What is proportion?
Year 6 solves problems with the relative sizes of two quantities, scale factors and unequal sharing. Below: what it means, a worked example, the mistake to watch for and an 11+ question.
The answer
Proportion compares a part with the whole, like "3 out of every 10", and tells you how amounts grow or shrink together.
What it means
If 3 out of every 10 sweets in a bag are red, the proportion of red sweets is 3/10, or 30%.
Two amounts are in proportion when they grow at the same rate: double the people, double the ingredients.
A worked example
A recipe for 4 people uses 200 g of flour. How much is needed for 6 people?
- Find the amount for 1 person: 200 ÷ 4 = 50 g.
- Multiply by 6: 50 × 6 = 300 g.
The common mistake
Adding instead of multiplying. Going from 4 people to 6 people is not "add 2 to everything". Find the amount for one first, then multiply.
How it comes up in the 11+
5 pencils cost 90p. How much do 8 pencils cost?
Answer: £1.44
- One pencil costs 90 ÷ 5 = 18p.
- 8 pencils cost 18 × 8 = 144p.
- 144p = £1.44.
Related words and practice
More maths words
Questions parents ask
What is the difference between ratio and proportion?
A ratio compares one part with another part. A proportion compares a part with the whole. In a bag of 3 red and 7 blue sweets, the ratio of red to blue is 3 : 7, and the proportion of red is 3/10.
What is the unitary method?
Finding the value of one first, then scaling up. It is the method in the pencils question on this page.
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.