Number Sense – Workbook 7, Part 1

Number Sense – Workbook 7, Part 1

Worksheet NS7-9 page 51

1. a) 3: 0, 3, 6, 9, 12, 15, 18.

b) 4: 0, 4, 8, 12, 16, 20, 24.

c) 5: 0, 5, 10, 15, 20, 25, 30.

2. a) Yes.

b) No.

c) Yes; Yes; Yes.

3. a) 0

b) All whole numbers, since any whole number times zero is zero.

4. a) 5 is a factor of 20.

b) 1 is a factor of 9.

c) 8 is a factor of 0.

d) 4 is not a factor of 11.

Investigation 1 A. a) 9, 10, 11, 12

b) 6, 8, 10, 12

c) 9, 12

d) 8, 12

e) 10, 15

f) 12

g) 14

h) 16.

i) 18

j) 20

k) 22

l) --

m) 13

B. The largest factor of any number, n is n.

C. a) 1, 2, 3, 4, 6, 12.

b) Yes.

5. a) 0, 0, 0.

b) No.

c) No.

d) 0

e) 0

6. a) 0, 13

b) If n is a whole number then we can always write n 1 = n.

7. a) 0, 1, 2, 3, 4, 5, 6, 7, 8.

b) If n is a whole

number then we can always write n 1 = n.

8. a) 0

0

0

0

b) Any number n.

No.

c) All numbers since any number times zero is zero.

9. a) 1 is a factor of 5

b) 1 is a factor of every number

c) 8 is a factor of 8

d) Every number has itself as a factor

e) 7 is a factor of 0

f) Every number is a factor of 0

10. a) 15 is a multiple of 5

b) 0 is a multiple of 3

c) Any non-zero multiple of 12 is at least 12

d) Any non-zero multiple of a number is at least the number

e) 6 is a multiple of 6

f) Any number is a multiple of itself


1. a) 10 is the largest factor of 10

b) 0 is not a factor of 10

2. a) 1st 2nd

1 6 2 3 3 2 4 5 6 1

b) 1st 2nd

1 8 2 4 3 4 2 5 6 7 8 1

c) 1st 2nd

1 9 2 3 3 4 5 6 7 8 9 1

3. All except (3,3)

4. a) Connor thinks that if the blank is smaller than 4 then the rest of the pairs of factors will be repeats of the ones he already has.

b) His list contains all unordered pairs of factors

5. The rest of the pairs of factors are the ones that he has but in reversed order.

6. a) 1st 2nd

1 20 2 10 3 4 5 5 4

b) 1st 2nd

1 12 2 6 3 4 4 3

c) 1st 2nd

1 15 2 3 5 4 5 3

d) 1st 2nd

1 14 2 7 3 4 5 6 7 2

e) 1st 2nd

1 25 2

3 4 5 5

f) 1st 2nd

1 5 2 3 4 5 1

g) 1st 2nd

1 26 2 13 3 4 5 6 7 8 9

10 11 12 13 2

h) 1st 2nd

1 30 2 15 3 10 4 5 6 6 5

i) 1st 2nd

1 42 2 21 3 14 4 5 6 7 7 6

j) 1st 2nd

1 72 2 36 3 24 4 18 5 6 12 7 8 9 9 8

k) 1st 2nd

1 63 2 3 21

Number Sense – Workbook 7, Part 1 (Continued) 2

4 5 6 7 9 8 9 7

l) 1st 2nd

1 100 2 50 3 4 25 5 20 6 7 8 9

10 10

m) 1st 2nd

1 64 2 32 3 4 16 5 6 7 8 8

n) 1st 2nd

1 91 2 3 4 5 6 7 13 8 9

10 11 12 13 7

8. a) 1 2 4

b) 1 2 4 8

c) 1 2 3 4 6 12

d) 1 3 5 15

e) 1 7

f) 1 2 3 4 6 8 12 24

g) 1 2 3 6 7 14 21 42

9. a) Yes.

b) 144

72

48

36

24

12

c) 144 n becomes smaller.

d) 1, 2, 3, 4, 6, 12, 24, 36, 48, 72, 144 These are not all of the factors since 8 18 = 144 [Since products of factors are factors].

10. 2 is the second smallest factor. The largest factor is 3 256 2 = 1 628


1. 18

3. a) 10, 20

b) 6, 12

c) 4, 8

d) 12, 24

e) 12, 24

f) 12, 24

4. a) 2 (first common multiple)

b) 2 126 = 252

5. a) 6, 12, 18, 24

b) 30

6. a) 10

b) 6

c) 4

d) 12

e) 12

7. a) 15

b) 20

c) 9

d) 6

e) 10

f) 14

g) 12

h) 8

i) 40

j) 15

k) 30

l) 30

m) 24

n) 18

8. a) 1, 2, 3, 4, 10, 20

b) 1, 2, 11, 22

c) 1, 2, 13, 26

d) 1, 5, 13, 65

e) 1, 2, 3, 6, 11, 22, 33, 66

9. a) 2

b) 22

c) 5

d) 1

e) 13

f) 1

g) 1

h) 2

10. a) i) 10: 1, 2, 5, 10 15: 1, 3, 5, 15

ii) 1, 5

iii) GCF = 5

b) i) 18: 1, 2, 3, 6, 9, 18 24: 1, 2, 3, 4, 6, 8, 12, 24

ii) 1, 2, 3, 6

iii) GCF = 6

c) i) 20: 1, 2, 4, 5, 10, 20 30: 1, 2, 3, 5, 6, 10, 15, 30

ii) 1, 2, 5

iii) GCF = 5

d) i) 28: 1, 2, 4, 7, 14, 28 42: 1, 2, 3, 6, 7, 14, 21, 42

ii) 1, 2, 7, 14

iii) GCF = 14

11. a) ii) 5: 1, 5 15: 1, 3, 5, 15 GCF = 5

iii) 6: 1, 2, 3, 6 30: 1, 2, 3, 5, 6, 10, 15, 30 GCF = 6

iv) 10: 1, 2, 5, 10 50: 1, 2, 5, 10, 25, 50 GCF = 10

b) a

Investigation 1

A. b) 20: 1, 2, 4, 5, 10, 20 21: 1, 3, 7, 21 GCF = 1

c) 15: 1, 3, 5, 15 16: 1, 4, 16 GCF = 1

d) 35: 1, 5, 7, 35 36: 1, 2, 4, 6, 9, 18, 36 GCF = 1

B. GCF = 1

Investigation 2 A. a) GCF = 1

LCM = 12 3 4 = 12

b) GCF = 1 LCM = 10 2 5 =10

c) GCF = 2 LCM = 12 4 6 = 24

d) GCF = 5 LCM = 30 10 15 =150

e) GCF = 5 LCM = 10 5 10 = 50

f) GCF = 1 LCM = 15 1 15 =15

g) GCF = 1 LCM = 20 4 5 = 20

h) GCF = 3 LCM = 18 6 9 =54

B. a), b), f), g)

C. GCF = 1


2. 5, 7

3. 4, 9

4. No. Explanations may vary

8. 1 4 9 16 25 36 49 64 81 100

9. b) 9

c) 64


d) 0

e) 49

10. a) Yes.

b) 131 < 132

11. a) 32, 42, 52

b) 82, 92, 102

c) 52, 72, 122

12. a) 22, 5,32, 10, 42

b) 72, 50, 82, 92, 85

13. a) 3 3

b) 7

c) 0 0

d) 5 5

14. a) 7

b) 4

c) 3

d) 6

e) 1

f) 10

g) 9

h) 8

15. a) 7

b) 30

c) 5

d) 5

e) 15

f) 1

g) 3

h) 10

Bonus: 17

16. b) 5

c) 9

d) 4105

e) n

17. a) 5 cm

b) 7 mm

c) 10 km

18. a) The square with area 64cm2. It has sides of length 8cm and the other has sides of length 6cm.

b)

19. a) , , , ,

b) , 5, , , ,

c) , , ,

, , ,


1. a) White circle

b) Shaded triangle

c) Small white circle

d) Large white Square

2. a) American football

b) Bicycle and tricycle

c) thing, bcjxp, bcjxe

d) ¿Cual es tu nombre?

3. A banana is not a vehicle.

4. a) No. Since 3 is not even, it can be paired with any letter.

b) (12,R), (J,16), (C,28)

5. a) (E,13)

b) True

c) True

d) (r,15)

e) True

f) (r,15)

g) True

h) True

i) (E,13)

j) True

6. Answers will vary.

7. a) C B

b) A F

c) D E

8. a) Reverse: -people -boys Counter-example: -Hannah Montana

b) Reverse: -fruit -banana Counter-example: -apple

c) Reverse: -animals that live in the water -fish Counter-example: -dolphin.

d) Reverse: -start with a capital letter -form a sentence. Counter-example: -A nice day.

9. b) Statement is false. Reverse is false: All red fruits are apples.

c) Statement is false. Reverse is false: All soccer players are girls.

d) Statement is true. Reverse is false: All shapes are circles.

e) Statement is true. Reverse is true: All toonies are Canadian coins worth $2.

Worksheet NS7-14 page 64 Investigation 1 A. Are all whole numbers with

ones digit 0 divisible by 10?

B. 10 = 1 10 20 = 2 10 870 = 87 10

C. 40 4 50 5 60 6 70 7 80 8 90 9 100 10 110 11 120 12 130 13 140 14 150 15

D. 1

2 3 12 n

E. Yes.

Investigation 2 A.

8 4

10 5 12 6 14 7 16 8 18 9 20 10 22 11 24 12 26 13 28 14 30 15

B. N

Investigation 3 A. 10 3R1

13 4R1 16 5R1 19 6R1 20 6R2 23 7R1 26 8R2

B. 10

1. a) -divisible by 2 -ones digit divisible by 2

b) Divisible by 2

ones digit

6 6 8 8 10 0 12 2 14 4 16 6 18 8 20 0 22 2 24 4 26 6 28 8

c) 0, 2, 4, 6, 8 is a

repeating pattern

d) Yes.

2. a) -divisible by 3 -ones digit divisible by 3

b) No. Counter-example:12

3. a) The statement is false. The reverse is false: Any number divisible by 4 has ones digit divisible by 4.


b) The statement is true. The reverse is true: Any number divisible by 5 has ones digit divisible by 5.

4. a) The ones digit should be 0, 2, 4, 6, or 8.

b) The ones digit should be either 5 or 0.

c) The ones digit should be 0.

5. 418, 312, 64, 76, 234, 94, 560

6. 45, 150, 190, 65, 235, 1 645

7. 190


2. b) 2

c) 2

4. a) Yes. Explanations will vary.

b) Yes.

5. b) 1

c) 9 is a multiple of 3.

d) i) 1

ii) 2

iii) 2

iv) 2

v) 2

vi) 0

6. 12+15 is a multiple of 3.

7. a) 2333R1

b) 1666R2

c) 2666R2

d) 666R2

e) 3000R0

f) 1333R1

8. a) 2

b) 1

9. a) No. 8 is not a multiple of 3.

b) 8

c) 999 is a multiple of 3.

d) Both 99 and 9 are divisible by 3.

10. No. 8 is not divisible by 3.

11. b) 8 + 4 = 12. 12 3 = 4R0 84 3 = 28R0

c) 4 + 7 = 11 11 3 = 3R2 47 3 = 15R2

12. a) 5 + 4 + 2 + 8 = 19. 19 3 = 6R1 5 + 4 + 8 + 2 = 19. 19 3 = 6R1 2 + 4 + 8 + 5 = 19 19 3 = 6R1

b) No. All rearrangements have sum of digits equal to 19.

13. If the sum of the digits of a number divided by 3 has remainder 0, then the number is divisible by 3.

14. a) Answers will vary.

b) If the sum of the digits of a number divided by 9 has remainder 0, then the number is divisible by 9.

15. a) Number

Sum of Digits

28 10 37 10 42 6 61 7 63 9 87 15 93 12 123 6

b) 3 3 and

9 9

42 9 87 63 93 123

c) The column

“divisible by 9”. All numbers divisible by 9 are also divisible by 3. Numbers can only belong to one column.

16. a) 2 2 and 3

3

2 0 3

4 6 9 8 12 15 10 18 21 14 24 27 16 30 20 22 26 28

b) In the intersection.

c) Divisible by 6 If the number is even and its sum of digits is divisible by 3.

d) 3 174 7314


1. a) ii) 7, 7, 175

iii) 30,30,750

b) Yes.

2. b) 82, no

c) 60, yes

d) 46, no

e) 67, no

f) 84, yes

g) 26, no

h) 22, no

3. If the last 2 digits of a number form a number which is divisible by 4, then we can write it as a sum of a term divisible by 100 and a term divisible by 4. Sums of numbers both divisible by 4 are divisible by 4.

4. a) Yes. Since any number that ends in 3 zeros is a multiple of 1000.

b) Yes. Similar to #3. If the last 2 digits of a number form a number which is divisible by 4, then we can write it as a sum of a term divisible by 1000 and a term divisible by 8. Sums of numbers both divisible by 8 are divisible by 8.

5 b) 688, yes

c) 408, yes

d) 546, no

e) 767, no

f) 936, yes

6. c) 36, no

d) 600, 146, no

e) 800, 176, yes

f) 600, 72, yes


1. a) # Factors 1 1 2 1,2 3 1,3 4 1,2,4 5 1,5 6 1,2,3,6 7 1,7 8 1,2,4,8 9 1,3,9 10 1,2,5,10 11 1,11 12 1,2,3,4,6,

12 13 1,13 14 1,2,7,14 15 1,3,5,15 16 1,2,4,8,16 17 1, 17 18 1,2,3,6,9,

18 19 1,19 20 1,2,4,5,10,

20

b) 2,3,5,7,11,13,17,19

c) 23

d) 4,9,16

e) +5,9,+7,16,+9,25, +11,36

f) Perfect squares

g) 121

2. 3+2+7+4=16 Possible values: 2,5,8

3. 2,4,5,8,10

4. a) Yes since 1+4+4=9, 2+4+0=6 and both 6 and 9 are divisible by 3.

b) Yes since, 1+3+4+7+4+2=21, 1+2+3+4+6+9 +8=33 and both 21 and 33 are divisible


by 3.

5. a) 120

b) 264720

6. a) Yes since the last digit is 2.

b) No, the last digit is not 0 or 5

c) 325

d) No, the last digit is not 0

e) No, none of the digits are 0

7. 8. a) i,iv

b) i)2 ii)9 iii)2 iv)0 v)444

9. 73 008

10. a) 27=1+2+3+4+17 1+2+3+4+8=12348

b) 666660

11. 12

12. 2

13. 9mm x 9mm

14. a) True

b) False, 60


1. a)

b)

c)

2. a)

b)

c)

d)

4. 3,7,4

6. a) The total number of pieces in a whole pie.

b) The number of parts of the pie that I have.

7. a) Yes.

b)

8. a) Pentagons

b)

c)

d) Triangles

e)

f)

9. a)

b)

c)

10. ,

11. a) A P B 7 4 G 5 7 S 12 11

b) ,

c) ,

12. Drawings will vary


1. b) 1, , 1

c) 2, , 2

2. a) 4

b) 1

c) 3

d) 2

5. 4

6. 6


1. a)

b)

c)

d)

e)

f)

g)

4.

5. a) No

b) Yes

c) Yes


1. a) 3

b) 3

c) 3

d) 2

e) 3

f) 2

2. a)

b)

3. a) 2

b) 2

c) 2

d) 2

4. a) 3

b)

c)

d)

5. Answers will vary.

6. a) 2

b) 4

c) 8

d) 7

e) 9

f) 11

7. b) 6

c) 12

d) 4

e) 8

f) 17

8. a) 8

b) 9

c) 15

9. a) 13

b) 31

c) 47

10. a) 7

b) 11

c) 22

d)

e)

11. 17

12. 19

13. 18

14. a) 11

b) 22

15. a) 2

b) 5

c) 2

d) 3

e) 4

f) 4

16. b) 4,1,4

c) 3,1,3

d) 3,1,

17. b) 2R1, 2

c) 3R3, 3

d) 1

e) 2

f) 4

g) 4

h) 7

i) 7

18. 2

19. 2


1. b)

2. a) 2, , 6, 4

b) , 2, , 8, 6

c) , 3, , 9, 6

d) , 10, 6

e) , 12, 9

5. a) 6

b) 6

6. a) 3, 6

b) 2, 6

c) 5, 10

d) 5, 15

e) 9, 18

7. 12

8. 10, 5

9.

10. 7

11. 8:47

12. 1

Bonus 0


1. b)

c)

2. The fraction with the greater numerator

3. b)

c)

4. The greater fraction is the one with the smaller


denominator

5. a)

b)

c)

d)

e)

f)

Bonus

6. a)

b)

7. a)

b) since

8.

9. a) Improper

Fraction

Mixed #

6

2

3

2

1

4

b)

c)

d) The improper and

mixed fractions represent the same total amount of parts.

11. 3 since is closer to 1

than 0. Bonus


1. b) =

c) <

d) =

e) <

f) >

2.

3. b) 2

c) 5

4.

5. b) 2,3,4

6. b) 6

c) 9

d) 20


1. a) 15

b) 8

c) 9

d) 24

e) 18

f) 50

g) 8

h) 12

2. a) 4,6,8,10,12,14

b) 6,9,12,15,18,21

3. a)

using #2a,b

b) since

c) Yes.

4. a) 8,12,16,20

b)

5. b)

c)

d)

e)

f)

g)

6. a) 2,3,4,5,6,7,8,9,10

b)

c)

7. b) 9

c) 20

d) 18

e) 16

f) 21

g) 4

h) 10

8.


1. a)

b) Blue

c) White

3. 0

4. a)

b)

c)

d)

5. a)

b)

c)

6.

7.


1.

2. 1,2,

1,1,

3. a)

b)

c)

d)

e)

f)

g)

h)

4. a)

b)

5. a)

b)

c)

d)

e)

f)

g)

h)

6. a)

b)

c)

A.

B.

C. No, since A and B imply that

A. 2,3,4,5

4,6 B. 6,5,11

C.

7. b) 8 2,1

c) 20 1,4

d) 12 3,4

e) 21 3,7

f) 12 3,2

g) 10 2,1

h) 56 7,8

8. a)

b)

c)

1 d)

e)

f)

g)

h)

i)

9. a)

b)

c)

d)

e)

f)

g)

h)

i)



1. b) 1,yes

c) 1,yes

d) 1,yes

e) 2,no

f) 1,yes

g) 1,yes

h) 2,no

i) 1,yes

j) 4,no

2. b)

c)

d)

e)

f)

g)

h)

3. b)

c)

d)

e)

f)

g)

h)


1. a)

b)

c)

d)

2. c)

d)

e)

f)

g)

h)

i)

j)

k)

l)

3.

4. a) i)

ii)

iii)

iv)

v)

vi)

vii)

viii)

b) i)

ii)

iii)

iv)

v)

vi)

c) i)

ii)

iii)

iv)

v)

vi)

5. a) ii)

iii)

iv)

b) ii)

iii)

iv)

c) ii)

iii)

iv)

6. b)

c)

d)

e)

f)

g)

h)

7.

8.

9. 2m


1. a)

b) ,1,

2. a)

b)

c)

3. a)

b)

c)

d)

4. b)

5. a)

b)

c)

d)


1. a) 4

b) 10

c) 2

d) 11

e) 9,6

f) 8,12

2.

3.

4.

5.

6. a)

b) 12

7.

8.

9.

10.

11. She did not find a common denominator before adding the numerator.

12.

13.

14. Sadia

15. No.

16. a) ,65 minutes

b) 30+20+15=65 minutes

17. a)

b)

c)

d)

e)

18. a) True. Can divide numerator and denominator by 2.

b) False. .

c) True.

19. No, since 6>5

Number Sense – Workbook 7, Part 1

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Transcript of Number Sense – Workbook 7, Part 1