At Higher tier, ratio problems involve more complex contexts: algebraic ratios, ratios involving fractions and decimals, combining ratios, and solving problems where the difference between shares is given.
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Revising simplifying & using ratios the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Simplifying & using ratios GCSE” on the site for the complete guide.
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Key facts to remember
1To simplify a ratio, divide all parts by their highest common factor (HCF).
2To simplify ratios with fractions: multiply every part by the LCM of all denominators.
3To combine ratios: make the shared quantity the same in both ratios.
4If a:b = m and b:c = n, express a:b:c by making b the same in both.
5The unitary method: find the value of one part, then multiply for other parts.
6Algebraic ratio: if a:b = 3:5 and a + b = 40, form an equation.
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Worked examples
Example 1
A:B = 3:5 and A:C = 2:7. Find A:B:C.
Working
A:B = 3:5 and A:C = 2:7.
Make A the same in both: LCM of 3 and 2 is 6.
A:B = 6:10 (multiply by 2) and A:C = 6:21 (multiply by 3).
So A:B:C = 6:10:21.
AnswerA:B:C = 6:10:21
Example 2
Jamie and Kira share money in the ratio 4:7. Kira gets £18 more than Jamie. How much does each person receive?
Working
Difference in ratio parts: 7 − 4 = 3 parts.
3 parts = £18, so 1 part = £6.
Jamie: 4 × £6 = £24.
Kira: 7 × £6 = £42.
Check: £42 − £24 = £18 ✓
AnswerJamie receives £24, Kira receives £42.
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Common mistakes
✗Only simplifying some parts of the ratio, not all.
✗When combining ratios, not making the shared quantity equal first.
✗Dividing the total by the wrong number of parts.
✗Forgetting to check the answer satisfies the original conditions.
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Exam tips
✓Always check your final ratio cannot be simplified further.
✓If the question gives a difference between shares, find the value of one part first.
✓For combining three-part ratios, make the shared value equal by finding the LCM.
✓Write out each step clearly — ratio questions are easy to lose marks through arithmetic slips.
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