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Multiplying fractionsPlace value

Adding fractionsThis topic is relevant for:

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.

**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

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

So to work out three quarters we multiply this by

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

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

In order to work out fractions of an amount:

**Multiply the fraction and the amount.****Write the final answer.**

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

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

DOWNLOAD FREEWork out:

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

**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.

2**Write the final answer**.

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

The final answer is

Work out:

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

**Multiply the fraction and the amount**.

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.

**Write the final answer**.

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

The final answer is

Work out:

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

**Multiply the fraction and the amount**.

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

Then, multiply by the numerator (top number):

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

So,

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

**Write the final answer**.

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

The final answer is

Work out:

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

**Multiply the fraction and the amount**.

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,

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

**Write the final answer**.

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

The final answer is

Work out:

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

**Multiply the fraction and the amount**.

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,

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

**Write the final answer**.

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

The final answer is

Work out:

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

**Multiply the fraction and the amount**.

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,

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

**Write the final answer**.

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

The final answer is

**Not writing money with two decimal places**

If the answer to a question involving money is a decimal and the units are £ you need

E.g.

\[\frac{2}{9} \quad of \quad£6.30\]

\[\frac{2}{9}\times6.3=1.4\]

The final answer

**Not fully answering the question**

A common error is to

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

9

9.5

1.8

6

\frac{1}{2}\times18=\frac{18}{2}=18\div2=9

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

15

6

25

7

\frac{1}{5}\times30=\frac{30}{5}=30\div5=6

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

23

16

8

20

\frac{2}{3}\times24=\frac{2\times24}{3}=(24\div3)\times2=16

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

34

40

28

35

\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

4.5 kg

6.3 kg

5.9 kg

\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

6.4 km

3.2 km

4.2 km

\frac{4}{9}\times14.4=\frac{4\times14.4}{9}=(14.4\div9)\times4=6.4

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)**

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)**

For working out the half of seats on the train.

**(1)**

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

**(1)**

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

**(1)**

NO, only 135 seats are used

**(1)**

You have now learned how to:

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

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