Ratio, Proportion, and Percent
What you must understand
This domain covers simplifying and sharing in a ratio, direct and inverse proportion, percentage change, reverse percentages, and compound interest or repeated percentage change. You should be comfortable moving between fractions, decimals, and percentages, and using multipliers such as 1.15 for a 15% increase or 0.85 for a 15% decrease.
Traps to watch for
- Reverse percentages: if a price after a 20% discount is £80, the original is £80 ÷ 0.8 = £100, not £96. Never add the percentage back to the reduced amount.
- Percentage change base: always divide the change by the original value.
- Ratio order: sharing £60 in the ratio 2:3 gives £24 and £36; check which share the question asks for.
- Inverse proportion: doubling workers halves time; the product (workers × time) stays constant.
- Successive changes: a 10% rise then a 10% fall gives 0.99 of the original, a 1% net loss, not zero change.
Worked example
A jacket is reduced by 15% to £68. What was the original price? The sale price is 85% of the original, so original = 68 ÷ 0.85 = £80. Check: 15% of £80 = £12, and £80 − £12 = £68. ✓
Rule of thumb: for repeated percentage change, multiply by the multiplier raised to the power of the number of periods, e.g. 1.05³ for three years at 5%.