Ratio & Proportion — GCSE Mathematics Revision
Revise Ratio & Proportion for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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Go to Scale Drawings & MapsWhat is Ratio & Proportion?
A ratio compares two or more quantities. Simplify ratios like fractions by dividing by the HCF. To share an amount in a given ratio, add the parts, divide the total by the sum of parts to find one part, then multiply. Proportion means two quantities change at the same rate. Direct proportion: as one increases, so does the other. Inverse proportion: as one increases, the other decreases.
Step-by-step explanationWorked example
Share £120 in the ratio 3:5. Total parts = 3+5 = 8. One part = £120 ÷ 8 = £15. Shares: 3 × £15 = £45 and 5 × £15 = £75.
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Common mistakes
- 1Not simplifying the ratio fully — always divide by the HCF of all parts.
- 2Adding the parts of the ratio incorrectly when sharing an amount.
- 3Confusing ratio with fraction — a ratio 2:3 means 2/5 and 3/5 of the total, not 2/3.
- 4Not converting units before comparing (e.g. comparing 2 m with 150 cm without converting).
Ratio & Proportion exam questions
Exam-style questions for Ratio & Proportion with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel and OCR specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Ratio & Proportion
Core concept
A ratio compares two or more quantities. Simplify ratios like fractions by dividing by the HCF. To share an amount in a given ratio, add the parts, divide the total by the sum of parts to find one par…
Frequently asked questions
How do I simplify a ratio with decimals?
Multiply all parts by 10 (or 100) to remove decimals, then simplify by dividing by the HCF. For example, 0.5:1.5 → 5:15 → 1:3.
What is the difference between ratio and proportion?
A ratio compares parts to parts (e.g. 2:3). A proportion compares a part to the whole (e.g. 2/5). Proportion can also describe how two variables change together.