Maths · Fractions, Decimals & Percentages
Percentage increase / decrease
Apply percentage change to amounts.
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What is percentage change?
A percentage change shows how much a quantity has increased or decreased compared to its starting value. We often see percentage change in sales, prices, and statistics. A 20% increase means adding 20% of the original amount.
Finding the multiplier
To apply a percentage increase, we can use a multiplier instead of two steps. For a 15% increase, the multiplier is 1.15 (the whole amount plus 15% extra). For a 15% decrease, the multiplier is 0.85 (the whole amount minus 15%).
Percentage increase step-by-step
To increase £40 by 25%: first find 25% of £40, which is £10. Then add £10 to the original £40 to get £50. Alternatively, multiply £40 by 1.25 to get £50 directly.
Percentage decrease step-by-step
To decrease 80 kg by 30%: first find 30% of 80 kg, which is 24 kg. Then subtract 24 kg from the original 80 kg to get 56 kg. Alternatively, multiply 80 by 0.70 to get 56 kg directly.
Common mistakes to avoid
Don't confuse increase with decrease multipliers. A 40% increase uses 1.40, not 0.60. Also, remember to work from the original amount, not an already-changed value. Always check if your answer is larger (increase) or smaller (decrease) than the start.
Worked examples
1. Increase £60 by 35%.
- Find the multiplier: 100% + 35% = 135% = 1.35
- Multiply the original amount: £60 × 1.35
- £60 × 1.35 = £81
2. Decrease 120 m by 45%.
- Find the multiplier: 100% − 45% = 55% = 0.55
- Multiply the original amount: 120 × 0.55
- 120 × 0.55 = 66 m
3. A book costs £8. The price increases by 12.5%. Find the new price.
- The multiplier for a 12.5% increase is 1.125
- New price = £8 × 1.125
- £8 × 1.125 = £9
Try it yourself
A plant is 50 cm tall. It grows by 20%. How tall is it now?
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