Multiplying and dividing fractions

To multiply fractions, multiply the tops and multiply the bottoms. To divide, keep the first fraction, flip the second and multiply (Keep, Change, Flip). Turn mixed numbers into improper fractions first.

Key facts

  • a/b × c/d = ac/bd
  • Dividing: keep, change ÷ to ×, flip the second fraction.
  • Simplify before or after: cancelling first keeps the numbers small.
  • 2 1/3 = 7/3 because 2 × 3 + 1 = 7.

Worked examples

Example 1

Work out 2/3 × 9/10.

  1. Multiply the tops and the bottoms. (2 × 9)/(3 × 10) = 18/30
  2. Simplify by 6. 18/30 = 3/5

Answer: 3/5

Example 2

Work out 1 1/2 ÷ 3/4.

  1. Make the mixed number improper. 1 1/2 = 3/2
  2. Keep 3/2, change ÷ to ×, flip 3/4. 3/2 × 4/3
  3. Multiply and simplify. 12/6 = 2

Answer: 2