GCSE Mathematics · Edexcel 1MA1 · Topic N.2

Fractions, decimals and percentages

Key points

To add or subtract fractions, use a common denominator. To multiply, multiply tops and bottoms. To divide, multiply by the reciprocal.
Convert mixed numbers to improper fractions before multiplying or dividing, e.g. $2\frac{1}{3} = \frac{7}{3}$ .
Percentage of an amount: use a multiplier, e.g. 15% of £80 = $0.15 \times 80 = 12$ , so £12.
Percentage increase/decrease: multiply by $1 + \frac{r}{100}$ or $1 - \frac{r}{100}$ . Percentage change = $\frac{\text{change}}{\text{original}} \times 100$ .
Reverse percentages: divide by the multiplier to find the original value, e.g. after a 20% rise, original = new ÷ 1.2.
Compound interest/depreciation: $\text{amount} = P \times (\text{multiplier})^n$ .
Recurring decimals to fractions (higher): e.g. if $x = 0.\dot{4}$ , then $10x - x = 4$ , so $x = \frac{4}{9}$ .

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Fractions, decimals and percentages are three ways of writing the same proportion, and exam questions expect you to move between them fluently. The most useful single idea is the multiplier: one number that applies a percentage change in…

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