Foundation Unit 4: Fractions and percentages

Numerical fluency

1 Write the fraction of each shape that is shaded.

2 Which of these fractions are equivalent? 312

38

28

3 Circle the equivalent fractions.

35

34

48

68

912

4 Work out 15

+ 35

15 + 3

5 =

5 Work out

a 25

+ 15

.................. b 310

+ 410

.................. c 59

+ 29

................ d 215

+ 915

..................

6 Work out 78

– 48

...................

78 – 4

8 =

a

b

c

d

e

f

g

h

Fractions with a common denominator have the same denominator.

Draw the fractions as bars.

Equivalent fractions are fractions that represent the same amount but use different numerators and denominators.

Draw the fractions as bars, all the same length.

–

A fraction is a part of a whole.

Three thirds make 1 whole. There are 2 thirds left over.

Multiplying or dividing the numerator and denominator by the same number gives an equivalent fraction. When the numerator and denominator are as small as possible, the fraction is simplified. For example

7 Work out

a 57

– 27

b 910

– 210

c 59

– 19

d 36

– 26

8 a Draw a line from each fraction to the correct shaded bar.

47

27

57

b Now write the fractions 47

, 27

and 57

in ascending order.

9 Write each set of fractions in ascending order.

a 59

29

89

b 910

310

710

10 Simplify 36

11 Simplify these fractions.

a 68

= ...

... b 10

15 = ...

... c 30

40 = ...

...

d 1620

= ...

... e 12

18 = ...

... f 20

30 = ...

...

12 Write these improper fractions as mixed numbers.

a 53

= 1 ...3

b 74

c 76

d 125

e 83

An improper fraction is a fraction in which the numerator is greater than the denominator.

A mixed number has a whole number part and a fraction part.

An improper fraction can be written as a mixed number.

Literacy hint Numbers in ascending order go from smallest to largest.

Strategy hint Draw and shade a diagram to help.

Both 3 and 6 can be divided by 3, so divide the numerator and denominator by 3.

Divide the numerator and denominator by the same number.

8 5.0200 0.6.......

13 Write these mixed numbers as improper fractions.

a 212

= ... ... + ......

= ...

... b 5

14

= ...

... c 3

35

= ...

... d 2

47

= ...

...

14 Complete this table of equivalent fractions, decimals and percentages.

15 Write these fractions as decimals.

a 58

b 320

c 154

d 4575

= ..........

=

16 Write these fractions as percentages.

a b

c d e

17 Draw lines to match each percentage and its equivalent fraction.

18 Write these percentages as fractions and as decimals.

a 50% = ...100 = ...

2 50% = 0.50 = b 20% = ...100 = ...

5 20% =

19 Write these percentages as fractions in their simplest form.

a 27% b 61% c 10% d 40%

20 Convert these decimals to percentages.

a 0.49 b 0.33

c 0.06 d 1.5

21 Write in order of size, starting with the smallest.

a 0.6, 25%, 410

b 40%, 14

, 0.7

Equivalentfractions, decimals and percentages have the same value. You can convert a fraction to a decimal by dividing the numerator by the denominator.

Fraction 110

25

710

Decimal 0.2 0.3 0.5 0.75

Percentage 25% 60%

30% 20% 75% 70% 4% 49%

125

710

49100

15

310

34

Convert the fraction to an equivalent fraction with denominator 100.

Convert the fraction and the percentage to a decimal.

To convert a decimal to a percentage, multiply by 100.For example, 0.75 = 0.75 × 100 = 75%

20% is double 10%. Find 10% and use this to find other

percentages.

10% is the same as 110

.

To find 10% of a number you divide by 10.

22 Write

a 7 as a fraction of 10 ...

...

b 5 as a fraction of 11 ...

... c 3 as a fraction of 9

...

...

23 Find 10% of

a 300 b 70

c 172

24 Work out

a 20% of 140

10% of 140 is 140 ÷ 10 = 14 20% is 2 × 14 =

b 20% of 70 c 30% of 110 d 70% of 80

Fluency with measures

25 Work out 15

of £35.

£35 ÷ 5 = ..............

26 Work out

a 12

of £10 = £10 ÷ 2 = ........ b 110

of 50 kg c 14

of 80 ml

27 Work out

a 10% of 40 g b 10% of 450 m

c 20% of £60 d 90% of 30 t

28 Write these numbers of seconds as a fraction of 1 minute, in their simplest form.

a 30 seconds b 15 seconds

c 10 seconds d 50 seconds

Fluency with probability

29 Work out the probability that this spinner will land on

a an even number

Probability of landing on an even number = 25

b an odd number

c a multiple of 3

20% = 2 × 10%

First work out 10% of £140.

1 minute = 60 seconds

Successful outcomes are the outcomes you want.

7 as a fraction of 10 is 7 parts in 10 parts:

...10

Write your answer in its simplest form.

How many in each ? 15 Draw a bar for 35.

Divide it into fifths.

There are two successful outcomes: 2 and 4

There are five possible outcomes: 1, 2, 3, 4, 5

Foundation Unit 4 answers1 a 1

4

b 4

9

c 3

8

d 11

16

e 3

4

f 5

8

g 3

10

h 5

6

2 3

12and 2

8

3 3

4, 6

8and 9

12

4 4

5

5 a 3

5

b 7

10

c 7

9

d 11

15

6 3

8

7 a 3

7

b 7

10

c 4

9

d 1

6

8 a

b 2

7, 4

7, 5

7

9 a 2

9, 5

9, 8

9

b 3

10, 7

10, 9

10

10 1

2

11 a 3

4

b 2

3

c 3

4

d 4

5

e 2

3

f 2

3

12 a 1

2

3

b 1

3

4

c 1

1

6

d 22

5

e 22

3

 

 

13 a

2 2 1

2

5

2

b 21

4

c 18

5

d 18

7

14 Fraction 110

15

14

310

25

12

35

710

34

Decimal 0.1 0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.75

Percent 10% 20% 25% 30% 40% 50% 60% 70% 75%

15 a 0.625

b 0.15

c 3.75

d 0.6

16 a 90%

b 48%

c 55%

d 18%

e 40%

17 30% and 3

10

20% and 1

5

75% and 3

4

70% and 7

10

4% and 1

25

49% and 49

100

16 a 50

100

1

2,0.5

b 20

100

1

5,0.2

 

 

19 a 27

100

b 61

100

c 1

10

d 2

5

20 a 49%

b 33%

c 6%

d 150%

21 a 25%, 4

10, 0.6

b 1

4, 40%, 0.7

22 a 7

10

b 5

11

c 1

3

23 a 30

b 7

c 17.2

24 a 28

b 14

c 33

d 56

25 £7

26 a £5

b 5 kg

c 20 ml

   

27 a 4 g

b 45 m

c £12

d 27 t

28 a 1

2

b 1

4

c 1

6

d 5

6

29 b 3

5

c 1

5