topic badge

1.05 Calculations with fractions

Worksheet
Fraction calculations
1

Simplify the following fractions:

a
\dfrac{3}{9}
b
\dfrac{20}{60}
c
\dfrac{6}{20}
d
\dfrac{27}{45}
e
\dfrac{63}{28}
f
\dfrac{40}{30}
g
\dfrac{26}{50}
h
\dfrac{24}{66}
i
\dfrac{32}{80}
j
\dfrac{64}{92}
k
\dfrac{80}{100}
l
\dfrac{60}{200}
m
\dfrac{2}{10}
n
\dfrac{8}{64}
o
\dfrac{21}{231}
p
\dfrac{150}{270}
2

Simplify the following fractions, writing your answers as mixed numbers:

a
\dfrac{11}{7}
b
\dfrac{24}{10}
c
\dfrac{18}{4}
d
\dfrac{63}{45}
3

Evaluate the following, writing your answers in simplest form:

a

\dfrac {5}{9} + \dfrac {8}{9}

b
\dfrac{1}{5} + \dfrac{2}{4}
c
\dfrac{7}{8} + \dfrac{5}{6}
d
\dfrac{6}{5} + \dfrac{5}{3}
e
\dfrac{1}{3} - \dfrac{1}{10}
f
\dfrac{3}{4} + \dfrac{1}{8} - \dfrac{1}{4}
g
\dfrac{5}{9} + \dfrac{2}{3} + \dfrac{5}{6}
h
\dfrac{8}{9} \times \dfrac{9}{56}
i
\dfrac{8}{15} \times \dfrac{9}{7}
j
\dfrac{5}{3} \times \dfrac{21}{2}
k
\dfrac{9}{10} \times \dfrac{10}{9}
l

\dfrac {11}{9} \times \dfrac {2}{99}

m

- \dfrac {3}{7} \times \dfrac {2}{3}

n

\left(\dfrac {4}{9}\right)^{2}

o
\dfrac{2}{7} \div \dfrac{5}{3}
p
\dfrac{9}{10} \div \dfrac{10}{9}
q
\dfrac{2}{7} \div \dfrac{7}{18}
r
\dfrac{3}{15} \div \dfrac{4}{3}
s

\dfrac {3}{8} \div \dfrac {3}{4}

t

\dfrac {11}{35} \div \dfrac {55}{49}

u

\left( - \dfrac {4}{5} \right) \div \dfrac {3}{4}

v

\dfrac{3}{5} \times \dfrac{2}{3} + \dfrac{5}{15}

w

\left(\dfrac{2}{3} + \dfrac {3}{5}\right) \times \dfrac{3}{7}

4
Evaluate the following, writing your answers as mixed numbers in simplest form where necessary:
a
2\dfrac{3}{11} + 4\dfrac{7}{11}
b
3\dfrac{2}{6} + 4\dfrac{4}{5}
c
3\dfrac{1}{3} + 4\dfrac{11}{12}
d
2\dfrac{2}{3} + 3\dfrac{11}{15}
e
6+ 1\dfrac{4}{5}
f
7 + 3\dfrac{3}{4}
g
11 + 4\dfrac{3}{8}
h
4 - \dfrac{7}{9}
i
5\dfrac{10}{11} - 4\dfrac{8}{11}
j
4\dfrac{6}{7} - 3\dfrac{6}{8}
k
6\dfrac{1}{2} - 4\dfrac{1}{10}
l
6\dfrac{1}{2} - \dfrac{3}{8}
m
2 - \dfrac{3}{4}
n
8 - 2\dfrac{1}{2}
o
10 - 5\dfrac{1}{3}
p
9-2\dfrac{5}{7}
q
1\dfrac{1}{2} \times \dfrac{2}{3}
r
1\dfrac{3}{5} \times 2\dfrac{1}{4}
s
1\dfrac{3}{4} \times \dfrac{4}{9}
t
2\dfrac{1}{4} \times 3\dfrac{1}{3}
u
1\dfrac{2}{5} \div \dfrac{3}{4}
v
2\dfrac{1}{4} \div 1\dfrac{2}{5}
w
1\dfrac{2}{7} \div 3\dfrac{1}{2}
x
3\dfrac{1}{3} \div 2\dfrac{1}{2}
5

Evaluate:

a
\left(\dfrac{4}{7} + \dfrac{2}{5}\right) \div \dfrac{5}{8}
b
\dfrac{4}{16} - \dfrac{2}{16} + \dfrac{12}{16}
c
\dfrac{4}{35} - \left(\dfrac{6}{7} - \dfrac{4}{5}\right)
d
\left(\dfrac{2}{5} - \dfrac{3}{8}\right) \times \dfrac{5}{9}
e
\dfrac{47}{72} - \left(\dfrac{2}{8} + \dfrac{3}{9}\right)
f
\dfrac{6}{7} \times \left(\dfrac{2}{3} - \dfrac{2}{7}\right)
g
\dfrac{7}{8} \div \left(\dfrac{3}{8} + \dfrac{2}{7}\right)
h
\dfrac{5}{8} \div \left(\dfrac{6}{7} - \dfrac{2}{9}\right)
i
\left(\dfrac{3}{5} - \dfrac{1}{4}\right) \div \dfrac{1}{2}
j
\left(\dfrac{1}{4} + \dfrac{3}{8}\right) \times \left(\dfrac{2}{5} + \dfrac{1}{5}\right)
k
\dfrac{5}{7} \times \left(\dfrac{1}{3} + \dfrac{5}{6} - \dfrac{1}{2}\right)
l
\left(\dfrac{2}{5} + \dfrac{3}{10} \times \dfrac{2}{3}\right) \div \dfrac{6}{7}
m
\left(\dfrac{1}{3} + \dfrac{3}{4}\right) \div \left(\dfrac{1}{2} - \dfrac{3}{8} \right)
n
8\dfrac{1}{4} - 2\dfrac{1}{5} \times 3 \dfrac{1}{2}
Applications
6

A class has 40 students. \dfrac{2}{5} of the class are boys.

a

What fraction of the class is girls?

b

How many girls are in the class?

7

Ellie wants to install a rectangular swimming pool in her backyard.

If the space available for a pool in her backyard measures 10\dfrac{1}{4}\text{ m} by 4\text{ m}, what will be the total area of the pool?

8

Sally is a sales assistant. She earns \$192 per week, plus a commission of \dfrac{1}{3} on anything she sells. Last week, she sold \$726 of printers.

a

What was Sally's commission for last week?

b

What was Sally's pay for last week?

9

In a survey of 270 people, \dfrac{1}{10} said their favourite sport was soccer, and \dfrac{1}{9} said their favourite sport was tennis.

a

What is the total fraction of people who said their favourite sport was soccer or tennis?

b

What is the fraction of people who did not put soccer or tennis as their favourite sport?

c

How many people did not put soccer or tennis as their favourite sport?

10

At the end of last month, a dam was \dfrac{5}{7} full. Over the current month, \dfrac{52}{63} of the dam's capacity was used up by the town. Meanwhile, rain filled \dfrac{5}{9} of the dam's capacity over the duration of the month. What fraction of the dam is full at end of this month?

11

After an earthquake, \dfrac{3}{7} of all claims were paid within a month. Of the remaining claims that had not yet been paid, \dfrac{5}{7} of them were paid within the second month. What fraction of all claims were paid in the second month?

12

During a sale, a number of computers were sold. 6 computers were sold at a loss, which represents \dfrac{1}{6} of the total number of computers that were sold.

If 89 computers were up for sale, how many weren't sold?

13

A bottle is \dfrac{2}{7} full of cordial. If 230\text{ ml} of cordial is added to it, the bottle is \dfrac{5}{6} full. How much cordial does the bottle hold when full?

14

At the Easter Show, Tobias spends half an hour visiting chickens and \dfrac{1}{3} of an hour visiting alpacas. What fraction of an hour has he spent visiting animals?

15

A bag of oranges weighing \dfrac{8}{9} \text{ kg} was divided among 6 children. What was the mass of the oranges given to each child?

16

Katrina and Luigi ordered a pizza to share. Katrina ate \dfrac{3}{7} of the pizza while Luigi ate \dfrac{1}{2}.

a

Who ate more pizza?

b

What fraction of the pizza did they eat together?

c

What fraction of pizza is left?

17

Luke has a dice tin that is \dfrac{1}{4} full. He puts 8 extra dice in and the tin is now \dfrac{1}{3} full.

a

What fraction of the tin do the 8 extra dice take up?

b

How many dice can fit inside the tin?

18

Victoria borrows a 360-page novel from the library. She reads \dfrac{3}{4} of the novel.

a

How many pages did she read?

b

How many more pages does she have to read to finish her novel?

19

In the morning, a dam contains 635\text{ L} of water. Throughout the day, \dfrac{1}{5} of the water is lost through evaporation and cattle drinking from it.

a

How many litres of water are lost throughout the day?

b

How many litres of water are left in the dam at the end of the day?

20

Maria is a sales assistant. She earns \$293 per week, plus a commission of \dfrac{2}{9} on anything she sells. Last week she sold \$1377 of sofas.

a

Find Maria's commission for last week.

b

Find Maria's pay for last week.

Sign up to access Worksheet
Get full access to our content with a Mathspace account

Outcomes

F.1

solve practical problems requiring basic number operations

F.2

apply arithmetic operations according to their correct order

F.5

use a calculator for multi-step calculations

F.6

check results of calculations for accuracy

F.8

evaluate decimal fractions to the required number of decimal places

What is Mathspace

About Mathspace