GCSE Maths Number Fractions

Fractions of Amounts

Fractions of Amounts

Here we will learn about fractions of amounts.
There are also fractions worksheets, fraction activity sheets and fraction word problems (with answer sheets) based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What are fractions of amounts?

Fractions of amounts are when we are asked to find a certain fraction of a given amount by multiplication. They are also called finding fractions of numbers.

Using a bar model is a useful way of doing this.

E.g.
Calculate

\[\frac{3}{4} \quad of \quad 36\]

As we are asked to work out three quarters of 36, let’s start by working out one quarter:

\[\frac{1}{4} \quad of \quad 36 = 9\]

So to work out three quarters we multiply this by 3:

\[\frac{3}{4} \quad of \quad 36 =27\]

We can find fractions of any amount including integers (whole numbers), decimals and fractions. 

What are fractions of amounts?

What are fractions of amounts?

How to calculate fractions of amounts

In order to work out fractions of an amount:

  1. Multiply the fraction and the amount.
  2. Write the final answer.

Explain how to work out fractions of amounts in 2 steps

Explain how to work out fractions of amounts in 2 steps

Fractions of amounts worksheet

Fractions of amounts worksheet

Fractions of amounts worksheet

Get your free fractions of amounts worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Fractions of amounts worksheet

Fractions of amounts worksheet

Fractions of amounts worksheet

Get your free fractions of amounts worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE

Fractions of amounts examples

Example 1: unit fractions of amounts

Work out:

\[\frac{1}{2} \quad of \quad 16\]

  1. Multiply the fraction and the amount.

The “of” means that we multiply the fraction and the amount.

\[\frac{1}{2}\times16\]

\[\frac{1}{2}\times16=\frac{16}{2}=16\div2\]

You divide the amount by the denominator (bottom number) of the fraction.

2Write the final answer.

\[\frac{1}{2}\times16=8\]

The final answer is 8.

Example 2: unit fractions of amounts

Work out:

\[\frac{1}{7} \quad of \quad 28\]

The “of” means that we multiply the fraction and the amount.

\[\frac{1}{7}\times28\]
\[\frac{1}{7}\times28=\frac{28}{7}=28\div7\]

You divide the amount by the denominator (bottom number) of the fraction.

\[\frac{1}{7}\times28=4\]

The final answer is 4.

Example 3: non-unit fractions

Work out:

\[\frac{3}{4} \quad of \quad 20\]

The “of” means that we multiply the fraction and the amount.

\[\frac{3}{4}\times20\]
\[\frac{3}{4}\times20=\frac{3\times20}{4}=15\]

Alternatively, you could split the calculation into two parts.
First divide the amount by the denominator (bottom number) of the fraction to find one quarter of 20.
Then, multiply by the numerator (top number):

\[\frac{1}{4} \quad of \quad 20=20\div4=5\]

So,

\[\frac{3}{4} \quad of \quad 20=3\times5=15\]

\[\frac{3}{4}\times20=15\]

The final answer is 15.

Example 4: non-unit fractions

Work out:

\[\frac{2}{7} \quad of \quad 21\]

The “of” means that we multiply the fraction and the amount.

\[\frac{2}{7}\times21\]
\[\frac{2}{7}\times21=\frac{2\times21}{7}=6\]

Alternatively, you could split the calculation into two parts.
First divide the amount by the denominator (bottom number) of the fraction.
Then multiply by the numerator (top number):

\[\frac{1}{7} \quad of \quad 21=21\div7=3\]

So,

\[\frac{2}{7} \quad of \quad 21=2\times3=6\]

\[\frac{2}{7}\times21=6\]

The final answer is 6.

Example 5: calculator allowed

Work out:

\[\frac{3}{5} \quad of \quad 62 kg\]

The “of” means that we multiply the fraction and the amount.

\[\frac{3}{5}\times62\]
\[\frac{3}{5}\times62=\frac{3\times62}{5}=37.2\]

Alternatively, you could split the sum into two parts.
First divide the amount by the denominator (bottom number) of the fraction.
Then, multiply by the numerator (top number):

\[\frac{1}{5}\quad of \quad62=62\div5=12.4\]

So,

\[\frac{3}{5}\quad of \quad62=62\times12.4=37.2\]

\[\frac{3}{5}\times62=37.2\]

The final answer is 37.2 kg.

Example 6: calculator allowed

Work out:

\[\frac{7}{10}\quad of \quad135km\]

The “of” means that we multiply the fraction and the amount.

\[\frac{7}{10}\times135\]

\[\frac{7}{10}\times135=\frac{7\times135}{10}=94.5\]

Alternatively,  you could split the sum into two parts.
First divide the amount by the denominator (bottom number) of the fraction.
Then multiply by the numerator (top number):

\[\frac{1}{10}\quad of \quad135=135\div10=13.5\]

So,

\[\frac{7}{10}\quad of \quad135=13.5\times7=94.5\]

\[\frac{7}{10}\times135=94.5\]

The final answer is 94.5 km.

Common misconceptions

  • Not writing money with two decimal places

If the answer to a question involving money is a decimal and the units are £ you need 2 digits after the decimal point for the pence.

E.g.

\[\frac{2}{9} \quad of \quad£6.30\]
\[\frac{2}{9}\times6.3=1.4\]

The final answer £1.40

  • Not fully answering the question

A common error is to

Practice fractions of amounts questions

1. Work out: \frac{1}{2} \quad of\quad18

9
GCSE Quiz True

9.5
GCSE Quiz False

1.8
GCSE Quiz False

6
GCSE Quiz False
\frac{1}{2}\times18=\frac{18}{2}=18\div2=9

2. Work out: \frac{1}{5} \quad of \quad 30

15
GCSE Quiz False

6
GCSE Quiz True

25
GCSE Quiz False

7
GCSE Quiz False
\frac{1}{5}\times30=\frac{30}{5}=30\div5=6

3. Work out: \frac{2}{3} \quad of \quad 24

23
GCSE Quiz False

16
GCSE Quiz True

8
GCSE Quiz False

20
GCSE Quiz False
\frac{2}{3}\times24=\frac{2\times24}{3}=(24\div3)\times2=16

4. Work out: \frac{5}{8} \quad of \quad 56

34
GCSE Quiz False

40
GCSE Quiz False

28
GCSE Quiz False

35
GCSE Quiz True
\frac{5}{8}\times56=\frac{5\times56}{8}=(56\div8)\times5=35

5. Calculator allowed. Work out: \frac{3}{7} \quad of \quad 14.7 kg

2.1 kg
GCSE Quiz False

4.5 kg
GCSE Quiz False

6.3 kg
GCSE Quiz True

5.9 kg
GCSE Quiz False
\frac{3}{7}\times14.7=\frac{3\times14.7}{7}=(14.7\div7)\times3=6.3

6. Calculator allowed. Work out: \frac{4}{9} \quad of \quad 14.4 km

1.6 km
GCSE Quiz False

6.4 km
GCSE Quiz True

3.2 km
GCSE Quiz False

4.2 km
GCSE Quiz False
\frac{4}{9}\times14.4=\frac{4\times14.4}{9}=(14.4\div9)\times4=6.4

Fractions of amounts GCSE questions

1.   A jigsaw normally costs £9.60.

How much does a jigsaw cost in the sale?

(2 marks)

Show answer

\frac{1}{3}\times9.60=9.60\div3=3.2                                                                                                 (1)

9.6-3.2=6.4

The jigsaw costs £6.40 in the sale.

(1)

2. The average age of people in an office is 40 years old.

Sam’s age is \frac{11}{8} of the average.

How old is Sam?

(2 marks)

Show answer
\frac{11}{8}\times40

(1)

 Sam is 55.

(1)

3. A train has 1 first-class carriage and 4 standard carriages.

The first-class carriage has 40 seats.

\frac{7}{8} of the seats are being used.

Each standard class carriage has 60 seats.

\frac{5}{12} of the seats are being used.
Are more than half the seats on the train being used?

You must show your working.

(5 marks)

Show answer
40+(4\times60)=280

For working out the total number of seats on the train.

(1)

280\div2=140

For working out the half of seats on the train.

(1)

\frac{7}{8}\times40=35 \frac{5}{12}\times60=25

For working out the number of seats used the first-class carriage or second class carriage.

(1)

35+(4\times25)=135

For working out the total number of seats used on the train (1)

(1)

NO, only 135 seats are used

(1)

Learning checklist

You have now learned how to:

  • Find the fraction of an amount
  • Find the fractions of quantities

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