Finding a Fraction of an Amount

What you will learn

• Find a unit fraction of an amount.
• Find any fraction of an amount.
• Solve simple problems with money and objects.

Before you start: you should know what a fraction is and be able to divide equally. See Fractions Explained and Division: Sharing and Grouping.

The idea

“Half of 12” is $12 \div 2 = 6$: you share 12 into 2 equal parts. “One quarter of 12” shares into 4 equal parts. A fraction with $1$ on top is just a division by the bottom number.

For a fraction such as $\frac{3}{4}$, find one part first, then take as many parts as the top number says.

Two steps

1. Divide the amount by the denominator to find one part.
2. Multiply by the numerator to find the parts you need.

What is left

The parts you did not take are a fraction too. If $\frac{3}{8}$ of 24 is $9$, the other $\frac{5}{8}$ is $15$, and $9 + 15 = 24$.

Worked examples

Example 1: Find a fraction of a number

Find $\frac{3}{5}$ of $35$.

1. Divide by the denominator: $35 \div 5 = 7$.
2. Multiply by the numerator: $7 \times 3 = 21$.

Answer: $21$

Example 2: Money

A bike costs £$250$. The shop takes $\frac{7}{10}$ off. How much is taken off, and what is the new price?

1. One tenth of £$250$ is £$25$.
2. Seven tenths is $7 \times 25 = 175$, so £$175$ is taken off.
3. New price: $250 - 175 = 75$.

Answer: £$175$ off, so the bike costs £$75$.

Example 3: Work backwards

$\frac{3}{4}$ of a number is $18$. What is the number?

1. Three quarters is $18$, so one quarter is $18 \div 3 = 6$.
2. The whole is four quarters: $4 \times 6 = 24$.
3. Check: $\frac{3}{4}$ of $24$ is $18$.

Answer: $24$

Tip: if the amount does not divide by the denominator, you will not get a whole number. Check that the answer makes sense.

Why it matters

Sale prices, recipes, sharing out sweets and finding how much of a journey is left all use a fraction of an amount. It is also the first step to percentages: finding $25\%$ of something is finding $\frac{1}{4}$ of it.