Ratio & Proportion - AQA GCSE Mathematics Revision

Topic overview

What you need to know

Ratio & Proportion is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. A way of comparing two or more quantities. Written as a:b. E.g. mixing paint in the ratio 3:2 means 3 parts of one colour to 2 parts of another. Divide all parts of the ratio by their HCF. E.g. 12:8 = 3:2. Add the ratio parts to find total shares, divide the amount by total shares, then multiply by each part.

Exam tip

Write every stage of your method. Method marks can still be earned when the final answer is wrong.

Revision notes

Core ideas

Secure these ideas first. Say each definition in your own words, then connect it to the topic overview.

Ratio: A way of comparing two or more quantities. Written as a:b. E.g. mixing paint in the ratio 3:2 means 3 parts of one colour to 2 parts of another.
Simplifying Ratios: Divide all parts of the ratio by their HCF. E.g. 12:8 = 3:2.
Sharing in a Given Ratio: Add the ratio parts to find total shares, divide the amount by total shares, then multiply by each part.
Direct Proportion: Two quantities are directly proportional if when one increases, the other increases at the same rate. y = kx.

Revision notes

Apply it in the exam

The exam will rarely ask for an isolated definition. Practise selecting the right idea and using it as part of a complete explanation or method.

Inverse Proportion: Two quantities are inversely proportional if when one increases, the other decreases. y = k/x.
Unitary Method: Find the value of one unit first, then scale up or down. E.g. if 5 items cost £20, one costs £4.
Scale Factor: The multiplier used to enlarge or reduce a shape or convert between measurements. E.g. scale factor 3 means 3 times bigger.
Proportionality Constant (k): In y = kx (direct) or y = k/x (inverse), k is the constant of proportionality found using given values.

Core knowledge

Key facts for Ratio & Proportion

8 essentials

Ratio

A way of comparing two or more quantities. Written as a:b. E.g. mixing paint in the ratio 3:2 means 3 parts of one colour to 2 parts of another.

Simplifying Ratios

Divide all parts of the ratio by their HCF. E.g. 12:8 = 3:2.

Sharing in a Given Ratio

Add the ratio parts to find total shares, divide the amount by total shares, then multiply by each part.

Direct Proportion

Two quantities are directly proportional if when one increases, the other increases at the same rate. y = kx.

Inverse Proportion

Two quantities are inversely proportional if when one increases, the other decreases. y = k/x.

Unitary Method

Find the value of one unit first, then scale up or down. E.g. if 5 items cost £20, one costs £4.

Scale Factor

The multiplier used to enlarge or reduce a shape or convert between measurements. E.g. scale factor 3 means 3 times bigger.

Proportionality Constant (k)

In y = kx (direct) or y = k/x (inverse), k is the constant of proportionality found using given values.

Active recall

Close the notes and answer these

1.Without looking, explain ratio and give one example or consequence.
2.Without looking, explain simplifying ratios and give one example or consequence.
3.Without looking, explain sharing in a given ratio and give one example or consequence.
4.Without looking, explain direct proportion and give one example or consequence.

Content reviewed 23 July 2026 against the current linked specification.

Finished learning?

Mark the notes complete, then test what you can recall.

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