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�2 2.1 Adding and subtracting fractions and mixed numbers
69A
1 Work out
a 27
37
+ ................................................................................ b 811
111
– ..................................................................
c 915
215
– ..............................................................................
d 623
1223
+ ..................................................................
2 Work out and give your answers in their simplest form.
a 920
1720
+ b
815
1115
+
.................................................................. ..................................................................
c 29
79
49
+ + d 1516
1116
716
+ –
.......................................................................................... ..........................................................................................
3 Work out
a 12
13
+ b
14
17
–
.......................................................................................... ..........................................................................................
c 25
16
– d
14
23
+
.......................................................................................... ..........................................................................................
e 79
15– f
34
15
+
.......................................................................................... ..........................................................................................
g 9
1014
– h
47
13
+
.......................................................................................... ..........................................................................................
4 Work out the following. Give each answer as a fraction or mixed number in its simplest form.
a 37
25
+ b 1
834
+
.......................................................................................... ..........................................................................................
c 79
23
– d 49
25
+
.......................................................................................... ..........................................................................................
Guided practice worksheet
If the bo� om numbers of a fraction are the same, just add (or subtract) the top numbers.
Change the fractions into fractions with the same denominator before you add the fractions.
D
Questions are targeted at the grades indicated
�2 2.1 Adding and subtracting fractions and mixed numbers
69B
Guided practice worksheet
e 27
23
+ f 7
1023
–
.......................................................................................... ..........................................................................................
g 16
45
+ h 34
23
–
.......................................................................................... ..........................................................................................
5 Work out
a 45
710
+ b 89
23
–
.......................................................................................... ..........................................................................................
c 56
34
+ d 78
25
–
.......................................................................................... ..........................................................................................
e 79
56
+
f 710
34
+
.......................................................................................... ..........................................................................................
g 78
16
– h 23
712
–
.......................................................................................... ..........................................................................................
D
�2 2.1 Adding and subtracting fractions and mixed numbers
69C
Guided practice worksheet
6 Work out
a 5 314
23+ b 3 61
312+
.......................................................................................... ..........................................................................................
c 4 235
34+ d 7 17
856+
.......................................................................................... ..........................................................................................
7 Work out
a 5 178
34– b 6 25
623–
.......................................................................................... ..........................................................................................
c 8 325
34– d 7 41
523+
.......................................................................................... ..........................................................................................
8 Anya bought two melons. One melon weighed 134 kg, the other melon weighed 5
8 kg. Work out the total
weight of the two melons.
...............................................................................................
C
�2 2.1 Adding and subtracting fractions and mixed numbers
69D
Guided practice worksheet
9 The distance from Hal’s house to the shops is 612 miles. Hal cycles to the shops from his house. When he
has cycled 4 45 miles his bike gets a puncture. He pushes his bike the rest of the way to the shops. How far
does Hal push his bike?
...............................................................................................
C
�2 2.2 Multiplying fractions and mixed numbers
71A
In all these questions give your answer in its simplest form.
1 Work out
a 3 15×× b 6 1
7×× c 19 4×× d 3
10 3××
................................................. ................................................. ................................................. ...............................................
e 2 513×× f 3
10 15×× g 78 16×× h 3
4 20××
................................................. ................................................. ................................................. ...............................................
2 Work out
a 16 of 24 m b 3
4 of 12 kg c 4
5 of 15 km d 710
of 25 g
................................................. ................................................. ................................................. ...............................................
e 34
of £672 f 25
of 750 m g 78
of 400 kg h 56
of £288
................................................. ................................................. ................................................. ...............................................
i 57
of 4.27 m j 611
of 3.85 kg k 29
of 48.69 m l 613
of £79.30
................................................. ................................................. ................................................. ...............................................
Guided practice worksheet
In part a write 3 as 3–1 then multiply the top numbers and the bo� om numbers.
Questions are targeted at the grades indicated
�2 2.2 Multiplying fractions and mixed numbers
71B
Guided practice worksheet
3 Work out
a 57
12
×× b 3
1014
××
.......................................................................................... ..........................................................................................
c 13
27
×× d 6
1115
××
.......................................................................................... ..........................................................................................
e 89
23
×× f 1
745
××
.......................................................................................... ..........................................................................................
g 18
56
×× h 9
1037
××
.......................................................................................... ..........................................................................................
4 Work out
a 45
12
×× b 23
19
××
.......................................................................................... ..........................................................................................
c 37
56
×× d 78
221
××
.......................................................................................... ..........................................................................................
e 67
29
×× f 1516
825
××
.......................................................................................... ..........................................................................................
It is easier to cancel fractions before multiplying rather than afterwards.
�2 2.2 Multiplying fractions and mixed numbers
71C
Guided practice worksheet
g 914
712
×× h 1021
625
××
.......................................................................................... ..........................................................................................
5 Work out
a 2 12
310
×× b 45
131××
.......................................................................................... ..........................................................................................
c 38
121×× d 3 42
312××
.......................................................................................... ..........................................................................................
e 2 117
25×× f 6 23
1017××
.......................................................................................... ..........................................................................................
g 9 123
129×× h 2 12
95
16××
.......................................................................................... ..........................................................................................
6 Becky receives £7.25 pocket money each week. One week she spends 25 of her pocket money on make-up.
How much money does she spend on make-up?
........................................................................................................................................
Remember to change mixed numbers to improper fractions before multiplying.
C
�2 2.2 Multiplying fractions and mixed numbers
71D
Guided practice worksheet
7 A book weighs 125 kg. How much will 6 books weigh?
........................................................................................................................................
8 Malik takes 513 minutes to run 1 mile. If he runs at the same rate, how long will it take him to run 31
2 miles?
........................................................................................................................................
C
�2 2.3 Dividing fractions and mixed numbers
73A
Give all your fractions in their simplest form.
1 Work out
a 45 2÷ b 3
4 2÷ c 23 3÷ d 7
8 3÷
.......................................... .......................................... .......................................... ..........................................
2 Work out
a 13
12÷ b 1
813÷
c 15
23÷ d 1
935÷
.......................................... .......................................... .......................................... ..........................................
e 34
25÷ f 8
945÷ g 6
734÷ h 9
1045÷
.......................................... .......................................... .......................................... ..........................................
3 Work out
a 56
23÷ b 4
589÷ c 6
734÷ d 12
252120÷
.......................................... .......................................... .......................................... ..........................................
e 1516
58÷ f 8
94
15÷ g 10
2157÷ h 20
275
18÷
.......................................... .......................................... .......................................... ..........................................
Guided practice worksheet
To divide a fraction by a whole number, multiply by the reciprocal. For example, to divide by 2, multiply by 1–2.
To divide fractions, turn the second fraction upside down and multiply.
Questions are targeted at the grades indicated
�2 2.3 Dividing fractions and mixed numbers
73B
Guided practice worksheet
4 Work out
a 4 712
12÷ b 1 23
57
10÷ c 10 21
214÷ d 3 11
7521÷
.......................................... .......................................... .......................................... ..........................................
e 13 512
14÷ f 12 41
238÷ g 5 11
335÷ h 4 54
513÷
.......................................... .......................................... .......................................... ..........................................
C
Turn mixed numbers into improper fractions before dividing.
�2 2.4 Fraction problems
75A
1 There are 1240 students in a school. 25
of the students eat school lunch.
How many students eat school lunch?
........................................................................................................
2 There are 10 500 people watching a concert.
25
of the audience are boys, 37
of the audience are girls.
a How many girls watched the concert?
........................................................................................................
b What fraction of the audience are adults?
........................................................................................................
3 There are 28 cookies in a box. 37 of the cookies have chocolate chips in them.
How many cookies have chocolate chips in them?
........................................................................................................
4 A bag of sugar weighs 215 pounds. Work out the weight of 7 bags of sugar.
........................................................................................................
5 In a box of cookies, 23 of the cookies are made using white chocolate, 1
4 of the cookies are made using milk chocolate and the rest of the cookies are made using plain chocolate. What fraction of the cookies are made using plain chocolate?
........................................................................................................
6 There are 1500 pupils in a school. 35 of the pupils are boys; how many girls are there in the school?
........................................................................................................
Guided practice worksheet
D
Remember that you cannot add or subtract fractions unless they have the same number on the bo� om.
To multiply mixed numbers you must change them to improper fractions � rst.
Questions are targeted at the grades indicated
�2 2.4 Fraction problems
75B
Guided practice worksheet
7 A bottle contains 112 litres of water. The volume of a glass is 1
6 litre.
How many full glasses of water can be poured if all the water in the bottle is used?
........................................................................................................
8 At a concert, 15 of the audience are boys and 2
7 of the audience are girls.
Work out what fraction of the audience are adults.
........................................................................................................
9 Marty watches a � lm that lasts for 2 14 hours and then a documentary that lasts for 2
3 of an hour. How long does he watch television for?
........................................................................................................
1 0 A rectangle has width 558 cm and length 62
5 cm. Work out the area of the rectangle.
........................................................................................................
1 1 One piece of wood measures 423 m, another piece of wood measures 2 3
5 m.
Work out the difference in length between the two pieces of wood.
........................................................................................................
1 2 Martin runs for 2 12 km then walks for 13
5 km. Jack runs for 134 km then walks for 2 km. Who goes the further
and by how much?
........................................................................................................
D
C
