Multiplying fractions

To multiply fractions, multiply the tops and multiply the bottoms, then simplify. “Of” means multiply, so 1/2 of 3/4 is 3/8. Multiplying by a fraction less than 1 makes a number smaller.

Key facts

  • a/b × c/d = (a × c)/(b × d). Simplify at the end, or cancel common factors first.
  • A whole number n is n/1: 3/4 × 8 = 24/4 = 6.
  • “Of” means multiply: 2/3 of 12 is 2/3 × 12 = 8.
  • Change mixed numbers into improper fractions before multiplying or dividing.

Worked examples

Example 1

Work out 1/4 × 12.

  1. 1/4 × 12 is the same as 1/4 of 12. 12 ÷ 4 = 3

Answer: 3

Example 2

Work out 2/3 × 3/5.

  1. Multiply the numerators and the denominators. (2 × 3)/(3 × 5) = 6/15
  2. Simplify. 6/15 = 2/5

Answer: 2/5

Example 3

Work out 2/3 × 9/10.

  1. Multiply the tops and the bottoms. 2/3 × 9/10 = 18/30
  2. Divide both by 6. 18/30 = 3/5

Answer: 3/5

Example 4

A recipe uses 3/4 of a cup of flour. How much flour is in 2/3 of the recipe?

  1. Multiply the tops and the bottoms. 2/3 × 3/4 = 6/12
  2. Simplify. 6/12 = 1/2

Answer: 1/2 of a cup

Example 5

Work out 2 1/2 × 1 3/5.

  1. Change both to improper fractions. 5/2 × 8/5
  2. Multiply, then simplify. 40/10 = 4

Answer: 4