What is a ratio?
Ratio and proportion is its own strand in Year 6. Below: what it means, a worked example, the mistake to watch for and an 11+ question.
The answer
A ratio compares one amount with another: 2 : 3 means 2 of one thing for every 3 of another.
What it means
Order matters: boys to girls 2 : 3 is not the same as girls to boys 2 : 3.
Ratios simplify like fractions, by dividing both sides by the same number: 12 : 18 = 2 : 3.
To share an amount in a ratio, add the parts to find how many there are, then find what one part is worth.
A worked example
A class has 12 boys and 18 girls. What is the ratio of boys to girls?
- Boys : girls = 12 : 18.
- Both numbers divide by 6: 12 ÷ 6 = 2 and 18 ÷ 6 = 3.
- The ratio is 2 : 3.
The common mistake
Reading a ratio as a fraction of the whole. If boys to girls is 2 : 3, boys are 2 of every 5 children, so ⅖ of the class, not ⅔.
How it comes up in the 11+
Share £40 between Amy and Ben in the ratio 3 : 5.
Answer: Amy gets £15 and Ben gets £25
- 3 + 5 = 8 parts altogether.
- One part is £40 ÷ 8 = £5.
- Amy gets 3 × £5 = £15 and Ben gets 5 × £5 = £25. Check: £15 + £25 = £40.
Try it yourself
It opens on 40 shared in the ratio 3 : 5, the 11+ question above: find one part first, then build each share from it.
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
What is the difference between a ratio and a fraction?
A ratio compares part with part (2 boys : 3 girls). A fraction compares part with the whole (2 out of 5 children are boys, ⅖).
What does the colon in a ratio mean?
It is read "to". 2 : 3 is read "two to three".
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.