Sheet № 36 · Foundation + Higher · AQA · Edexcel · OCR
Percentages: Increase & Decrease –
Percentage increase and decrease questions appear on virtually every GCSE Maths paper — at both Foundation and Higher tier. From sale prices and tax calculations to compound interest and depreciation, this topic has real-world applications that examiners love to test. The key to getting these questions right every time is learning the mul
§Key definitions
Percentage increase:
multiply by (1 + percentage as a decimal).
Percentage decrease:
multiply by (1 − percentage as a decimal).
Question:
A laptop costs £480. In a sale, the price is reduced by 15%. Find the sale price.
Step 1:
Multiplier for 15% decrease = 1 − 0.15 = 0.85
Step 2:
Sale price = £480 × 0.85 = £408
§Formulas to memorise
New value = Original × (1 + r/100)
New value = Original × (1 − r/100)
Percentage change = ((new − original) / original) × 100
Final value = Original × (multiplier)ⁿ
Percentage increase:: multiply by (1 + percentage as a decimal).
Percentage decrease:: multiply by (1 − percentage as a decimal).
Examples of multipliers:: | Change | Multiplier |
Convert — the percentage to a decimal (divide by 100).
Calculate — the multiplier: add to 1 for increase, subtract from 1 for decrease.
Multiply — the original value by the multiplier.
Worked example
A laptop costs £480. In a sale, the price is reduced by 15%. Find the sale price.
Step 1: Multiplier for 15% decrease = 1 − 0.15 = 0.85
⚠ Common mistakes
- ✗Adding or subtracting the percentage separately. Using the multiplier method (e.g., × 0.85 for a 15% decrease) is more efficient and avoids the common error of calculating the percentage correctly but then forgetting to subtract it.
- ✗Using the wrong multiplier direction. An increase of 20% is × 1.20, not × 0.80. A decrease of 20% is × 0.80, not × 1.20.
- ✗Applying simple interest instead of compound interest. For compound interest, you must raise the multiplier to a power. Do not multiply the single-year interest by the number of years — that is simple interest.
- ✗Percentage change from the wrong base. Percentage change is always calculated relative to the original value, not the new value. This is a common error in profit/loss questions.
- ✗Rounding intermediate values. When calculating compound interest, keep full calculator accuracy until the final step.
✦ Exam tips
- →Learn your multipliers. Being able to instantly convert percentages to multipliers saves time. Practise until 35% increase = × 1.35 and 12% decrease = × 0.88 come naturally.
- →On AQA papers, compound interest questions often ask you to "show that" or "calculate to the nearest penny". Show the full calculation including the power.
- →For Edexcel "find the percentage change" questions, always state whether it is an increase or decrease as part of your answer — marks are awarded for this.
- →Use the multiplier for VAT calculations. VAT at 20% means the price including VAT is the original × 1.20. This is faster than finding 20% and adding it on.
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