Starter Questions

Starter Questions

1. Multiply out the brackets and simplify:

a) 4(x + 3) + 2 b) 3 + 2( x + 4) c) 10 + 2(3x + 4)

2. Find the highest common factor of:

a) 8 and 12 b) 16 and 18 c) 18x and 24

3. Factorise the following:

a) 10p + 15q b) 8d – 12f c) 4a + 10b +14c

FractionsFractions

Learning IntentionLearning Intention

To understand the term Fraction and be able to simplify fraction.

A Fraction consists of 2 parts.

35

Top number is called the numerator

Bottom number is called the denominator

FractionsFractions

The denominator tells us the type of fraction we have

The numerator tells us the how many we have

It is possible to find a fraction equivalent to any fraction that you have by multiplying the numerator

and the denominator by any number.

24

15

Find a fraction equivalent to :

x3

x3

612

210

x2

x2

FractionsFractions

We can sometimes simplify a fraction by finding a HCFbetween the numerator and denominator.

24

312

Simplify the fractions below :

÷2

÷2

12

14

÷3

÷3

FractionsFractions

Fractions of a quantityFractions of a quantity


To explain the 2 step process of finding a fraction of a quantity.

Q. Do the calculations below.

12

Fractions of a Fractions of a quantityquantity

of 12014

of 120

Simply divide by the bottom number

602 120

304 120

Q. Do the calculation below.

23


of 24

Simply divide by the bottom numberThen multiply the answer by top number

83 24 8 x 2 = 16Step 1: Step 2:

Q. Do the calculation below.

58


of 360

Simply divide by the bottom numberThen multiply the answer by top number

458 360 45 x 5 = 225Step 1: Step 2:


To understand how to calculate simple percentages without a

calculator.

Simple Simple PercentagesPercentages

Remember money 2 decimal places

Q. Find 17% of £450

17 100 x 450

PercentagesPercentages

17 450

100

= £76.50

of means times

Calculator Keys

1 1 x 4 = 76.57 0 0 5 0

Copy down and learn the following basic percentages

Simple Simple PercentagesPercentages

100% 50%1

33 %3 25% 20% 10% 5% 1%

112

13

14

15

110

120

1100

Q. Find 25% of £40


1 40

4

40 ÷4 =10

Q. Find 5% of £300


1 300

20

300 ÷20 =15

Copy down and learn the following basic percentages

100% 50%1

33 %3

266 %

3 20% 40%60% 80%

112

13

23

15

25

35

45

10% 30%70% 90%

110

310

710

910

Extended Extended PercentagesPercentages

Q. Find 30% of £40

3 40

10

40 ÷10 x 3 =12


Q. Find 75% of £600

3 600

4

600 ÷4 x 3 =450



To understand how to add and subtract basic fractions.

Add / Sub Fractions

FractionsFractions

A fraction, like, where the numerator is bigger

than the denominator is called a ‘Top-Heavy’ fraction.

73

A number,like, consisting of

a ‘whole number’ part and a ‘fraction’ part is called a Mixed fraction

35

4

Top Heavy to Top Heavy to MixedMixed

means seven thirds73

7 1 1 1 1 1 1 13 3 3 3 3 3 3 3

7 3 3 13 3 3 3

7 12

3 3

NUMERATOR DENOMINATOR


can be written as 7 373

23 7

remainder 1

12

3

NUMERATOR DENOMINATOR


can be written as 17 5175

35 17

remainder 2

23

5

Changing a mixed fraction to a top-heavy.

WHOLE NUMBER DENOMINATORthen add NUMERATOR

5 4 3

7 5 2

Mixed to Top Mixed to Top HeavyHeavy

35

4

27

5

234

375

23 quarters

37 fifths


Examples

1 37 7

47

8 79 9

19

3 15 3

7 7

48

7

3 115 4

7 7

211

7


Examples

6 37 7

97

9 715

11 11

1615

11

217

5

1611

5

15 111

Subtract Fractions

When dealing with mixed fractions deal with ‘whole’ part first then the fraction part

5 1

7 46 6

5 1

7 4 6 6

43

6

23

3

Harder FractionsHarder Fractions


To understand how to add and subtract fractions with different

denominators.


How can we add /subtract fractions that have different denominators

Step 1 : Do the smile

Step 2 : Do the kiss

Step 3 : Add/Subtract the numerator

and simplify

We are going to use the kiss

and smile method

2+


1 12 4

68

Example 1

Step 1 : Do the smile

Step 2 : Do the kiss

Step 3 : Add/Subtract the numerator

and simplify

84

34

÷2

÷2

6-


5 16 5

3025

1930

18+


5 36 4

3824

2420

14124

÷2

÷214

124

7

112

General


How can we add /subtract mixed fractions that have different denominators


Simple !


1 22 3

2 3

1 22 3

2 3

1 25

2 3 4+

76

63

116

15 1

6

16

6


7 27 4

8 3

7 27 4

8 3

7 23

8 3 16-

524

2421

53

24

53

24

3 54

4 6 3 5

44 6

20+

3824

2418

14124

75 1

12

76

12

7112

Most Difficult Most Difficult FractionsFractions

Subtracting Subtracting FractionsFractions

1 26 2

4 3

1 26 2

4 3

1 24

4 3 8-

512

123

54

12

12 5

312 12

7

312

Most Difficult Most Difficult FractionsFractions

1 17 1

5 6

1 17 1

5 6

1 16

5 6 5-

130

306

16

30

16

30

Subtract Fractions


11

6

6 16 6

56

Multiplying FractionsMultiplying Fractions


To show how to multiply basic fractions.

Multiplying Multiplying FractionsFractions

Example 1 Example 2

Multiplying basic fractions

3 34 5

3 34 5

9

20

4 55 6

4 55 6

2030

23

1. Multiply the numerators

2. Multiply the denominators

Multiplying Multiplying FractionsFractions

Example 3 Example 4

Multiplying basic fractions

32

5

2 31 5

65

4 21 3

2

43

83

2

23

5

16

Starter Questions

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