GCSE Maths · Topic guide
GCSE Maths fractions revision
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.
Common mistakes in exams
- Adding numerators without a common denominator.
- Cancelling across addition (only multiply/divide allows cancelling factors).
- Dividing fractions without inverting the second fraction.
- Leaving answers with surds or π when a simple fraction was required.
Worked examples & mini quiz
GCSE Maths: Fractions
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.
Worked examples
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.
Mini quiz (3 questions)
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1. 2/3 × 3/4 =
- A.1/2
- B.5/7
- C.6/12
- D.2/4
Show answer
Correct: 1/2
(2×3)/(3×4) = 6/12 = 1/2 after cancelling.
2. Which is equivalent to 0.375?
- A.3/8
- B.3/10
- C.375/1000 unsimplified only
- D.1/4
Show answer
Correct: 3/8
0.375 = 375/1000 = 3/8 in lowest terms.
3. Before adding fractions you should:
- A.Use a common denominator where needed
- B.Always multiply numerators only
- C.Convert to percentages only
- D.Add denominators
Show answer
Correct: Use a common denominator where needed
Same denominator (or equivalent fractions) before adding numerators.
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