Percentage Change & Reverse Percentages — GCSE Mathematics Revision
Revise Percentage Change & Reverse Percentages for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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Go to Ratio of AmountsWhat is Percentage Change & Reverse Percentages?
Percentage change = (change ÷ original) × 100. A percentage increase of 20% means multiplying by 1.20. A percentage decrease of 15% means multiplying by 0.85. Reverse percentages work backwards: if a price after a 20% increase is £60, the original was £60 ÷ 1.20 = £50. The key insight is that the amount after the change represents a specific percentage of the original.
Step-by-step explanationWorked example
A jacket costs £84 after a 30% reduction. Find the original price. £84 represents 70% (100% - 30%). Original = £84 ÷ 0.70 = £120.
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Common mistakes
- 1Dividing by the new amount instead of the original when calculating percentage change.
- 2In reverse percentages, taking the percentage of the new amount instead of dividing by the multiplier.
- 3Confusing percentage increase with percentage of — a 20% increase on £50 is £60, not £10.
- 4Not using the multiplier method for repeated percentage changes (compound changes).
Percentage Change & Reverse Percentages exam questions
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Percentage Change & Reverse Percentages
Core concept
Percentage change = (change ÷ original) × 100. A percentage increase of 20% means multiplying by 1.20. A percentage decrease of 15% means multiplying by 0.85. Reverse percentages work backwards: if a …
Frequently asked questions
How do I find the percentage change between two values?
Percentage change = ((new - original) / original) × 100. A positive result means an increase, negative means a decrease.
What is a reverse percentage?
When you know the final amount after a percentage change and need to find the original. Divide the final amount by the multiplier (e.g. divide by 1.2 for a 20% increase, or by 0.85 for a 15% decrease).