#### Tier: #Foundation #Higher
Fractions, decimals, and percentages are three different ways of expressing the same value. Being able to move between them fluently is an essential skill.
Fraction → Decimal: divide the numerator by the denominator. $$\frac{3}{8} = 3 \div 8 = 0.375$$
Decimal → Percentage: multiply by 100. $$0.375 \times 100 = 37.5%$$
Percentage → Fraction: write over 100 and simplify. $$45% = \frac{45}{100} = \frac{9}{20}$$
Common values worth memorising:
| Fraction | Decimal | Percentage |
|---|---|---|
| $\frac{1}{2}$ | 0.5 | 50% |
| $\frac{1}{4}$ | 0.25 | 25% |
| $\frac{1}{5}$ | 0.2 | 20% |
| $\frac{1}{3}$ | $0.\dot{3}$ | $33.\dot{3}%$ |
| $\frac{1}{8}$ | 0.125 | 12.5% |
Common error: converting 5% as 0.5 rather than 0.05 — divide by 100, not 10.
Equivalent fractions Basic percentages Simplifying fractions
New to Bow Tie Maths? It generates questions on this topic, marks them instantly, and tracks what you've mastered. Free to sign up.
2025 Jun 3H GCSE Q6 (1 mark) 2022 Jun 1H GCSE Q3 (2 marks) 2022 Jun 3H GCSE Q6 (1 mark) 2017 Jun 1H GCSE Q3 (1 mark) 2017 Jun 2H GCSE Q2 (2 marks) 2017 Nov 3H GCSE Q5 (1 mark)