What is a percentage?
Year 5 introduces the per cent sign. Year 6 finds percentages of amounts, such as 15% of 360, and uses them to compare. Below: what it means, a worked example, the mistake to watch for and an 11+ question.
The answer
A percentage is a number out of 100, so 35% means 35 out of every 100.
What it means
Per cent means "for every hundred". 50% is ½, 25% is ¼ and 10% is 1/10.
To find a percentage of an amount, build it from easy pieces: 10% is the amount divided by 10, 5% is half of that, and 1% is the amount divided by 100.
A worked example
Find 35% of 60
- 10% of 60 is 60 ÷ 10 = 6, so 30% is 6 × 3 = 18.
- 5% is half of 10%: 6 ÷ 2 = 3.
- 35% = 30% + 5% = 18 + 3 = 21.
The common mistake
Thinking 10% is always 10. It is one tenth of the amount: 10% of 350 is 35, and 10% of 8 is 0.8.
How it comes up in the 11+
A coat costs £48. In a sale the price is reduced by 25%. What is the sale price?
Answer: £36
- 25% is a quarter: £48 ÷ 4 = £12.
- The price falls by £12: £48 − £12 = £36.
Try it yourself
The bar opens on 35% of 60, the worked example, built from 10% and 5% blocks. Change either number to try your own.
A bar model builds a percentage from 10%, 5% and 1% blocks, or shares an amount in a ratio by finding one part first.
Related words and practice
More maths words
Questions parents ask
How do you turn a fraction into a percentage?
Make the denominator 100 if you can: ⅗ = 60/100 = 60%. Or divide the top by the bottom and multiply by 100.
Can a percentage be more than 100%?
Yes. 100% is the whole amount, so 150% is one and a half times it. 150% of 20 is 30.
Knowing the words is half of an 11+ maths question
11+ papers use maths vocabulary without explaining it. The free diagnostic checks maths, English and both kinds of reasoning, and shows what to practise next. No card is required.