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2. Fractions
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iGCSE (2021 Edition)

2.06 Fractions and division

Lesson
Worksheet
Practice
Worksheet
Dividing fractions
1

Simplify:

a
\dfrac{1}{8} \div \dfrac{1}{5}
b
\dfrac{1}{2} \div \dfrac{9}{10}
c
\dfrac{1}{5} \div \dfrac{3}{7}
d
\dfrac{3}{4} \div \dfrac{1}{9}
e
\dfrac{1}{10} \div \dfrac{1}{3}
f
\dfrac{1}{2} \div \dfrac{1}{9}
g
\dfrac{2}{3} \div \dfrac{1}{8}
h
\dfrac{1}{11} \div \dfrac{3}{7}
2

Simplify:

a
\dfrac{2}{7} \div \dfrac{5}{3}
b
\dfrac{9}{10} \div \dfrac{10}{9}
c
\dfrac{2}{7} \div \dfrac{7}{18}
d
\dfrac{3}{15} \div \dfrac{4}{3}
e
\dfrac{28}{9} \div \dfrac{4}{9}
f
\dfrac{3}{15} \div \dfrac{15}{4}
g
\dfrac{21}{27} \div \dfrac{3}{2}
h
\dfrac{5}{7} \div \dfrac{45}{2}
i
\dfrac{2}{3} \div \dfrac{11}{15}
j
\dfrac{10}{7} \div \dfrac{10}{7}
k
\dfrac{4}{5} \div \dfrac{36}{35}
l
\dfrac{3}{7} \div \dfrac{14}{27}
m
\dfrac{2}{36} \div \dfrac{4}{7}
n
\dfrac{3}{55} \div \dfrac{7}{20}
o
\dfrac{10}{99} \div \dfrac{45}{22}
p
\dfrac{22}{27} \div \dfrac{3}{2}
3

Simplify:

a
3 \div \dfrac{1}{11}
b
\dfrac{1}{9} \div 8
c
\dfrac{4}{3} \div 5
d
\dfrac{6}{11} \div 8
e
\dfrac{3}{5} \div 4
f
\dfrac{65}{9} \div 5
g
3 \div \dfrac{39}{10}
h
7 \div \dfrac{98}{12}
4

Simplify:

a
1\dfrac{2}{5} \div \dfrac{3}{4}
b
2\dfrac{1}{4} \div 1\dfrac{2}{5}
c
1\dfrac{2}{7} \div 3\dfrac{1}{2}
d
3\dfrac{1}{3} \div 2\dfrac{1}{2}
e
2\dfrac{1}{3} \div 6\dfrac{2}{12}
f
3\dfrac{3}{8} \div 2\dfrac{1}{4}
g
6\dfrac{3}{4} \div 4\dfrac{2}{7}
h
8\dfrac{1}{2} \div 1\dfrac{5}{6}
5

Simplify:

a
\dfrac{1}{5} \times \dfrac{1}{3}\div \dfrac{1}{2}
b
\dfrac{2}{3} \div \dfrac{1}{9} \times \dfrac{2}{5}
c
\dfrac{3}{6} \div \dfrac{12}{5} \div \dfrac{1}{2}
d
\dfrac{3}{4} \div \dfrac{2}{5} \times \dfrac{1}{6}
e
\dfrac{1}{7} \times \dfrac{2}{9} \div \dfrac{4}{27}
f
\dfrac{1}{7} \times \dfrac{5}{8} \div \dfrac{15}{49}
g
\dfrac{18}{25} \div \dfrac{9}{10} \times \dfrac{1}{3}
h
\dfrac{8}{11} \div \dfrac{2}{3} \times \dfrac{15}{2}
Applications
6

A family drinks \dfrac{3}{4} of a carton of milk per day. How many days will 6 cartons of milk last the family?

7

A glass holds \dfrac{3}{8} of a litre of lemonade. How many glasses of lemonade can be filled with 6 litres of lemonade?

8

Yang eats \dfrac{2}{5} of a packet of bicuits each day. If he buys 12 packets, how many days will the packets last?

9

If \dfrac{2}{3} of a tart is shared equally between 5 people, what fraction of the tart would each person receive?

10

A truck tank contains 42 \text{ L} when \dfrac{3}{4} full. What is the capacity of the tank when full?

11

If a garden snail can move \dfrac{1}{100} \text{ km/h}, how many hours would it take for the garden snail to reach \dfrac{3}{4} \text{ km}?

12

Christine has 1\dfrac{3}{4} of a metre of ribbon. She uses \dfrac{7}{20} to wrap a present. How many presents can she wrap with her ribbon?

13

Sheldon is planning to sell banana bread on the upcoming school fair. If a loaf requires \dfrac{3}{4} cups of sugar, how many banana bread loaves can Sheldon make if he has 8 \dfrac{2}{8} cups of sugar on hand?

14

Jean is making bows for her gift wrapping business. A bow requires 6\dfrac{1}{6} inches of ribbon. If she has 55 \dfrac{1}{2} inches of ribbon, how many bows can Jean make?

15

Benjamin wants to engrave his name on a metal plate. There is 1 \dfrac{2}{4} \text{ cm} space on the plate. There are three sizes of letters to choose from: \dfrac{1}{8} \text{ cm} wide, \dfrac{1}{6} \text{ cm} wide and \dfrac{1}{4} \text{ cm} wide.

a

Find the maximum number of letters that Benjamin can engrave on the plate using the following sizes:

i

\dfrac{1}{8} \text{ cm} wide

ii

\dfrac{1}{6} \text{ cm} wide

iii

\dfrac{1}{4} \text{ cm} wide

b

Which letter sizes could he use for his name?

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Outcomes

0580C1.1F

Identify and use reciprocals.

0580C1.8C

Use the four rules for calculations with fractions (including mixed numbers and improper fractions), including correct ordering of operations and use of brackets.

0580E1.1F

Identify and use reciprocals.

0580E1.8C

Use the four rules for calculations with fractions (including mixed numbers and improper fractions), including correct ordering of operations and use of brackets.

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