 = 0 j = 3

k a ÷ 3 = 6 l k − 6 = 14 m h − 8 = 15 n x ÷ 6 = 8 o x ÷ 7 = 9

p = 6 q c − 20 = 10 r p − 15 = 5 s m − 8 = 8 t = 1

Exercise

c4---

c4--- x

10------

n5--- a

7---

Puzzle | What do you get when you cross a galaxy with a toad?Solve each equation and match each letter with the answers below.

A 3x = 12 R x + 7 = 12 S x − 9 = 5 T x ÷ 6 = 2 W 7 + x = 10

!14 12 4 5 3 4 5 12 14

Examples

1 + 5 = 9

(What number add 5 gives 9?)

= 4

2 3 × = 24

(3 times what number gives 24?)

= 8

[What number goes into 24 three times?]

4 = 3

(What number divided by 5 gives 3?)c = 15

c5---

In reverse

To find the number that makes the equation true• read the sentence to yourself, thinking ‘what

number . . .’• thinking in reverse can be a help.

3 a − 9 = 7

(What number take away 9 gives 7?)

a = 16

[What number is 9 more than 7?] In reverse



Name: Class:

12C Solving Problems Using Algebra

1 Solve each equation.a x + 9 = 10 b 5x = 30 c y − 4 = 11 d t ÷ 3 = 6 e 13 + m = 20

f a + 5 + 7 = 30 g 15x = 120 h p + 18 + 13 + 6 = 45 i = 10

2 Form an equation, then solve it.

d The sum of two numbers is 40. If one is 18, what is the other?e If two numbers multiply to give 40 and one number is 8, what is the other?f The difference between a number and 12 is 13, what is the number?g Five copies of a CD cost me $74.50. Form an equation, then find the cost, c.h Three sisters shared $100. If Tina got $30, and Janet got $24, how much did Helen receive?i An amount of money is divided evenly between 6 people. If they each get $22, how much was

the original amount?

m A box of 144 apples is shared evenly. If each person gets 9 apples, how many people are there?n Duncan starts shopping with $120. If he ends up with $84, how much did he spend?

Exercise

c6---

a b cPerimeter = 18Find x.

Perimeter is 24.Find y.

Perimeter = 50Find x.

3

6

x

y

18x

7

x

j k lPerimeter = 70Find x.

Area = 180.Find x.

Perimeter = 85Find a.

17

30x

x

20

a

Examples

1 The total of 5, 9, 13 and a number is 45. What is the missing number?Let n = number.∴ n + 5 + 9 + 13 = 45

n + 27 = 45n = 18 Subtract 27

∴ number is 18.

2 The product of a number and 21 is 273.Find the number.Let x = number.

21 × x = 273x = 273 ÷ 21x = 13

∴ number is 13.

3 Find the side a if the perimeter is 80.a + 20 + 11 + 17 + 25 = 80

a + 73 = 80 (-73)a = 7

∴ side is 7.

• Form an equation.• Solve this equation to

answer the problem.

20

25

11

17

a



Name: Class:

12E Language and Symbols

1 True or false?

a 3 = 5 × 2 b 8 � 5 c 10 − 2 � 3 × 5

d 7 × 4 = 24 e 12 � 15 f 10 ÷ 2 ≠ 6 − 3

2 Use symbols to write these.

a 5 is less than 6 b 10 is greater than 4

c 12 minus 5 equals 7 d 4 times 3 is greater than 7

e 10 is not equal to 4 times 3 f the sum of 6 and 3

Exercise

Puzzle | Why do cats make the best pets?Work out each answer. Put the letter for each part in the box above the correct answer.

C 10 less 4 E product of 2 and 7 F sum of 3 and 7

H decrease 8 by 6 P increase 6 by 9 R sum of 2, 3, 4

T divide 10 by 2 U average of 6 and 10 Y 6 times 4

’5 2 14 24 9 14 15 8 9 9 10 14 6 5

Examples

1 True or false? 16 � 3 × 7This means 16 is less than 3 × 7.

ie 16 � 21∴ True

2 True or false? 6 × 3 = 10 + 6This means 6 × 3 is equal to 10 + 6.

ie 18 = 16∴ False

4 Write using symbols.5 times 6 is greater than 20

5 × 6 � 20

3 Write using symbols.The sum of 12 and 8

12 + 8

MATHS DIMENSIONS 7 CHALLENGE WORKSHEETS © Pearson Education Australia (a division of Pearson Australia Group Pty Ltd) 2006.This page may be photocopied for classroom use.

Challenge Worksheet

Name: Class:

Ch1 Solving Puzzles

Examples

Complete this magic square.You can see from the bottom line 1 that the total is 120. Each row, column and diagonal must have a sum of 120, the magic number.You find the 26 from column 2.Then find the 40 from row 3.Then move to column 4 to fill in the empty box, and so on until completed.

16 42 28

38 14 40 26 2

24 0

46 22 34

20 6 32 18 44

4

3 120

120

1 120

2120

1 Find the missing numbers in these giant magic squares.

2 A carpenter has two lengths of timber, each with a square cross section of 100 mm by 100 mm.He saws one length into 3 pieces in six minutes. At this rate of sawing how long would it take him to saw the second length into 6 pieces?

3 Here are six different views of the same cube. What letter is on the opposite face To F? To E? To C?(Hint: Make a cube.)

4 How would you place the numbers1, 2, 3, 4, 5 and 6

in the circles so that the sum of the numbers on each side of the triangle is 10?

a 6 32 18 44 30 b 6 19 15 c 3 10 17 26

16 42 28 18 1 14 22 22

14 26 38 5 13 21 9 11 20

48 24 36 12 8 16 25 7 9 16

34 20 46 7 3 14 23 5 12

Exercise


Challenge Worksheet

Name: Class:

Ch2 HCF and LCM by Prime Factors

• HCF is the highest factor common to both numbers and must contain all the common prime factors.

• LCM is the lowest number both numbers divide into and may be found by listing the factors of the bigger number and including factors of the smaller number not yet included.

Find the HCF and LCM of the following pairs of numbers.1 16 and 24 2 18 and 24 3 36 and 100

4 80 and 140 5 81 and 108 6 48 and 72

7 30 and 75 8 36 and 54 9 90 and 135

10 60 and 84 11 50 and 75 12 70 and 98

Exercise

Examples

Find the HCF and LCM of the following.1 80 and 112

2 84 and 156

∴ 80 = 2 × 2 × 2 × 2 × 5 ∴ 112 = 2 × 2 × 2 × 2 × 7HCF= 2 × 2 × 2 × 2 = 16 (all the factors that are common to both)LCM= 2 × 2 × 2 × 2 × 7 × 5 = 560 (the factors of 112 and the 5 not included from 80)

112

562

2 2 28

×

× ×

2 2 2×× 14×

2 × 2 2× 2 7××

80

402

2 2 20

×

× ×

2 2 2×× 10×

2 × 2 2× 2 5××

84

422

2 2 21

×

× ×

2 2 3×× 7×

∴ 84 = 2 × 2 × 3 × 7 ∴ 156 = 2 × 2 × 3 × 13HCF= 2 × 2 × 3 = 12 (all the factors that are common to both)LCM= 2 × 2 × 3 × 13 × 7 = 1092 (the factors of 156 and the 7 not included from 84)

156

782

2 2 39

×

× ×

2 2 3×× 13×


Challenge Worksheet

Name: Class:

Ch11 Describing Number Patterns

1 This table of values gives the number of small squares in each figure.

Hint: 1 × 2 2 × 3 3 × 4 4 × 5a What rule links the number of small squares to the height of each figure?b Complete the table for heights up to 8.

2 a Write down the number pattern that these matches represent.

b Write the next two numbers in the pattern.

3

a Complete this table.

b The pattern in words is . . . .c Write the rule using s, d.

4 Find the rule connecting the top row number with the bottom row number. (B = . . .)What would the tenth bottom number be?

5 Find the pattern, then write the next two numbers.a 5, 9, 13, 17, . . . , . . . . b 8, 4, 2, 1, . . . , . . . .c 20, 15, 10, 5, . . . , . . . . d 400, 4000, 40 000, 400 000, . . . , . . . .

6 Write the first four numbers in the pattern with these rules.a 3n + 2 b 6 − n c 2n − 7 d n2 + 5

Height of figure 1 2 3 4 5 6 7 8

Number of small squares 2 6 12 20

Number of sides (s) 3 4 5 6 7 8 9 10

Number of diagonals (d)

a Top (T) 1 2 3 4 b Top (T) 1 2 3 4

Bottom (B) 1 4 9 16 Bottom (B) 11 10 9 8

Exercise

43

12

Diagonals Drawn from One Vertex

Worksheets

Answers

1D Know Your Tables1 7, 8, 11, 10, 14, 9, 15, 13, 12, 16 2 9, 3, 6, 10, 2, 5, 8, 1, 4, 7

3 0, 14, 7, 35, 70, 21, 49, 28, 56, 42, 63, 77 4 12, 24, 8, 28, 32, 4, 16, 36, 20, 40, 0, 44

5 9, 12, 8, 11, 5, 6, 10, 14, 13, 15 6 6, 1, 2, 5, 8, 3, 0, 7, 9, 4

7 24, 12, 18, 27, 21, 15, 6, 3, 0, 33, 9, 30 8 13, 14, 10, 12, 16, 8, 15, 11, 17, 9

9 42, 12, 24, 60, 36, 48, 54, 18, 66, 6, 0, 30 10 9, 8, 12, 5, 7, 10, 3, 13, 6, 11

11 9, 27, 72, 99, 18, 81, 90, 0, 36, 63, 54, 45 12 1, 10, 4, 2, 7, 6, 9, 3, 0, 5

1G Grouping Symbols1 a 50 b 42 c 9 d 30 e 49 f 28

2 a 18 b 4 c 2 d 20 e 30 f 16

3 a 3 b 2 c 5 d 2 e 7 f 0

1H Rounding Numbers1 a 370 b 80 c 40 d 140 e 570 f 6080 g 590 h 8020

i 40 j 880 k 60 l 210

2 a 8700 b 1200 c 300 d 500 e 6600 f 900 g 2800 h 200i 500 j 9900 k 7000 l 300

2D Divisibility Tests1 a 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 b 1, 3, 5, 7, 9, 11, 13, 15, 17, 19

c 5, 10, 15, 20, 25, 30, 35

2 a 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 b 3, 6, 9, 12, 15, 18, 21, 24, 27, 30c 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 d 10, 20, 30, 40, 50, 60, 70, 80, 90, 100e 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 f 7, 14, 21, 28, 35, 42, 49, 56, 63, 70g 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 h 9, 18, 27, 36, 45, 54, 63, 72, 81, 90

3 a 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28 b 3, 6, 9, 12, 15, 18, 21, 24, 27 c 10, 20

4 a 15, 54 321 b 40, 125, 100 000c 12, 201, 54 321, 12 345 d 24, 42, 66, 888

2F Powers of Numbers1 a 16 b 64 c 9 d 1 e 81 f 4 g 25 h 100

i 49 j 36 k 8 l 1 m 125 n 27 o 1000

2 a 49 b 100 c 25 d 64 e 4 f 1 g 36 h 16i 9 j 81 k 27 l 8 m 64 n 1000 o 216

3 a 103 b 62 c 26 d 72 e 54 f 95 g 84 h 43

i 105

2G Square and Cube Roots1 a 4 b 2 c 5 d 9 e 11 f 20

2 a 7 b 8 c 10 d 12 e 1 f 15

3 a 5 b 3 c 4 d 9

4 a 6 b 2 c 8 d 30

3F Addition and Subtraction of Fractions

1 a = b 2 a b = 3 a b

4 a b c d e f g h

i j k l m n o p

510------ 1

2--- 9

11------ 5

8--- 8

12------ 2

3--- 2

5--- 4

9---

38--- 1

8--- 3

10------ 19

20------ 2

5--- 11

15------ 7

11------ 27

100---------

35--- 7

8--- 10

13------ 17

25------ 14

25------ 11

20------ 7

10------ 2

15------

MATHS DIMENSIONS 7 WORKSHEET ANSWERS © Pearson Education Australia (a division of Pearson Australia Group Pty Ltd) 2006.This page may be photocopied for classroom use.

q r s t u = v = w = x =

y =

3G Addition and Subtraction of Mixed Numbers

1 a 1 b 5 c 2 d 7 e 3 f 4 g 10 h 6

i 1 j 5

2 a 3 b 5 c 9 d 6 e 8 f 10 g 9 h 8

i 2 j 5

3 a b 1 c 2 d 3 e 1 f 2 g h 3

i 2 j 9

4 a 2 b 2 c 1 d 2 e 2 f 1 g 1 h 4

i j

3I Multiplication of Fractions

1 a b c d e f g h

i j k l m n o

2 a b c d e f g h

i j k l m n o

3 a b c d e f g h

i j

3J Division Involving Fractions

1 a 8 b 4 2 a 9 b 2 3 a 2 b 34 a 4 b 2 5 a 2 b 7 6 a 3 b 47 a 3 b 5 c 2 d 5 e 5 f 5 g 3 h 3

i 7 j 1 k 3 l 3 m 6 n 11 o 2 p 3q 9 r 1 s 4 t 2

3K Fractions of Quantities1 a 10 min b 3 kg c $5 d 30 m e 7 mm f $3

g $50 h 9 km i 11 t j 15 kg k 18 L l $60m 22 mm n 120 t o 12 h p 111 min

2 a 10 b 20 c 30

3 a $8 b $24 c $56

4 a $6 b $12 b $18

5 a $15 b 21 mm c $15 d $350 e 28 t f 30 kg g $120 h 333 mini 20 cm j 35 L k 15 kg l 12 h m 18 m n $48 o $57 p 15 cm

4C Application of Decimals1 a $106 b $90 c $4 d $91 e $25 f $67 g $13 h $3

i $7 j $40

2 a 75c b 85c c 30c d 40c e 60c f 10c g 65c h 25ci 95c j 5c

37100--------- 29

40------ 11

12------ 83

100--------- 5

10------ 1

2--- 4

16------ 1

4--- 4

12------ 1

3--- 5

20------ 1

4---

68--- 3

4---

34--- 1

10------ 5

9--- 13

20------ 7

8--- 11

12------ 4

5--- 12

25------

11100--------- 5

6---

12--- 1

4--- 5

8--- 3

10------ 1

9--- 2

5--- 17

20------ 7

12------

815------ 3

10------

12--- 3

4--- 5

6--- 5

8--- 7

10------ 7

12------ 17

20------ 7

9---

316------ 1

5---

12--- 3

4--- 2

3--- 7

8--- 1

5--- 17

20------ 8

15------ 15

16------

47100--------- 8

9---

12--- 1

2--- 11

20------ 11

20------ 2

3--- 1

4--- 3

4--- 7

10------

56--- 7

8--- 19

20------ 8

9--- 1

5--- 13

15------ 8

11------

14--- 2

5--- 1

4--- 3

10------ 2

11------ 3

10------ 1

10------ 3

16------

445------ 5

18------ 3

8--- 1

8--- 3

25------ 4

31------ 7

100---------

16--- 1

12------ 1

70------ 1

20------ 1

15------ 1

32------ 1

100--------- 1

16------

130------ 1

100---------


3 a $4 b $4.25 c $1.70 d $5.60 e $3.10 f $7.60 g $2.95 h $3.35i $8.10 j $2.35

4C Rounding Off1 a 85c b 8c c 61c d 19c e 40c f 53c g 3c h 46c

i 27c j 30c k 88c l 14c m 10c n 40c o 71c p 18cq 60c r 6c

2 a $8 b $9 c $4 d $4 e $2 f $2 g $8 h $9i $12 j $6 k $6 l $2 m $4 n $10 o $5 p $10q $7 r $4

4D Addition and Subtraction of Decimals1 a 6⋅6 b 8⋅9 c 7⋅84 d 3⋅866 e 7⋅54 f 6⋅53 g 17⋅73 h 18⋅1

i 11⋅168 j 14⋅523

2 a 3⋅6 b 4⋅2 c 12⋅13 d 2⋅27 e 1⋅8 f 0⋅84 g 17⋅73 h 1⋅09i 0⋅559 j 5⋅88

3 a 3⋅3 b 9⋅5 c 3⋅6 d 15⋅68 e 23⋅92 f 3⋅125 g 1⋅73 h 10⋅82i 24⋅49 j 18⋅86

4F Multiplying a Decimal1 a 0⋅6 b 4⋅2 c 1⋅77 d 23⋅55 e 28⋅8 f 69⋅2 g 92 h 61⋅2

i 23⋅4 j 22⋅47 k 0⋅32 l 0⋅063

2 a 1⋅2 b 3⋅15 c 6⋅3 d 0⋅22 e 10⋅5 f 10⋅83 g 9⋅52 h 66⋅5i 20⋅7 j 5⋅04 k 0⋅108 l 11⋅8

3 a 6 b 52 c 40 d 0⋅7 e 35⋅4 f 370 g 1660 h 42i 414 j 810 k 0⋅32 l 20

4F Multiplying by Decimals1 a 0⋅82 b 0⋅81 c 8⋅4 d 18⋅5 e 1⋅17 f 29⋅05 g 1⋅66 h 0⋅036

i 0⋅375 j 24⋅4 k 21⋅28 l 0⋅76

2 a 0⋅28 b 0⋅06 c 0⋅035 d 0⋅05 e 0⋅4 f 3⋅6 g 0⋅027 h 0⋅0048i 0⋅09 j 0⋅25 k 0⋅0032 l 0⋅006

3 a 2⋅16 b 1⋅25 c 0⋅72 d 0⋅136 e 0⋅427 f 0⋅066 g 0⋅52 h 0⋅0052i 0⋅000 84 j 0⋅146 k 2⋅37 l 0⋅24

4G Using Decimals1 a 0⋅6 kg b $6.72 c 43⋅8 cm d 41⋅1 L

e $16.24 f 5⋅4 t g 22⋅82 m h 2⋅72 gi 15⋅21 h j $25.36 k 0⋅24 l 75⋅6 L

2 a 1⋅1 m b $4.81 c $3.80 d 10 cme 10⋅73 t f 0⋅975 kg g 4⋅241 kg h $10.61i 0⋅26 m j 9⋅86 mL k $2.27 l 8⋅63 m

3 a 0⋅6 L b $0.47 c 1⋅57 m d 0⋅27 kge $1.02 f 2⋅32 mL g 0⋅041 m h 0⋅11 ti 2⋅31 cm j 0⋅081 g k $1.72 l 0⋅8 m

4H Decimal Problems1 $35 2 $55.40 3 $65.50 4 33 5 $10.32, $10.30

6 344, 86 7 54 8 20 000 000 9 24 10 $840

4H Dividing a Decimal1 a 0⋅4 b 0⋅1 c 0⋅2 d 0⋅01 e 0⋅01 f 0⋅01 g 0⋅3 h 0⋅03

i 0⋅02 j 0⋅22 a 0⋅23 b 0⋅12 c 0⋅09 d 0⋅11 e 0⋅13 f 0⋅13 g 0⋅03 h 0⋅03

i 0⋅16 j 0⋅31

3 a 0⋅5 b 2⋅1 c 1⋅7 d 1⋅1 e 4⋅3 f 1⋅8 g 1⋅2 h 3⋅1i 2⋅3 j 2⋅2


4 a 1⋅02 b 2⋅12 c 1⋅01 d 4⋅13 e 1⋅15 f 0⋅41 g 0⋅42 h 1⋅12i 1⋅03 j 1⋅04

4K Review of Decimals1 a 0⋅3 b 0⋅07 c 0⋅93 d 0⋅6 e 0⋅004 f 0⋅133

g 0⋅1 h 0⋅73 i 0⋅43 j 0⋅024 k 0⋅92 l 0⋅28m 0⋅36 n 0⋅555 o 0⋅002 p 0⋅99 q 0⋅031 r 0⋅607

2 a b c d e f

g h i j k l

m n o p q r

3 a 0⋅7 b 0⋅71 c 0⋅3 d 0⋅83 e 0⋅51 f 0⋅12g 0⋅63 h 0⋅3 i 0⋅43 j 0⋅92 k 0⋅68 l 0⋅5

4M Changing Fractions and Decimals to Percentages1 a 15% b 2% c 47% d 93% e 72% f 6% g 25% h 20%

i 1% j 33% k 5% l 84% m 90% n 45% o 24% p 50%q 22% r 75% s 48% t 10% u 77% v 82% w 70% x 95%y 19%

2 a 14% b 7% c 64% d 99% e 2% f 31% g 30% h 85%i 80% j 18% k 44% l 40% m 53% n 23% o 1% p 29%q 71% r 90% s 25% t 58%

4M Review of Percentages

1 a 34% b 66% c = d =

2 a 65% b 35% c = d =

3 a = 0⋅03 b = 0⋅17 c = 0⋅63 d = 0⋅99

e = 0⋅27 f = = 0⋅2 g = = 0⋅05 h = = 0⋅06

i = = 0⋅15 j = = 0⋅44 k = = 0⋅25 l = = 0⋅5

m = = 0⋅18 n = = 0⋅62 o = = 0⋅55 p = = 0⋅36

q = 0⋅83 r = = 0⋅46 s = 0⋅77 t = 0⋅01

4 a 7% b 7% c 23% d 78% e 52% f 20%g 39% h 75% i 90% j 16% k 35% l 45%m 2% n 58% o 50% p 47% q 71% r 90%s 25% t 58%

4N Finding a Percentage of a Quantity1 a $15 b 8 g c 10 kg d 30 m e 4 f 9 L g $20 h 15 cm

i 14 t j 12 g k 9 l 22 m m 25 h n 211 t o 30 kg p $45

2 a $4 b $35 c 18 t d 35 kg e 160 m f 54 g g 60 h 24 si $40 j 24 km k 54 d l $18 m 240 m n 54 cm o 160 g p $200q 33 t r $28 s 300 L t 30

5E Measuring Length1 a 5 cm b 4 cm c 2 cm d 2 cm e 7 cm f 4 cm g 5 cm h 3 cm

i 8 cm j 2 cm

2 a 32 mm b 8 mm c 35 mm d 25 mm e 51 mm f 18 mm g 63 mm h 74 mm

5F Units of Length1 a 2 cm b 3 cm c 6 cm d 9 cm e 9 cm f 12 cm

710------ 3

100--------- 53

100--------- 9

100--------- 123

1000------------ 91

1000------------

13100--------- 59

100--------- 563

1000------------ 21

100--------- 303

1000------------ 299

1000------------

350------ 2

5--- 1

4--- 16

25------ 1

200--------- 7

500---------

34100--------- 17

50------ 66

100--------- 33

50------

65100--------- 13

20------ 35

100--------- 7

20------

3100--------- 17

100--------- 63

100--------- 99

100---------

27100--------- 20

100--------- 1

5--- 5

100--------- 1

20------ 6

100--------- 3

50------

15100--------- 3

20------ 44

100--------- 11

25------ 25

100--------- 1

4--- 50

100--------- 1

2---

18100--------- 9

50------ 62

100--------- 31

50------ 55

100--------- 11

20------ 36

100--------- 9

25------

83100--------- 46

100--------- 23

50------ 77

100--------- 1

100---------


2 a 80 b 3 c 9 d 8 e 7000 f 900 g 3000 h 120i 5 j 15 k 2000 l 11 000 m 5 n 10 000 o 8 p 6q 12 r 200 s 62 t 6000

3 a 180 b 120 c 2 d 10 e 300 f 8 g 1440 h 5

i 1200 j k 15 l 420 m 720 n 600 o 240 p

5H Perimeter1 a 9 cm b 31 cm c 24 cm d 64 cm e 56 m f 32 m g 23 m h 45 m

i 16⋅4 cm j 48⋅5 m k 40 mm l 64 m m 52 cm n 22⋅6 m o 30 mm p 50 cm

2 a 40 cm b 42 m c 200 m d 6 cm e 134 mm f 14⋅4 cm g 440 m h 8⋅4 cmi 77 cm j 60⋅2 m

6B The Definition of Area

1 a 4 cm2 b 5 cm2 c 7 cm2 d 12 cm2 e 6 cm2 f 12 cm2 g 8 cm2 h 8 cm2

i 10 cm2 j 5 cm2

2 Various possibilities—check with teacher.

6D Area of a Rectangle

1 a 12 u2 b 4 u2 c 6 u2 d 6 u2 e 10 u2 f 21 u2 g 15 u2 h 16 u2

2 a 18 u2 b 8 u2 c 14 u2 d 25 u2 e 28 u2 f 16 u2 g 30 u2 h 7u2

i 24 u2

3 a 40 cm2 b 28 cm2 c 100 cm2 d 32 cm2 e 45 cm2 f 33 cm2 g 36 cm2 h 64 cm2

i 100 cm2 j 30 cm2

6G Area of a Triangle

1 a 3 cm2 b 5 cm2 c 4 cm2 d 4 cm2

2 a 6 cm2 b 8 cm2 c 24 cm2 d 15 cm2 e 14 cm2 f 32 cm2

g 25 cm2 h 70 cm2 i 35 cm2 j 21 cm2 k 120 cm2 l 45 cm2

6J Volume of a Rectangular Prism

1 a 8 cm3 b 12 cm3 c 20 cm3 d 27 cm3

2 a 48 cm3 b 72 cm3 c 32 cm3 d 80 cm3 e 10 cm3 f 36 cm3

g 84 cm3 h 64 cm3 i 180 cm3

7B Clocks and Times1 a 60 b 120 c 600 d 1440 e 30 f 90 g 300 h 330

i 15 j 135 k 660 l 420

2 a 5 minutes to 9 b 20 minutes to 4 c 10 minutes past 12 d 20 minutes past 3e 15 minutes past 6 f 25 minutes to 1 g 10 minutes to 4 h 20 minutes to 1i 30 minutes past 12 j 15 minutes past 11 k 25 minutes past 9 l 25 minutes to 5

7C The Calendar and Dates1 a 14 b 3 c 1095 d 8 e 56 f 48 g 70 h 12

i 52 j 120 k 40 l 6

2 a 7 b 23 c 22 d 22 e 28 (or 29 in leap year) f 91 g 66h 28 i 61 j 25

7D Measuring Instruments1 a 5 cm b 3 cm c 2 cm d 8 cm

e 4 cm f 10 cm g 1 cm h 7 cmi 6 cm

2 a 5 o’clock b 9 o’clock c half-past three d 2 minutes past 11 pme 10 to 2 f 10 past 10 am g 12 o’clock h 29 past 1 ami 1 minute past 7 pm j quarter to 6 k 20 past 3 am l 6 o’clock

12--- 1

4---

12---


7D Operating With Time1 a 7 h 30 min b 7 h 20 min c 6 h 35 min d 5 h 40 min

e 10 h 55 min f 14 h 5 min g 13 h 30 min h 4 h 53 mini 10 h 26 min j 4 h 42 min k 2 h 46 min l 5 h 14 min

2 a 3 h b 4 h c 6 h d 7 h e 11 h f 11 hg 7 h h 5 h i 12 h j 5 h k 12 h l 9 h

3 a 15 min b 22 min c 30 min d 25 mine 1 h 20 min f 1 h 20 min g 2 h 30 min h 3 h 15 mini 34 min j 2 h 20 min k 1 h 5 min l 23 min

9G Finding the Size of an Anglea 40 b 60 c 28 d 111 e 125 f 123 g 50 h 81i 60 j 28 k 60 l 107 m 43 n 90 o 36 p 258q 80 r 40 s 22 t 58

11B Simplifying Algebraic Expressions1 a 2x + 5 b 2a + 4 c 4x + 3 d x + 3y e a + 8

2 a 5x b 4a c 14p d 6f e 11k f 9mg 2y h 7y i x j 16t k 15w l 5xm 7d n 0 o 14p p 6y q 2f r 22cs 24c t 12ab

3 a 5a + 7 b 6x + 3y c 7a + 6b d 15 + 4h e 4c + 1 f 10t + 5g 9m + 7 h 10 + 4c i 6 + 2x j 2x + 4y k 7m + 2n l 11 + 7am 15x + 3y n 13x + 2y o 7b + 5c p 9b + 3c q 5t + 6u r 11w + 9s 7x + 4 t 12 + 3y

11C Making Sense of Algebra1 a x + 2 b y + 3 c 3x d 6 e a + 8 f 4y + 3 g 2x + 3 h y + 5

i 3a + 3 j 5y + 3

2 a 2y + 1 b 2x + y c x + y d 3x + 2ye a + 3b f 2x + 3 g 2a + 3b h 3x + 4i 5x + 2y j 4y + 5 k 2x + y + 2 l a + 3b + 2m 3a + 2b + 1 n x + 2y + 3 o m + n + 4

11D Grouping Symbols1 a 2x + 6 b 5a − 20 c 3p + 6 d 8c − 8 e 10m + 50 f 4y + 32

g 14 − 7h h 8 + 2d i 5x + 30 j 36 − 9b k 18 − 6x l 4y + 20m 21 + 7t n 11c − 33 o 20a + 100 p 20 − 2x q y + 8 r 10x − 70s 3c − 12 t 6f + 54

2 a 15m − 3 b 4x + 10 c 21 + 14x d 12x + 4 e 20p + 90 f 7x − 8g 20x − 35 h 12x + 6 i 16 − 56a j 6 − 14a k 24c − 15 l 11 − 44cm 18y + 27 n 36 + 20t o 12d + 4 p 42y + 24 q 21 − 15x r 15x + 50s 22p − 4 t 16x − 48

11E Substitution1 a 36 b 40 c 11 d 3 e 9 f 15 g 0 h 63

i 8 j 36 k 17 l 24 m 1 n 6 o 4 p 5

2 a 2 b 8 c 20 d 16 e −3 f 8 g 19 h 20i 3 j 124 k 24 l 48 m −8 n −8 o 7 p 52q −3 r 12 s 28 t 30 u 3

11I Patterns and Rules1 a 20, 25 b 10, 12 c 14, 12 d 24, 48 e 50, 60 f 16, 32

2 a 8 b 14 c 20 d 3 e 18 f 3

3 a 6 b 1 c 7 d 10 e 6 f 1

4 a 2 b 10 c 5 d 3 e b = t × 3 f b = t + 2


12A Algebraic Sentences1 a 7 b 5 c 2 d 4 e 7 f 6

g 4 h 5 i 9 j 9 k 3 l 7m 1 n 8 o 21 p 22 q 27 r 6s 9 t 1

2 a 9 b 18 c 48 d 19 e 31 f 11g 8 h 15 i 7 j 30 k 18 l 20m 23 n 48 o 63 p 30 q 30 r 20s 16 t 7

12C Solving Problems Using Algebra1 a 1 b 6 c 15 d 18 e 7 f 18

g 8 h 8 i 60

2 a 9 b 6 c 12 d 22 e 5 f 25g $14.90 h $46 i $132 j 23 k 9 l 17m 16 n $36

12E Language and Symbols1 a F b T c T d F e T f T

2 a 5 � 6 b 10 � 4 c 12 − 5 = 7 d 4 × 3 � 7 e 10 ≠ 4 × 3 f 6 + 3

Challenge Worksheets

Ch1 Solving Puzzles

2 5 cuts → 15 minutes3 F is opposite A, E is opposite B, C is opposite D4

Ch2 HCF and LCM by Prime Factors1 HCF = 8, LCM = 48 2 6, 72 3 4, 900 4 20, 560 5 27, 324 6 24, 144

7 15, 150 8 18, 108 9 45, 270 10 12, 420 11 25, 150 12 14, 490

Ch11 Describing Number Patterns

1 a number = h (h + 1)

2 a 10, 15, 20 b 25, 30

b The number of diagonals is 3 less than the number of sides.c d = s − 3

4 a B = T2, 100 b B = 12 − T, 2

5 a 21, 25 b 0⋅5, 0⋅25 c 0, −5 d 4 000 000, 40 000 000

6 a 5, 8, 11, 14 b 5, 4, 3, 2 c −5, −3, −1, 1 d 6, 9, 14, 21

1 a 6 32 18 44 30 b 23 6 19 2 15 c 3 10 17 19 26

40 16 42 28 4 10 18 1 14 22 22 24 6 8 15

14 50 26 2 38 17 5 13 21 9 11 13 20 27 4

48 24 10 36 12 4 12 25 8 16 25 7 9 16 18

22 8 34 20 46 11 24 7 20 3 14 21 23 5 12

b 5 6 7 8

30 42 56 72

3 a Number of sides (s) 3 4 5 6 7 8 9 10

Number of diagonals (d) 0 1 2 3 4 5 6 7

5

31 6

24


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