11+ Ratio and Proportion
Ratio questions test whether a child can split amounts fairly and scale quantities — a favourite of 11+ word problems.
A ratio compares quantities, like 2:3. To share an amount in a ratio, add the parts together to find the total number of parts, divide the amount by that total to find the value of one part, then multiply for each share.
Proportion problems scale up or down: if 3 pens cost 90p, one pen costs 30p, so 7 pens cost 210p. Find the value of one unit first, then multiply.
Keep your working tidy and labelled — ratio mistakes usually come from losing track of which number is which share, not from the arithmetic itself.
Worked examples
Q. Share £45 in the ratio 2:3.
Total parts = 2 + 3 = 5. One part = 45 ÷ 5 = £9. So the shares are 2 × 9 = £18 and 3 × 9 = £27 (check: 18 + 27 = 45).
Q. If 4 apples cost 96p, how much do 9 apples cost?
One apple = 96 ÷ 4 = 24p. Nine apples = 9 × 24 = 216p = £2.16.
Common mistakes
- Dividing by one of the ratio numbers instead of by the total parts.
- Forgetting to check that the shares add back to the original total.
- Mixing up the order of the ratio.
FAQs
How can I check a ratio answer quickly?+
Add your shares back together — they must equal the original amount. If they do not, re-check the value of one part.
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