A ratio compares quantities using the same-sized parts. In a ratio of 2:3, the total is five parts, not three. To share a total, divide it by the number of parts to find one part, then multiply for each share. Equivalent ratios come from multiplying or dividing every part by the same non-zero number. Recipes use direct proportion: doubling the number of portions doubles every ingredient. If a question gives one ingredient rather than the total, match that ingredient to its own number of parts before finding the others.
Learning objectives
- Simplify ratios and divide an amount in a ratio.
- Scale every ingredient in a recipe consistently.
Key ideas
Convert quantities to matching units before simplifying a ratio.
Divide every ratio part by the same common factor.
The first share is this fraction of the total.
Find one part by dividing the total by the sum of all ratio parts.
Multiply every recipe ingredient by the same scale factor.
Worked examples
Example 1
Share the money in the given ratio.
Answer
Example 2
Scale flour from four portions to ten portions.
Answer
Question styles to prepare for
Original practice guidance aligned to the specification, not a count of past-paper appearances or a prediction. The AO labels below describe the intended practice focus, not official AQA mark allocations.
AO1 · Methods
Simplify a ratio, share an amount or scale a recipe.
AO2 · Reasoning
Explain why a part-to-part ratio is not the same as a fraction of the whole.
AO3 · Problem solving
Link a given difference or one person's share to the total amount.
When a task asks you to explain, include a mathematical reason. When solving a problem, show how the information becomes a calculation, equation or diagram, then interpret your result.
Avoid this mistake
When sharing a total, divide by the sum of all ratio parts. The individual parts are not separate denominators.
Try it yourself
Attempt each question before opening its answer.
Check 1: Simplify the ratio 150 cm:2 m.
Answer: 3:4
Convert 2 m to 200 cm. Then simplify 150:200 by dividing both parts by 50.
Check 2: A recipe for 4 people uses 300 g flour. How much flour is needed for 10 people?
Answer: 750 g
The scale factor is 10 ÷ 4 = 2.5. Multiply 300 g by 2.5.
Explain it in your own words
- Draw a bar model for sharing £60 in the ratio 1:4.
- Explain why the first share of a 2:3 ratio is 2/5 of the total.
- Scale all ingredients in your own recipe by the same factor.
Keep practising
Download the compact topic guide (PDF) · Practise this topic in Blitz · All foundation notes
Specification source
AQA Ratio specification · Assessment objectives. Checked 16 October 2026. Topic references identify related content; these notes do not cover every specification statement.