Key Terms
- Percentage decrease: Subtracting a percentage of the original from the original
- Multiplier: The decimal you multiply by to apply the decrease in one step
- Multiplier (decrease): Always less than 1 (e.g. 25% decrease → multiplier = 0.75)
- Depreciation: When an asset (e.g. a car) loses value over time as a percentage
- Key words: discount, reduction, sale, depreciation, fall, decline
Must-Know Facts
- Multiplier for a percentage decrease = 1 - (percentage ÷ 100)
- New amount = original × multiplier
- A 25% decrease means the new amount is 75% of the original
- The multiplier method works in one step — no need to find the decrease separately
- The new amount is ALWAYS smaller than the original for a decrease
Key Formulas
- Multiplier = 1 - (% ÷ 100)
- New amount = original × multiplier
- Decrease amount = original × (% ÷ 100)
- New amount = original - decrease amount
Common Mistakes
- Multiplier > 1: A 20% decrease uses multiplier 0.8, not 1.2 (that's an increase)
- Subtracting % directly: 20% off £60 is NOT £60 − 20 = £40 — find 20% of £60 (= £12) then subtract
- Reverse percentage error: After a 20% decrease to £40, the original is £40 ÷ 0.8 = £50, NOT £40 + 20% of £40
- Successive decreases: Two 10% decreases give 0.9 × 0.9 = 0.81, so a 19% decrease — not 20%
This topic summary covers Knowledge Organiser: Percentage Decrease within Percentage Decrease for GCSE Mathematics. Revise Percentage Decrease in Ratio & Proportion for GCSE Mathematics with 12 exam-style questions and 22 flashcards. Use this page as part of a wider topic revision path rather than treating it as an isolated fact. 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 Decrease
What multiplier is used to decrease a value by 35%?
A shop advertises '25% off everything'. A student says: 'The multiplier is 0.25 because 25% = 0.25.' Explain what is wrong with the student's reasoning and state the correct multiplier.
Quick recall flashcards
What is the multiplier for a 10% decrease?
0.90 (because 1 - 0.10 = 0.90)
What is a percentage decrease?
Finding a new amount after subtracting a percentage from the original amount