GCSE Maths: Ratio and Proportion

Ratio and proportion form their own strand of GCSE Mathematics — weighted at up to a quarter of the Foundation tier assessment — because proportional reasoning underlies so much of everyday numeracy: recipes, prices, mixtures, maps and rates. This quiz covers the strand's core question types in the forms they actually take on exam papers.

The ratio questions run through the standard repertoire: simplifying a ratio to lowest terms with the highest common factor, sharing £120 in the ratio 3:5 by finding the value of one part, recognising equivalent ratios, and converting a ratio into fractions of the total — where the denominator must be the sum of the parts, not the other part. Two harder variants follow: finding a missing quantity when one side of the ratio is known, and the difference-style problem where two numbers in ratio 2:5 differ by 18, which requires reasoning from the difference in parts rather than the total.

Direct and inverse proportion make up the second half. You will construct and use y = kx from a given value pair, identify the defining properties of inverse proportion — constant product xy and the form y = k/x — and solve a full inverse proportion problem by finding k first. A best-buy question about two pack sizes of pasta rounds out the set, testing unit pricing, the comparison skill that exam boards love because it merges proportion with money.

Every question uses concrete numbers and is fully self-contained, and each explanation names the method — value of one part, constant of proportionality, price per gram — so the technique transfers to any numbers an exam throws at you.

• Simplify ratios and share amounts in a given ratio via the value of one part
• Solve ratio problems where one part or the difference between parts is known
• Convert ratios to fractions of the total correctly
• Construct and use equations of direct proportion (y = kx) and inverse proportion (y = k/x)
• Compare value for money using unit pricing

Topic scope follows the Ratio, proportion and rates of change strand of the Department for Education's GCSE mathematics subject content: ratio notation and sharing, relating ratios to fractions, and solving direct and inverse proportion problems including constructing equations of proportionality.