GCSE Maths: Ratio Revision

Ratio — simplifying, sharing in a given ratio, and working from a difference Percentages — of an amount, increase, decrease and percentage change Direct and inverse proportion — including proportion to a square or a root Exchange rates and best value — comparing price per unit Speed, distance and time — including average speed over more than one stage Density and pressure — mass, volume and force Compound measures — rates combined over time Growth and decay — repeated percentage change, and years to reach a target Reverse percentage — working back to the original amount Ratio and algebra — ratios that change when quantities are added or removed Proportion graphs — reading a rate from a straight line through the origin Unit conversion — including compound units such as km/h to m/s Similar shapes — length, area and volume scale factors

Sharing in a ratio. Add the parts, divide the total by that number to find one part, then multiply. If you are given the difference rather than the total, the difference is worth the difference between the parts. Percentage multipliers. An increase of 12% is × 1.12; a decrease of 12% is × 0.88. Two changes multiply — a 10% rise followed by a 10% fall does not return you to the start. Reverse percentages. Divide by the multiplier. After a 25% reduction, divide by 0.75. Speed, distance, time. Speed = distance ÷ time. Average speed over a journey is the total distance divided by the total time — not the mean of the speeds. Density and pressure. Density = mass ÷ volume. Pressure = force ÷ area. Direct and inverse proportion. y ∝ x gives y = kx. y ∝ 1/x gives y = k/x. Find k from the pair you are given, then use it. Similar shapes. If lengths are in the ratio 1 : k, then areas are in the ratio 1 : k² and volumes 1 : k³. Compound units. To convert km/h to m/s, multiply by 1000 and divide by 3600.

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Ratio and proportion shares its arithmetic with number and its scale factors with geometry, so improvement here tends to show up across the paper. Every topic and your progress across all of them is on the revision hub. All of our revision engines are free to use.