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Fractions of Amounts

Fractions are split into the top (called the numerator) and the bottom (called the denominator). The bottom shows the number of total parts and the top shows the number of parts of the total there are. A fraction is just a division.

 

Learning Objectives:

After this topic students will be able to:

  • Simplify fractions
  • Write one number as a fraction of another.
  • Calculate a fraction of an amount.

Examples

Example 1: 

Calculate \dfrac{\textcolor{blue}{2}}{\textcolor{red}{5}} of \textcolor{limegreen}{£240}.

First divide \textcolor{limegreen}{£240} by \textcolor{red}{5} and then multiply it by \textcolor{blue}{2}:

 \begin{aligned} \dfrac{2}{5} \text{ of } £240 &= (\textcolor{limegreen}{£240} \div \textcolor{red}{5}) \times \textcolor{blue}{2} \\ &= £48 \times \textcolor{blue}{2} \\ & = £96 \end{aligned}

Example 2: 

A football club has 560 members.

\dfrac{5}{8} of them are adults and the rest are children.

How many children are in the club?

If \dfrac{5}{8} of the members are adults, then \dfrac{\textcolor{blue}{3}}{\textcolor{red}{8}} are children.

To work out the number of children, divide \textcolor{limegreen}{560} by \textcolor{red}{8} and then multiply it by \textcolor{blue}{3}:

 \begin{aligned} \dfrac{3}{8} \text{ of } 560 &= (\textcolor{limegreen}{560} \div \textcolor{red}{8}) \times \textcolor{blue}{3} \\ &= 70 \times \textcolor{blue}{3} \\ & = 210 \end{aligned}

Example 3:

A warehouse stores 8400 boxes of products.

\dfrac{3}{7} of the boxes contain electronics.

\dfrac{5}{8} of the remaining boxes contain clothes.

The rest contain household items.

a) How many boxes contain electronics?

b) How many boxes contain clothes?

c) How many boxes contain household items?

Since \dfrac{3}{7}​ of the boxes contain electronics:

\dfrac{3}{7} \times 8400 = \dfrac{3 \times 8400}{7} = \dfrac{25200}{7} = 3600

So, 3600 boxes contain electronics.

The remaining boxes are:

8400−3600=4800

Since \dfrac{5}{8}​ of the remaining boxes contain clothes:

\dfrac{5}{8} \times 4800 = \dfrac{5 \times 4800}{8} = \dfrac{24000}{8} = 3000

So, 3000 boxes contain clothes.

The remaining boxes contain household items:

4800−3000=1800

So, 1800 boxes contain household items.

Test Example Questions

Question 1: There are 28000 people in a stadium. \dfrac{2}{7} of the people are children. How many people in the stadium are children?

[1 mark]

First, divide by 7 and then multiply by 2:

28000\div7 = 4000

4000 \times 2 = 8000

So, there are 8000 children in the stadium.

Question 2: There are 380 sweets in a party bag to hand out at a party. \dfrac{2}{5} of the sweets are lollipops. How many lollipops are there to give out?

[1 mark]

Firstly divide by 5 and then multiply by 2:

380 \div 5 = 76

76 \times 2 = 152

So, there are 152 lollipops to give out.

Question 3: A car costs \pounds32,000 to buy new. After a year the car is now only worth \dfrac{5}{8} of its original value. How much is it worth now?

[1 mark]

Firstly divide by 8 and then multiply by 5:

32000 \div 8 = 4000

4000 \times 5 = 20,000

So the car is now worth \pounds20,000