Part to part, or part to whole? ratio and proportion
The Short Answer
A ratio compares one part with another part: 4 to 3 means four of these for every three of those. A proportion compares a part with the whole, and the whole is found by adding the parts — so 4 to 3 is four in every seven. Confusing the two is the single commonest error on this topic and it produces answers that look reasonable.
The one distinction that decides this topic
A ratio compares part to part. A proportion compares part to the whole.
That is the whole of it, and a child who has it does well on this topic while a child who has not produces answers that look entirely reasonable and are wrong.
Add the parts to find the whole
Four to three means four of these for every three of those.
Now — how many things is that altogether? Seven. Four plus three.
So as a proportion, it is four in every seven. Not four in every three, and not four in every four.
Children answer "four in every three" because those are the two numbers written in front of them, and nothing on the page mentions a seven. So the habit worth building is mechanical: whenever a ratio appears, write the total underneath it straight away.
4 : 3 total 7
Do it before reading the rest of the question, and the number is there when it is wanted.
Can you show me a worked example?
Scaling is the same topic
A recipe for 4 people uses 200g of rice. How much for 6?
There is no colon anywhere, so children who have learnt ratio as questions with two numbers and a colon do not recognise it. It is proportion: 6 people is one and a half times 4 people, so the rice is one and a half times 200g — 300g.
Ask what is being compared with what, and the shape appears.
Where do pupils lose marks?
Not adding the parts, and giving four in every three.
Multiplying before finding what one part is worth.
Missing a proportion question because it does not look like a ratio question.
Not checking that the shares add back to the total.
Try it yourself
Ask first whether the question is about part to part or part to whole. Then add the parts.
- Paint is mixed in the ratio 4 parts blue to 3 parts white. What proportion of the mixture is blue?
- 56 sweets are shared in the ratio 4:3. How many does each person get?
- In a ratio of 4:3, how many parts are there altogether?
- Check your answer to the sharing question. How?
- A recipe for 4 people uses 200g of rice. How much for 6 people?
- Four sevenths. Add the parts: 4 + 3 = 7, so the whole is seven parts and blue is four of them. Not four in every three, and not four in every four.
- 32 and 24. Divide 56 by the total number of parts, 7, which gives 8 per part. Then 4 × 8 = 32 and 3 × 8 = 24.
- Seven. This is the step that decides the whole topic, and it is one addition.
- Add the two answers together and see whether they make the original amount: 32 + 24 = 56. That check takes two seconds and catches almost every error on this type.
- 300g. This is proportion rather than ratio — 6 people is one and a half times 4 people, so the rice is one and a half times 200g. Scaling like this is the same move as using a given fact in multiplication.
How much practice does this type need at home?
Cooking, genuinely. Halve a recipe, or make it for six instead of four, and ask your child to work out each ingredient. Every quantity is a proportion question and the answer gets eaten, which is better feedback than a tick.
Beyond that, one drill: say a ratio and ask for the total. Five to two. Seven. Three to four. Seven. Two to two to five. Nine. Ten seconds, and it builds the one habit this whole topic rests on.
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Frequently Asked Questions
What is the difference between ratio and proportion, in one sentence?
A ratio compares part with part; a proportion compares part with the whole. In a mixture of 4 parts blue to 3 parts white, the ratio is 4 to 3 and the proportion of blue is four sevenths. The number 7 never appears in the ratio and is essential to the proportion, which is exactly why children who do not add the parts get this wrong.
Why do children answer 'four in every three'?
Because those are the two numbers in front of them, and nothing on the page mentions seven. The habit that fixes it is mechanical: whenever a ratio appears, write the total underneath it immediately. 4 : 3, total 7. Doing it before reading the rest of the question means the number is there when it is needed.
How do you share an amount in a ratio?
Divide by the total number of parts to find what one part is worth, then multiply. 56 shared as 4:3 — the total is 7 parts, so one part is 8, so the shares are 32 and 24. Then check by adding the shares back together: they must make the original amount. That check is quick and it catches nearly every slip.
Is a scaling recipe question the same topic?
Yes, and it is worth saying so. A recipe for 4 people adapted for 6 is proportion — everything scales by the same factor. It looks different because there is no colon in it, and children who have learnt ratio as 'questions with two numbers and a colon' do not recognise it. Ask what is being compared with what, and the shape becomes obvious.
Sources
- GL Assessment — 11+ familiarisation materials and question type descriptions Published 2025.
- Clever Clogs Academy — our own Year 4 and Year 5 lesson records, Winslow Published September 2025 to July 2026.
We are not affiliated with, endorsed by or connected to GL Assessment or Buckinghamshire Council. Test arrangements change; always check the council's own pages for the current year's dates.
We Teach This Method Every Week in Winslow
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