Ch04 Fractions

4

Fractions

CHAPTER

4.1 Fractions revision
2
7 2

7

of this circle is shaded. is a fraction.

The top number shows that 2 parts of the circle are shaded The bottom number shows that the circle is divided into 7 equal parts

2

7

The top number of the fraction is called the numerator The bottom number of the fraction is called the denominator

Equivalent fractions are fractions that are equal. If both the numerator and the denominator of a fraction are multiplied by the same number then an equivalent fraction is obtained.

1


2
3 6

2

3

2 1 3  6

3 1 3  9

2

3

3

9

and are all equivalent fractions.

A fraction can be simplified if the numerator and denominator can both be divided by the same number. This process is called cancelling. 2

7

3 6 20  10

3 21 35  5

2

7

When a fraction cannot be simplified, it is in its simplest form or in its lowest terms.

Example 1 Find the simplest form of 1
3
80

Solution 1 6 is the highest common factor of 18 and 30 Divide both 18 and 30 by 6 The simplest form of 1
3
80 is 3
5


6

3 18 30  5 6

Fractions sometimes have to be put in order of size. To do this when fractions have the same denominator, compare the numerators. 53

Fractions

CHAPTER 4

When fractions have different denominators: ● find the lowest common denominator (lowest common multiple of the denominators) ● change each fraction to its equivalent fraction with this denominator ● compare the numerators to put the fractions in order.

Example 2 Write the fractions 1
4

12
0 and 2
5
in order of size. Start with the smallest fraction.

Solution 2 The lowest common denominator for the three fractions is 20 Equivalent fractions for each of 1
4

12
0 and 2
5
with a denominator of 20 are 5

2

4

5 1 4  20

4 2 10  20

8 2 5  20

5

2

4

Starting with the smallest fraction, the order is that is


4
20
2
10


5
20 1

4


8
20
2
5

An improper fraction is one in which the numerator is greater than the denominator. For example,
54

15
2 and
18
4 are improper fractions. The improper fraction 5
4
can be thought of as ‘5 over 4’ or as 5 quarters. Similarly, the improper fraction 1
5
2 can be thought of as ‘12 over 5’ or as 12 fifths. A mixed number consists of a whole number and a fraction. For example, 23
4
31
5
and 67
8
are mixed numbers. Mixed numbers can be changed to improper fractions and vice versa. For example, to change 23
4
to an improper fraction, work out how many quarters there are in 23
4
There are 4 quarters in 1 and so there are 8 (2  4) quarters in 2 Add the extra 3 quarters to get 11 quarters. So

23
4
 1
4
1

(2  4)  3 11 234





4 4

To change the improper fraction 1
6
7 to a mixed number, firstly work out how many whole ones there are. 6 sixths is 1; 12 sixths is 2 and so 17 sixths is 2 whole ones and 5 sixths. 1 7

6




 25
6


17  6  2 remainder 5 2 is the whole number 5

is the fraction 6

Exercise 4A 1 Copy the fractions and fill in the missing number to make the fractions equivalent.

b 2
7
 4

c 2
3

15
d 3
5
 12 a 1
5

10
3 4 5 15 7

e
8

32
f
9

45
g
6


h
8
 28 2 Copy the fractions and fill in the missing number to make the fractions equivalent.

b 5
8

48
c 2
9

54
d 3
5
 24 a 4
7

28
21 15 5 7 3 7














e 12  36 f 20  g 16  h 25 
100

54

4.2 Addition and subtraction of fractions

CHAPTER 4

3 Write each fraction in its simplest form. b
68
c
27
1 d a
36


1
0
40

e

2
0
25

f

1
2
16

g

4
2
48

h

3
6
40

4 Write each fraction in its simplest form. 0
0 2
5 b 2
5
40 c 1
d a
150 100

7
5
200

e

4 8

60

f

7 2

90

g

8
5
100

h

12
5
1000

d h


9
4


3
20 5 4 1 1
1
7



3

5

2 5 12 30 15

5 Write each set of fractions in order. Start with the smallest fraction. b 5
6

34
c 2
3

56

17
2 a 3
5

17
0 e
14
5 1
3

13
0 f 3
4

19
6 5
8
g 2
4
30
17
0 3
5
1
2
30 6 Julie and Susan have identical chocolate bars. Julie eats 3
4
of her chocolate bar. Susan eats 7
8
of her chocolate bar. Who eats more chocolate? Give a reason for your answer. 7 Ahmid says that
17
2 is bigger than
56
because 7 is bigger than 5 Is Ahmid correct? You must give a reason for your answer. 8 Change these mixed numbers to improper fractions. b 1
35
c 2
16
d 2
78
a 1
12


e 4
34


9 Change these improper fractions to mixed numbers. b 4
3
c 1
4
9 d a 7
5


e

1 4

5

f 6
25


2 7

5

f

3 0

7

4.2 Addition and subtraction of fractions 3

5

of the rectangle is shaded red and 1
5
of the rectangle is shaded green. 4

of the rectangle is shaded. 5 So


3
5


15

45


3 5

1 5

4 5

To add fractions with the same denominator, add the numerators but do not change the denominator. For example,
49

29

69
which in its simplest form is
23
To add fractions with different denominators, firstly find the lowest common denominator and then change each fraction to its equivalent fraction with this denominator.

Example 3 Work out
23

15


Solution 3 5

10 2 3  15 5

3

and

3 1 5  15

The lowest common denominator is 15 Change each fraction to its equivalent fraction with a denominator of 15

3

10 So
2

1



3
3 5 15 15 13
2

1


3 5 15

Add the numerators but do not change the denominator.

55

Fractions

CHAPTER 4

Example 4 Work out
78

12
Give your answer as a mixed number.

Solution 4 7

8

 1
2
 7
8
 4
8


The lowest common denominator is 8 Change 12

to the equivalent fraction with a denominator of 8

7

8

 4
8
 1
8
1

Add the numerators but do not change the denominator.

1 1

8 7

8

 138



Change the improper fraction to a mixed number.

 1
2
 13
8


Fractions can be subtracted in a similar way.

Example 5 Work out
45

34


Solution 5 4

5

 1
2
60 and

3

4

4

5

 3
4
 1
2
60  1
2
50

4

5

 34


21
0

 1
2
50

The lowest common denominator is 20 Change each fraction to its equivalent fraction with a denominator of 20 Subtract the numerators but do not change the denominator.

Exercise 4B In questions 1–5 give each answer as a mixed number or a fraction in its simplest form.




56

1 Work out a 1
3
 1
2
e 2
3
 1
4


b f

1

3 1

2

 1
4
 2
5


c g

1

5 1

5

 1
4
 2
3


d h

1

 1

8 4 1

 4

5 20

2 Work out a 2
5
 3
8
e
45

17
0

b f

3

4 5

6

 2
5

38


c g

2

 1

3 6
9

3
4 10

d h

2

 3

7 5
7

5
8 20

3 Work out a 1
2
 1
4
e 3
4
 1
2


b f

1

3 2

3

 1
4
 1
4


c g

1

3 1

2

 1
9
 2
5


d h

1


1
5 20 1 1 1



12  6

4 Work out a 3
4
 2
3
e 5
6
 3
5


b f


9
 3

5 10 3 2



4 7

c g

7

 2

8 5 1 7

 3

20 4

d h

8

9 5

6

5 Work out a 3
7
 2
5
e
78

23


b f

4

 1

9 5
7

3
4 12

c g

5

6 4

5

d h


3
 1

4 10 4


2

1
9 3 6


56


 2
3

12

17
0

 2
3
 7
9


4.3 Addition and subtraction of mixed numbers

CHAPTER 4

4.3 Addition and subtraction of mixed numbers When adding mixed numbers, add the whole numbers and the fractions separately.

Example 6 Work out 21
3
 41
2


Solution 6 24 6 1

3

Add the whole numbers.

 1
2
 2
6
 3
6
 5
6


Add the fractions.

21
3
 41
2
 6  5
6
 65
6


Add the two results.

Sometimes adding the fractions gives an improper fraction. For example, adding the fraction parts of 22
3
and 41
2
gives 2
3
 1
2
 4
6
 3
6
 7
6

7
is an improper fraction. As a mixed number,
7
 1
1
6 6 6 2 1 1 1







So 23  42  6  16  76 Mixed numbers can be subtracted in a similar way.

Example 7 Work out 3
23
 1
12


Solution 7 31 2 2

3

Subtract the whole numbers.

 1
2
 4
6
 3
6
 1
6


Subtract the fractions.

2  1
6
 21
6


Add the two results.

32
3
 11
2
 21
6


Example 8 Work out 41
4
 2
17
0

Solution 8 Method 1 41
4
 1
4
7 and 2
17
0  2
1
70

Change mixed numbers to improper fractions.

5

85 17 4  20

2

and

5 1
7
4


21
70 
82
50 
52
40 
32
10 3
1
20

 11
2
10

54 27 10  20

The lowest common denominator is 20 Change each fraction to its equivalent fraction with a denominator of 20

2

Subtract the numerators but do not change the denominator. Give the answer as a mixed number.

4
14
 2
17
0  1
12
10 57

Fractions

CHAPTER 4

Method 2 42 2 1

4

Subtract the whole numbers.


17
0 
25
0  1
2
40  
29
0

Subtract the fractions.

2 
29
0  1  1 
29
0  1  2
2
00 
29
0  1  1
2
10  11
2
10

Add the two results.

41
4
 2
17
0  11
2
10




Exercise 4C 1 Work out a 24
5
 13
5
e 23
5
 13
4


b 35
9
 8
9
f 12
3
 11
2


c 63
4
 11
2
g 43
4
 12
3


d 44
5
 1
2
h 32
3
 14
9


2 Work out a 21
2
 11
4


b 37
8
 11
2


c 32
3
 11
2


d 44
5
 12
3


3 Work out a 1 
13


b 3 
25


c 6  5
14


d 8  4
23


4 Work out a 21
4
 11
2
e 51
3
 13
4


b 31
4
 12
3
f 63
5
 22
3


c 41
2
 23
4
g 42
7
 13
5


d 31
6
 11
2
h 71
9
 32
3


5 Work out a 31
5
 2
14
5 e 125
8
 32
3


b 83
8
 33
4
f 35
6
 32
5


c 62
3
 8
9
g 8
17
0  31
3


d 15
6
 42
7
h 91
6
 17
9


4.4 Multiplication of fractions and mixed numbers Multiplication by an integer is the same as repeated addition. So 2  4
9
is the same as 4
9
 4
9
 8
9
To multiply a fraction by an integer, multiply the numerator of the fraction by the integer. Do not change the denominator of the fraction.

Example 9 Work out 6  2
3


Solution 9 6  2
3
 1
3
2 1 2

3

4

6  2
3
 4

Multiply the numerator of the fraction by the integer. Do not change the denominator. Simplify the fraction. The answer is an integer in this case.

To multiply 3
4
by 2
3

3
4

 23


16
2  12



Multiply the numerators 3  2  6 Multiply the denominators 4  3  12 Simplify the fraction. 1 6

(

) of the area of the square is shaded. 2 12 To multiply two fractions, multiply the numerators and then multiply the denominators.

58

3 4

2 3

4.4 Multiplication of fractions and mixed numbers

CHAPTER 4

Example 10 Work out
23

25


Solution 10 2

 2


4
3 5 15

Multiply the numerators 2  2  4 Multiply the denominators 3  5  15 4

is in its simplest form. 15

When multiplying fractions, it is sometimes possible to simplify the multiplication by cancelling.

Example 11 5 7 Work out



14 10

Solution 11 5 7 57





14 10 14  10 1


7 5 17



14  10
14  2

Cancel the 5 and the 10

2

1

7 11 1




14  2 2  2


Cancel the 7 and the 14

2

11 1



22 4 1 5 7





14 10 4 When multiplying mixed numbers, first write the mixed numbers as improper fractions.

Example 12 Work out 22
3
 14
5


Solution 12 22
3
 14
5
 8
3
 9
5


Change each mixed number into an improper fraction.

3

8
9 

35


Cancel the 9 and the 3

24 

 44
5
5

Change the improper fraction into a mixed number.

1

Exercise 4D Give each answer in its simplest form.




1 Work out a 2  1
3
e 3
8
 2

b 3  1
4
f
15
2  4

c 2  2
5
g
29
0  8

d 3  2
7
h 3
5
 25 59

Fractions

CHAPTER 4

2 Work out a
35

12
e 2
3
 2
7


b f


1
4 3

4


35
 3
5


c g


1

2
3 5
7
 3

5 10

d h


1
2 3

4

3 Work out a 3
4
 2
5
e
13
4  8
9


b f

2

 3

3 8 1 6


9
21 40

c g

1 0

11
9
28

d h

5


4
6 15 2 5 2 7



 36 40

4 Work out a 11
4
 1
3
e 113

 214



b 13
5
 1
2
f 312

 114



c 22
3
 1
5
g 313

 145



d 3
7
 31
2
h 217

 245



5 Work out a 1
13
 1
14
e 22
7
 43
8


b 2
12
 1
35
f 41
6
 44
5


c 3
34
 1
11
0 g 63
7
 15
9


d 1
23
 4
15
h 81
3
 2
17
0

6 Work out a 3
4
 5
6

13
6

b

c (12
3
 5
6
)  8
9


d (27
9
 11
3
)  41
2


1 7

20

 4
5
 3
8


 3
5
 1
1
45

4.5 Division of fractions and mixed numbers 3

4

of this rectangle is shaded red.

Divide the red area by 2 Now 3
8
of the rectangle is shaded. So 3
4
 2  3
8
also

3

4

 1
2
 3
8


So dividing by 2 is the same as multiplying by 1
2

1
is the reciprocal of 2 2 To work out 3 
34
consider how many times
34
goes into 3

There are
14
2 in 3 whole squares, this is 4 lots of
34


So 3 
34
 4

also

3 
43
 4

So dividing by 3
4
is the same as multiplying by 4
3
4 3



3 is the reciprocal of 4 Similarly, the reciprocal of 3 (or 3
1
) is 1
3
and the reciprocal of 2
7
is 7
2
To divide by a fraction ● change the division sign into a multiplication sign ● write down the reciprocal of the second fraction. 60


15
 5
7


4.5 Division of fractions and mixed numbers

Example 13

Example 14

Work out
45
 3

Solution 13 4

 3  4

 1

5 5 3 4

5

3

CHAPTER 4

Work out
56

34
Give your fraction in its simplest form. The reciprocal of 3 is
13
Multiply
45
by
13



4
15

Solution 14 2 5 3 5 4








6 4 6 3


The reciprocal of 3
4
is 4
3
So multiply 5
6
by 4
3


3

10 

9 5 3



 11
9
6 4

Write the improper fraction as a mixed number.

When dividing mixed numbers, first write the mixed numbers as improper fractions.

Example 15 Work out 2
45
 2
11
0

Solution 15 24
5
 2
11
0  1
5
4  2
1
10 2

2

1

3


14
10 



5 21



Write the mixed numbers as improper fractions. The reciprocal of 2
1
10 is 1
2
01

4 

3 245

 2
11
0  113






Write the improper fraction as a mixed number.

Exercise 4E Give each answer in its simplest form. 1 Work out a
56
 2 e 1
4
 1
3


b f


3
8 3

5

2  1
2


c g


5
6 4

9

3  1
3


d h


5
8 5

6

2 Work out a 2
3
 3
5
e 5
8
 1
3
52

b f

3

 4

7 5 4 7

 1

25 10

c g

4


3
5 10 2 0


8
 21 15

d h


9
16 2 5

32

3 Work out a 31
2
 7 e 11
2
 3
4


b 24
5

11
0 f 24
9
 2
3


c 21
3
 1
9
g 71
5

19
0

d 33
4
 5 h 51
3
 4
9


4 Work out a 213

 245

e 4
19
0  24
5


b 314

 149

f 55
6
 11
9


c 334

 145

g 71
2
 11
4


d 623

 289

h 2
11
2  11
9


5 Work out a (1
2

15
2)  3
4


b 3  3
4

19
0

c 31
8
 (21
2
 13
8
)

d 33
5
 11
4
 22
5


 10  1
4
 3
8
 1
1
56

61

Fractions

CHAPTER 4

4.6 Fractions of quantities A unit fraction has a numerator of 1 and the denominator is a non-zero positive integer. Examples of unit fractions are 1
2
14


15
and
11
0 To find a unit fraction of an amount, think of that amount divided into equal parts.

Example 16 Find 1
4
of £24

Solution 16 24  4  6 1

4

Finding 1
4
of an amount is the same as dividing the amount into 4 equal parts.

of £24  £6

To find a fraction of an amount where the numerator is more than 1, think of the calculation in two stages. Firstly, divide the amount by the denominator. Then multiply the result by the numerator.

Example 17 Find
23
of £24

Solution 17 24  3  8 8  2  16 2

3

Divide 24 by 3 The result is 8 Multiply 8 by 2

of £24  £16

Another way to find a fraction of a quantity is to multiply the quantity by the fraction. For example 8 2


24  16 3
1

In mathematics, the word ‘of’ means the same as ‘’

Example 18 Find 3
7
of 10

Solution 18
3
of 10 
3
 10 7 7

‘of’ means the same as ‘’

 3
7
0
3
7


62

of 10  4
27


Change the improper fraction into a mixed number.

Exercise 4F 1 Find a 1
4
of 12 e
11
0 of 70

b f

1

3 1

8

of 18 of 32

c g

1

of 35 5
1
of 48 12

d h

1

of 24 6
1
of 100 20

2 Find a 2
3
of 15 e 5
6
of 24

b f

3

4 4

9

of 12 of 27

c g

2

of 20 5
7
of 50 10

d h

3

7 7

8

of 14 of 48

4.7 Fraction problems



CHAPTER 4

3 Find a 2
5
of £150 e 5
6
of 240 m

b f

3

of 120 grams 4
7
of 120 cm 10

c g

2

3 3

7

4 Find a 2
3
of 5 e 7
8
of 12

b f

2

5 3

7

of 4 of 8

c g

5 Find a 1
3
of 2
5


b

8

9

of 3
7


6 Find a 3
4
of £184 e
11
56 of 336 m

b f

7 Find a
25
of £4 e 1
3
72 of 20 kg

b f

d h

4

5 2

9

2

of 6 9
9
of 8 10

d h


5
of 16 12 5

of 24 9

c

6

7

d

5

8

5

of £496 8 3
9
50 of £1750

c g

5

of £318 6
7
of 660 kg 40

d h

1 7

20 of £460 2
9
100 of 40 km


3
of 12 m 8
9
of 175 grams 10

c g


7
16
3
40

d h


5
of 78 cm 12 3

of £68.40 4

of 48 cm of 280 kg

of 1
1
45

of 6 km of £1420

of £230 of 6120 km

of 2
2
45

4.7 Fraction problems Problems can involve fractions.

Example 19 In a cinema 2

of the audience are women. 5 1

of the audience are men. 8 All the rest of the audience are children. What fraction of the audience are children?

Solution 19 2 6 2 1

 1

 1


5


5 8 40  40  40

Add 2
5
and 1
8
to find the fraction of the audience who are women or men.

1  2
4
10  4
4
00  2
4
10  1
4
90

Subtract 24

10 from 1 to find the fraction of the audience who are children.

1 9

40

of the audience are children.

Example 20 A school has 1800 pupils. 860 of these pupils are girls. 3

of the girls like swimming. 4 2

of the boys like swimming. 5 Work out the total number of pupils in the school who like swimming.

Solution 20 3

 860  645 4

Work out the number of girls who like swimming.

1800  860  940

Work out the number of boys in the school.

2

5

 940  376

Work out the number of boys who like swimming.

Work out the total number of pupils who like swimming. 645  376  1021 1021 pupils like swimming.

63

Fractions

CHAPTER 4

Exercise 4G 1 Simon spends
12
of his money on rent and
13
of his money on transport. a What fraction of his money does he spend on rent and transport altogether? b What fraction of his money is left? 2 Dawn drives for
34
of a journey. The journey lasts for 148 minutes. For how many minutes does Dawn drive? 3 There are 800 students in a school. 3
5
of the students are boys. Work out the number of boys in the school. 4 Last season, Pearson Athletic won
17
0 of its matches, drew 1
5
and lost the rest. What fraction of its matches did it lose? 5

1

2

of a garden is lawn. 2
5
of the garden is a vegetable patch. The rest of the garden is a flower bed. What fraction of the garden is a flower bed?

6

8

9

of an iceberg lies below the surface of the water. The total volume of an iceberg is 990 m3. What volume of this iceberg is below the surface?

7 There are 36 students in a class. Javed says that 3
8
of these students are boys. Explain why Javed cannot be right. 8 John walks 21
2
miles to the next village. He then walks a further 22
3
miles to the river. How far has he walked altogether? 9 Tammy watches 2 films. The first film is 134

hours long and the second one is 213

hours long. Work out the total length of the two films. 10 Two sticks are 21
2
metres and 11
3
metres long. Work out the difference between the lengths of the two sticks. 11


2
3

of a square is shaded.
34
of the shaded part is shaded blue. What fraction of the whole square is shaded blue?

12 In a crowd, 2
5
of the people are female.
17
0 of the females are girls. What fraction of the crowd is girls? 13 DVDs are sold for £14 each. 2
5
of the £14 goes to the DVD company. How much of the £14 goes to the DVD company? 14 A school buys some textbooks. The total price of the textbooks is £2400 The school gets a discount of 1
8
off the price of the textbooks. Work out how much the school pays for the textbooks. 15 Alison, Becky and Carol take part in a charity relay race. The race is over a total distance of 25
8
kilometres. Each girl runs an equal distance. Work out how far each girl runs. 64

Chapter 4 review questions

CHAPTER 4

Chapter summary You should now know:



that equivalent fractions are fractions that are equal



how to find an equivalent fraction by multiplying both the numerator and denominator by the same number



how to cancel a fraction to obtain its simplest form



how to order fractions by writing each fraction with the same denominator



that an improper fraction is one in which the numerator is greater than the denominator



that a mixed number consists of a whole number and a fraction



how to convert between mixed numbers and improper fractions



that to add (or subtract) fractions with the same denominator, add (or subtract) the numerators but do not change the denominator



that to add or subtract fractions with different denominators, firstly find the lowest common denominator and then change each fraction to its equivalent fraction with this denominator



how to add (or subtract) mixed numbers by adding (or subtracting) the whole numbers and the fractions separately



how to multiply fractions by multiplying the numerators and then multiplying the denominators



how to multiply or divide mixed numbers by firstly writing the mixed numbers as improper fractions



how to divide by a fraction by ● changing the division sign into a multiplication sign ● writing down the reciprocal of the second fraction



how to find a fraction of an amount by dividing the amount by the denominator and then multiplying the result by the numerator.

Chapter 4 review questions




1 Work out a
14
of £48

b


1
5

of £50

c


1
3

of £60

d


1
10

2 Work out a 3
4
of £44

b

2

3

of £18

c

2

5

of £35

d

c

1

3

 14



d

of £40

e


1
6

of £30

3

5

of £100

e

4

5

of £45

1

4

 35



e

4

5

 23



3 Change to improper fractions b 84
5
a 22
3
4 Work out a 12

 13



b

2

3

 14



5 Simon spent
13
of his pocket money on a computer game. He spent 1
4
of his pocket money on a ticket for a football match. Work out the fraction of his pocket money that he had left.

(1387 June 2003)

65

Fractions

CHAPTER 4

6 Asif, Curtly and Barbara share some money. Asif receives
38
of the money. Barbara receives 1
3
of the money. What fraction of the money does Curtly receive?

(1388 March 2004)

7 Work out 1  (1
2
 1
6
)

(1387 November 2004)

8 Work out, giving your answers as mixed numbers b 434

 245

a 345

 223

9 Work out and simplify where possible b
15
2  2 c a 1
7
 4

1

8

4

d


3
10

e

3

8

2

c

6

7

3

d

8

9

3

e

4

9

5

11 Work out and simplify where possible b 1
3
 4
5
c a 4
5
 1
4


1

4

 3
4


d

1

5

 1
2
01

e


6
11

12 Work out and simplify where possible b 1
4
of 3
5
c a 1
3
of 3
5


1

2

of 6
7


d

1

4

of
18
1

e

1

5

of 1
1
03

13 Work out, giving each answer in its simplest form b 5
6
 2
5
c
17
0  5
6
a 3
8
 2
5


d

5

6


19
0

e

5

9


26
5

14 Work out, giving each answer in its simplest form b 5
7
 1
1
01 c 2
9

32
0 a 3
4
 1
5


d

1
8
35

e

2 1

40

10 Work out a 2
5
 2

15 Work out a
16

49


b

4

7


3
7

2

2

 6
7


 1
3


 3
8


8

(1388 March 2002)

16 Work out
23

56
Give your fraction in its simplest form.

(1388 January 2004)

b

17 Work out, giving your answers as mixed numbers b 42
3
 12
5
a 12
3
 2
13
0 18 a Work out the value of 2
3
 3
4
Give your answer as a fraction in its simplest form. b Work out the value of 12
3
+ 23
4
Give your answer as a fraction in its simplest form. 19 A school has 1200 pupils. 575 of these pupils are girls. 2

of the girls like sport. 5 3

of the boys like sport. 5 Work out the total number of pupils in the school who like sport. 20 Work out 33
4
 22
3
21 Work out 31
2
 12
3
Give your answer as a mixed number in its simplest form. 66

(1387 June 2005)

(1387 November 2003) (1388 March 2003)