11+ Maths · Topic explained
Ratio
How do you share 20 sweets in the ratio 3 : 2?
The big idea
A ratio compares amounts: 3 : 2 means 3 of one for every 2 of the other.
Picture it
Like dealing out sweets: 3 to Ali, 2 to Ben, again and again until they run out.
Key words
- ratio
- How much of one thing there is compared with another, written 3 : 2.
- part
- One share of the ratio: 3 : 2 has 5 parts in all.
- simplify
- Divide both sides by the same number: 6 : 4 = 3 : 2.
Worked examples
- 1Warm-up
Simplify 6 : 4
- Both divide by 2
- 6 : 4 = 3 : 2
- 211+ standard
Share £35 in the ratio 2 : 5
- Parts: 2 + 5 = 7
- 1 part = £35 ÷ 7 = £5
- £10 and £25
- 311+ standard
The ratio of boys to girls is 3 : 4. There are 12 boys. How many girls?
- 3 parts = 12 boys, so 1 part = 4
- Girls: 4 parts = 4 × 4 = 16
- 411+ standard
Red to blue beads are in the ratio 2 : 3. What fraction are red?
- Parts in all: 2 + 3 = 5
- Red is 2 of the 5 parts: 2/5
The common mistake
The mistake
Red : blue = 2 : 3, so 2/3 of the beads are red.
Instead
2 : 3 has 5 parts in all, so 2/5 are red.
Why: A ratio compares part with part; a fraction compares a part with the whole.
Where it comes up in the 11+
Sharing in a ratio, recipes and mixtures, and 'there are 12 boys, how many girls?' questions.
The video
Video coming soon
We're making a short video that explains ratio step by step. Until then, everything it covers is on this page.
Free printable
Ratio worksheet
Practice questions on this topic to print and try on paper, at home or on the way to school.
Download the worksheet (PDF)Free account needed: it takes a minute.
Quick quiz
Have a go first, then tap to see the answer.
1. Simplify 15 : 10.
- 5 : 2
- 3 : 2
- 2 : 3
- 1 : 5
Show the answerHide the answer
3 : 2
Divide both by 5.
2. Share 40 in the ratio 1 : 3. What is the larger share?
- 10
- 13
- 30
- 36
Show the answerHide the answer
30
4 parts, so 1 part = 10, and the larger share is 3 × 10 = 30.
3. Cats to dogs is 5 : 2. There are 9 more cats than dogs. How many dogs?
- 3
- 6
- 15
- 18
Show the answerHide the answer
6
The difference is 3 parts = 9, so 1 part = 3 and dogs = 2 × 3 = 6.