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.
Related practice
Practise this topic
Exam-style questions with instant Study Coach feedback.
Flashcards
Quick-fire recall to lock in the key facts.
Worksheets
Printable practice you can work through offline.
Past papers
Full papers with examiner-grade marking.
Study Coach
Ask for a step-by-step explanation any time.
All Mathematics
Every Mathematics topic across every exam board.
Related topics
Key terms explained
Short, exam-ready definitions with a formula, a worked example and an examiner tip.
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.
Create a free account to practise percentage change with Study Coach feedback
Try 5 questions now, get instant examiner-grade marking and ask the Study Coach to explain anything. Free during our early launch period — no credit card required.
Related on MathsGradeUp
Keep studying
- Mathematics courses & specifications
Every board and level we cover for mathematics.
- Formula sheets
Every GCSE, IGCSE and A Level formula, searchable and explained.
- Maths & science glossary
Plain-English definitions with a formula, worked example and examiner tip.
- Free maths calculators & solvers
Step-by-step solvers for the calculations that come up in every paper.
- Past paper guides
Paper structure, timings and topic weightings board by board.
- Grade boundaries
Historic boundaries and what each grade typically needs.
- Browse subjects
Specification-mapped courses for every board and level.
Practise it
- Predicted papers
GCSE and A Level predicted papers with full mark schemes.
- Question bank
Filter thousands of exam-board questions by topic and difficulty.
- Past papers workspace
Write on real papers and get every line marked.