Topics
2. Fractions
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Middle Years

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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