Pengi Editor's Note: This article was originally published by Think Academy. We're sharing it here for educational value. Think Academy is a leading K-12 math education provider.
How to Multiply Fractions in 3 Simple Steps
Multiplying fractions sounds simple—but students often confuse it with adding fractions or forget to simplify their answers. Should you find a common denominator? Do you multiply across or cross-cancel first? This guide breaks it down into clear steps.
3 Steps to Multiply Fractions
Let's use an example: 3/8 × 2/3
Step 1: Multiply the Top Numbers (Numerators)
3/8 × 2/3 = (3 × 2) / ? = 6 / ?
Step 2: Multiply the Bottom Numbers (Denominators)
3/8 × 2/3 = (3 × 2) / (8 × 3) = 6/24
Step 3: Simplify
Both 6 and 24 can be divided by 6:
6/24 = 1/4
And that's it — Multiply the Top, Multiply the Bottom, Simplify!
Example Problems
Example 1: Fraction Times Whole Number
There is 1/4 of a chocolate bar, and you get 3 pieces of the same size. How much chocolate do you have altogether?
Solution:
1/4 × 3 = 1/4 × 3/1 = (1 × 3)/(4 × 1) = 3/4
A whole number is a fraction with denominator 1. Multiplying still follows the same rule.
Example 2: Fraction Times Fraction
A recipe needs 3/4 cup of sugar. Lisa is making half the recipe. How much sugar does she need?
Solution:
3/4 × 1/2 = (3 × 1)/(4 × 2) = 3/8
She needs 3/8 cup of sugar.
Summary: The Golden Rule for Multiplying Fractions
- If there are mixed numbers, change them to improper fractions first
- Multiply the numerators (top numbers) together
- Multiply the denominators (bottom numbers) together
- Simplify your final answer. If it's an improper fraction, rewrite it as a mixed number if needed
Once you get the hang of it, multiplying fractions feels like solving a puzzle — fast and satisfying!
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