IGCSE Maths Percentage Change Notes
Percentage change measures how much a value has increased or decreased relative to the original amount.
Key concepts
- Multiplier method
- Increase by r% → × (1 + r/100); decrease → × (1 − r/100).
- Percentage change formula
- Change ÷ original × 100 gives the percentage change.
- Reverse percentage
- Divide by the multiplier to find the original amount.
Key formulas
Percentage change
(change ÷ original) × 100
Multiplier
new = original × (1 ± rate)
Worked example
A £250 item is reduced by 12%. Find the sale price.
- 1A 12% decrease means a multiplier of 0.88.
- 2Sale price = 250 × 0.88.
- 3Calculate the result.
Answer: £220
Common mistakes
✗ Dividing change by the new value.
✓ Percentage change divides by the original value.
✗ Using 12 instead of 0.12 as the rate.
✓ Convert the percentage to a decimal for the multiplier.
✗ Treating a reverse percentage as a normal one.
✓ Divide by the multiplier to recover the original amount.
Quick check
Try these, then reveal the answers.
Increase £40 by 10%.Reveal answer
£44
Percentage change from 50 to 60?Reveal answer
20% increase
After a 25% rise a price is £75. Original?Reveal answer
£60
Exam tips
- Always compare the change to the original amount.
- Use one multiplier for repeated changes rather than several steps.
- Read carefully whether profit/loss is a percentage of cost or selling price.
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Frequently asked questions
How do I find percentage profit?+
Divide the profit by the original cost price and multiply by 100.
What is a reverse percentage problem?+
One where you are given the amount after a change and must find the original, done by dividing by the multiplier.
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