Key Terms
- Percentage increase: Adding a percentage of the original to the original
- Multiplier: The decimal you multiply by to apply a percentage change in one step
- Multiplier (increase): Always greater than 1 (e.g. 15% increase → multiplier = 1.15)
- Key words: rise, growth, inflation, mark-up, appreciation
Must-Know Facts
- Multiplier for a percentage increase = 1 + (percentage ÷ 100)
- New amount = original × multiplier
- A 15% increase means the new amount is 115% of the original
- The multiplier method works in one step — no need to find the increase separately
- The new amount is ALWAYS larger than the original for an increase
Key Formulas
- Multiplier = 1 + (% ÷ 100)
- New amount = original × multiplier
- Increase amount = original × (% ÷ 100)
- New amount = original + increase amount
Common Mistakes
- Adding % directly: 20% increase on £50 is NOT £50 + 20 = £70 — find 20% of £50 first (= £10), then add
- Multiplier < 1: A 20% increase uses multiplier 1.2, not 0.8 (that's a decrease)
- Percentage of wrong value: Always take the % of the ORIGINAL amount
- Multiple increases: 10% increase followed by 10% decrease does NOT return to original — each % is of the new amount
This topic summary covers Knowledge Organiser: Percentage Increase within Percentage Increase for GCSE Mathematics. Revise Percentage Increase in Ratio & Proportion for GCSE Mathematics with 12 exam-style questions and 22 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 6 of 6 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Percentage Increase
What multiplier is used to increase a value by 15%?
Ahmed says: 'To increase a price by 30%, I first find 30% of the price and then add it on. This always takes two steps.' Explain how Ahmed could use the multiplier method to find the answer in ONE step.
Quick recall flashcards
What is the multiplier for a 10% increase?
1.10 (because 1 + 0.10 = 1.10)
What is a percentage increase?
Finding a new amount after adding a percentage to the original amount