Learn · Grades 6–8

How to Multiply Fractions and Mixed Numbers

Multiplying fractions is the easy one: you do not need a common denominator. Multiply the tops, multiply the bottoms, and simplify.

Try it with your own problem ↓

The steps

  1. Turn any mixed number into an improper fraction. A whole number n becomes n/1.
  2. Optional shortcut: cancel any factor that is in a top and in a bottom.
  3. Multiply the numerators together.
  4. Multiply the denominators together.
  5. Simplify, and write the answer as a mixed number if it is improper.

A worked example

Work out 2 1/2 × 3/4.

  1. Turn 2 1/2 into an improper fraction: 2 × 2 + 1 = 5, so it is 5/2.
  2. Now we have 5/2 × 3/4. There is nothing to cancel.
  3. Multiply the tops: 5 × 3 = 15.
  4. Multiply the bottoms: 2 × 4 = 8.
  5. 15/8 is improper: 15 ÷ 8 = 1 remainder 7, so it is 1 7/8.

2 1/2 × 3/4 = 15/8 = 1 7/8. Check: 2.5 × 0.75 = 1.875. ✓

Why it works

Take half of 3/4. Cut each fourth in half and you have eighths, and you still keep 3 of them, so the answer is 3/8. The bottom doubled (4 × 2) while the top stayed at 3 (3 × 1). That is exactly "multiply across": 1/2 × 3/4 = (1 × 3)/(2 × 4).

Try it with your own problem

Open the free The Product Ladder with this example already filled in. It shows every step, and you can type over it with your own numbers.

Work it out: 2 1/2 * 3/4Opens The Product Ladder with this example

Or try these

Common mistakes

Questions people ask

How do I multiply a fraction by a whole number?

Write the whole number over 1: 3 × 2/5 = 3/1 × 2/5 = 6/5 = 1 1/5.

What does "of" mean in a fraction problem?

Multiply. Half of 3/4 means 1/2 × 3/4 = 3/8.

Why is the answer smaller than what I started with?

Taking a part of a part gives less than the part you started with. 1/2 of 3/4 is smaller than 3/4.

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