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, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP.
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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.
Mini lesson for Ratio & Proportion
1. Understand the core idea
A ratio compares two or more quantities. Simplify ratios like fractions by dividing by the HCF.
Can you explain Ratio & Proportion without copying the notes?
2. Turn it into marks
Share £120 in the ratio 3:5. Total parts = 3+5 = 8.
Underline the method, evidence, or command-word move that would earn credit in GCSE Ratio, Proportion & Rates of Change.
3. Fix the likely mark leak
Watch for this mistake: Not simplifying the ratio fully — always divide by the HCF of all parts.
Write one correction rule before doing another practice question.
Practise this topic
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Ratio & Proportion practice questions
These are original StudyVector questions for revision practice. They are not official exam-board questions.
Question 1
In one GCSE sentence, explain what Ratio & Proportion is testing.
Answer: A ratio compares two or more quantities. Simplify ratios like fractions by dividing by the HCF.
Mark focus: Precise definition and topic focus.
Question 2
A student sees a Ratio & Proportion question but is not sure how to start. What should the first method line establish?
Answer: It should identify the rule, equation, diagram feature, or transformation before any calculation. That protects method marks and makes later checking easier.
Mark focus: Method selection and command-word control.
Question 3
A student makes this mistake: "Not simplifying the ratio fully — always divide by the HCF of all parts." What should their next repair task be?
Answer: Do one Ratio & Proportion question and review the mistake type.
Mark focus: Error correction and next-step practice.
Ratio & Proportion flashcards
Core idea
What is the main idea in Ratio & Proportion?
A ratio compares two or more quantities. Simplify ratios like fractions by dividing by the HCF.
Common mistake
What mistake should you avoid in Ratio & Proportion?
Not simplifying the ratio fully — always divide by the HCF of all parts.
Practice
What is one useful practice task for Ratio & Proportion?
Answer one Ratio & Proportion question and review the mistake type.
Exam board
How should you use board notes for Ratio & Proportion?
Use your own GCSE specification for exact paper wording and depth.
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, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP 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.