Multiplying Fractions
Multiplying fractions appears in Year 5 and Year 6 of the UK National Curriculum, yet many pupils struggle with the concept that multiplying can make a number smaller. When Charlotte has 3/4 of a chocolate bar and gives away 1/2 of that portion, she's left with 3/8 of the original bar.
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Why it matters
Multiplying fractions underpins numerous real-world calculations pupils encounter daily. Baking recipes often require scaling ingredients—if a cake recipe calls for 23 cup of flour and you're making 34 of the recipe, you'll need 12 cup. Construction projects use fraction multiplication when calculating areas: a rectangular garden plot measuring 23 metres by 45 metres has an area of 815 square metres. In sports, understanding fractions helps calculate statistics—if a footballer completes 35 of passes in the first half and 23 in the second, knowing how to work with these fractions becomes essential. Year 6 pupils preparing for SATs must demonstrate fluency with fraction multiplication, as it appears regularly in reasoning papers and connects to percentage calculations needed for GCSE Foundation mathematics.
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
14 x 12 = _______
Answer: 18
- Multiply straight across → 1/8 — Numerator x numerator over denominator x denominator.
- Simplify → 1/8 — Divide numerator and denominator by their GCD.
- Verify → 1/8 ✓ — Answer.
A garden plot is 23 m wide and 13 m long. What is the area?
Answer: 29
- Multiply straight across → 2/9 — Area = width x length. Numerator x numerator over denominator x denominator.
- Simplify → 2/9 — Divide numerator and denominator by their GCD.
- Verify → 2/9 ✓ — Answer.
A garden plot is 23 m wide and 79 m long. What is the area?
Answer: 1427
- Multiply straight across → 14/27 — Area = width x length. Numerator x numerator over denominator x denominator.
- Simplify → 14/27 — Divide numerator and denominator by their GCD.
- Verify → 14/27 ✓ — Answer.
Common mistakes
- Pupils add denominators instead of multiplying them, calculating 1/3 × 1/4 = 1/7 instead of the correct answer 1/12.
- Students multiply across incorrectly, writing 2/5 × 3/7 = 6/35 but forgetting to simplify to 6/35, missing opportunities to cancel common factors beforehand.
- When working with mixed numbers like 2 1/4 × 1/3, pupils multiply the whole number by the fraction separately, getting 2/3 + 1/12 = 9/12 instead of converting to improper fractions first: 9/4 × 1/3 = 3/4.