Multiplying Fractions
Multiplying fractions involves multiplying numerators together and denominators together, then simplifying the result. The process appears throughout Year 5 and Year 6 of the UK National Curriculum, where pupils learn to multiply proper fractions and mixed numbers. This fundamental operation forms the foundation for more complex fraction arithmetic in secondary mathematics.
Why it matters
Multiplying fractions appears extensively in real-world calculations involving proportions and scaling. When a recipe serves 8 people but only 3 are coming to dinner, finding 38 of each ingredient requires fraction multiplication. Construction workers multiply measurements like 23 metre by 34 to calculate areas of 12 square metre. Financial calculations often involve multiplying fractions — finding 34 of a £120 discount means calculating 34 × 1201 = £90. In GCSE mathematics, fraction multiplication underpins probability calculations, where multiplying 12 × 13 gives the probability 16 of two independent events occurring together. The skill connects directly to algebra, where multiplying algebraic fractions follows identical principles but with variables replacing numbers.
How to solve multiplying fractions
Multiplying fractions — how to
- Multiply the numerators together.
- Multiply the denominators together.
- Simplify the result to lowest terms.
Example: 23 × 34 = 612 = 12.
Worked examples
A garden plot is 13 m wide and 14 m long. What is the area?
Answer: 112
- Multiply straight across → 112 — Area = width x length. Numerator x numerator over denominator x denominator.
- Simplify → 112 — Divide numerator and denominator by their GCD.
- Verify → 112 ✓ — Answer.
What is 35 of 24?
Answer: 310
- Multiply straight across → 620 — 'Of' means multiply: 3/5 x 2/4. Numerator x numerator over denominator x denominator.
- Simplify → 310 — Divide numerator and denominator by their GCD.
- Verify → 310 ✓ — Answer.
A recipe calls for 610 cup of milk. You make 110 of the recipe. How much milk do you need?
Answer: 350
- Multiply straight across → 6100 — Scaling a recipe means multiplying. Numerator x numerator over denominator x denominator.
- Simplify → 350 — Divide numerator and denominator by their GCD.
- Verify → 350 ✓ — Answer.
Common mistakes
- Adding numerators and denominators instead of multiplying gives 2/3 × 1/4 = 3/7 rather than the correct answer 2/12 = 1/6
- Forgetting to simplify the final answer leaves 6/12 instead of reducing it to 1/2 by dividing both parts by 6
- Cross-multiplying like in proportion problems produces 2 × 4 = 3 × 1, giving 8 = 3, rather than multiplying straight across