Numbers · Lesson 30 of 36

Percentages

Per cent means "out of one hundred". Percentages let us compare parts of different-sized wholes on a common scale.

Primary
Secondary
Updated 14 November 2026

What you will learn

Say what a percentage means.
Change between simple fractions, decimals and percentages.
Find a percentage of an amount.
Write one number as a percentage of another.

Before you start: you should know fractions and decimals, and how to find a fraction of an amount. See Fractions Explained and Finding a Fraction of an Amount.

The idea

The word per cent comes from Latin for “by the hundred”. $35\%$ means $35$ out of every $100$ , which is the fraction $\frac{35}{100}$ or the decimal $0.35$ .

35 of the 100 squares are shaded. That is 35 out of 100, written 35%, 35/100 or 0.35.

Percentages are useful because they put everything on the same scale. Scoring 18 out of 24 in one test and 27 out of 40 in another is hard to compare. Converted to percentages ( $75\%$ and $67.5\%$ ), the comparison is instant.

Friendly percentages

A few percentages are worth knowing as fractions: $50\% = \frac{1}{2}$ , $25\% = \frac{1}{4}$ , $75\% = \frac{3}{4}$ , $10\% = \frac{1}{10}$ .

The same bar split to show 10%, 25%, 50% and 75%.

Percentage of an amount

To find $p\%$ of an amount, divide by $100$ and multiply by $p$ . Or build it from $10\%$ and $1\%$ , which is quick for mental maths.

Percentages of £80. The bar for the full £80 would fill the whole width.

One number as a percentage of another

Divide the part by the whole, then multiply by $100$ . If you score $18$ out of $24$ , that is $\frac{18}{24} \times 100 = 75\%$ .

Three conversions to know

Percentage to decimal: divide by $100$ . $8\% = 0.08$ .
Decimal to percentage: multiply by $100$ . $0.125 = 12.5\%$ .
Fraction to percentage: divide top by bottom, then multiply by $100$ . $\frac{3}{5} = 0.6 = 60\%$ .

Worked examples

Example 1: Percentage of an amount

Find $35\%$ of £ $60$ .

$10\%$ of £ $60$ is £ $6$ .
$30\%$ is $3 \times 6 = 18$ .
$5\%$ is half of $10\%$ , which is £ $3$ .
$35\% = 18 + 3 = 21$ .

Answer: £ $21$

Example 2: A score as a percentage

A team wins $18$ of its $24$ games. What percentage is that?

Divide the part by the whole: $18 \div 24 = 0.75$ .
Multiply by $100$ : $75\%$ .

Answer: $75\%$

Example 3: An awkward percentage

Find $12.5\%$ of $80$ .

$12.5\% = \frac{1}{8}$ .
$80 \div 8 = 10$ .

Answer: $10$

Percentages above $100\%$ are fine. $150\%$ of a number is one and a half times it.

Why it matters

Percentages are the language of shops, banks, news headlines and exam results. Sales tax, pay rises, interest rates, battery levels and nutrition labels are all reported as percentages. See Percentage Increase and Decrease for changes and sale prices.

Practice

Your turn. Type or choose an answer, then press Check. Getting one wrong is fine, that is what practice is for. You can try as many times as you like.