How to multiply fractions

Good news: multiplying is the easiest thing you can do with fractions. Unlike adding, you don’t need a common denominator, even when the bottoms are different.

The basic method

3/4 × 2/5

Tops: 3 × 2 = 6

Bottoms: 4 × 5 = 20

6/20 simplifies to 3/10

Simplify first to keep numbers small

Before multiplying, look for a number on the top of one fraction and the bottom of the other that share a factor. Divide both by it. This is called cross-canceling.

In 3/4 × 2/5, the 2 on top and the 4 on the bottom share a factor of 2. Cancel them to 1 and 2:

3/2 × 1/5 = 3/10

Same answer, smaller numbers, no simplifying at the end.

Multiplying a fraction by a whole number

Put the whole number over 1.

4 × 2/3 = 4/1 × 2/3 = 8/3 = 2⅔

Multiplying mixed numbers

Turn mixed numbers into improper fractions first. Don’t multiply the whole parts and fraction parts separately, which is a very common mistake.

2½ × 1⅓ → 5/2 × 4/3 = 20/6 = 3⅓

Why the answer can be smaller

Multiplying by a fraction less than 1 gives a smaller result, because you’re taking only part of something. That’s the mirror image of division, where dividing by a small fraction gives a bigger result. See how to divide fractions for that side of the story.