IGCSE Maths Fractions, Decimals & Percentages Notes
Fractions, decimals and percentages are three ways of showing parts of a whole. Being fluent converting between them is essential across IGCSE.
Key concepts
- Conversions
- Fraction → decimal by dividing; decimal → percentage by × 100.
- Percentage of an amount
- Use a multiplier, e.g. 30% of 80 is 0.3 × 80.
- Reverse percentage
- Divide by the multiplier to find the original value before a change.
Key formulas
Percentage change
new = original × (1 ± rate)
Compound interest
A = P(1 + r)ⁿ
r as a decimal, n years.
Worked example
A price rises 20% to £72. Find the original price.
- 1A 20% rise means a multiplier of 1.2.
- 2Original = 72 ÷ 1.2.
- 3Calculate the original price.
Answer: £60
Common mistakes
✗ Adding percentages across years instead of compounding.
✓ Use A = P(1 + r)ⁿ for compound growth.
✗ Finding a percentage of the new value in reverse problems.
✓ Divide by the multiplier, don't take a percentage of the new amount.
✗ Converting fractions to percentages incorrectly.
✓ Turn the fraction into a decimal first, then × 100.
Quick check
Try these, then reveal the answers.
Write 0.35 as a percentage.Reveal answer
35%
Find 15% of 240.Reveal answer
36
£200 at 5% compound for 2 years?Reveal answer
£220.50
Exam tips
- Use multipliers for every percentage calculation — they are faster and less error-prone.
- Spot reverse-percentage wording ('after a … increase, the price is …').
- Distinguish simple from compound interest before choosing a method.
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Frequently asked questions
How do I do a reverse percentage?+
Identify the multiplier for the change and divide the final amount by it to recover the original value.
What is the difference between simple and compound interest?+
Simple interest is a fixed amount each year; compound interest is calculated on the growing total using A = P(1 + r)ⁿ.
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