GCSE Maths · Topic guide
Fractions sit in number questions, ratio, probability and algebra (algebraic fractions on Higher). Non-calculator papers expect fluency with cancelling, common denominators and ‘flip and multiply’ for division. Calculator papers still test interpretation — e.g. giving answers as fractions in simplest form when asked. Examiners penalise unsimplified answers and inconsistent mixing of fractions and decimals in the same working.
Worked examples & mini quiz
Find a common denominator to add or subtract. Multiply numerators and denominators for ×. For ÷, multiply by the reciprocal of the second fraction. Always cancel common factors in the final answer.
Example 1
Add 2/3 + 1/4
LCD = 12. 2/3 = 8/12, 1/4 = 3/12. 8/12 + 3/12 = 11/12.
Example 2
Divide 3/5 ÷ 2/7
Multiply by reciprocal: 3/5 × 7/2 = 21/10 = 2 1/10.
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1. 2/3 × 3/4 =
Correct: 1/2(2×3)/(3×4) = 6/12 = 1/2 after cancelling.
2. Which is equivalent to 0.375?
Correct: 3/80.375 = 375/1000 = 3/8 in lowest terms.
3. Before adding fractions you should:
Correct: Use a common denominator where neededSame denominator (or equivalent fractions) before adding numerators.
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