Multiplying fractions
Multiply the numerators, multiply the denominators. Cancel where possible. Year 5/6.
Multiplying fractions is simpler than adding them: multiply the tops, multiply the bottoms, simplify. Year 5 starts with proper fractions; Year 6 multiplies fractions by whole numbers and by mixed numbers.
Worked examples
½ × ¾ = &frac{1×3}{2×4} = ⅜.
⅔ × 6 = &frac{12}{3} = 4. Multiply by 6 = 6/1.
1½ × ⅔ = &frac32; × ⅔ = &frac66 = 1. Convert mixed to top-heavy first.
Frequently asked questions
Why not common denominators here?
Common denominators are for adding/subtracting, where pieces must be the same size. Multiplication scales: ½ of ¾ is a quarter of three, which is ⅜.
Cancelling before multiplying?
Yes — if any numerator shares a factor with any denominator, cancel before multiplying to avoid simplifying afterwards. &frac49 × ¾ = &frac{4×3}{9×4} = &frac13 (cancel the 4s).