How to Multiply and Divide Fractions

Unlike adding fractions, multiplying and dividing fractions don't require a common denominator. The rules are straightforward once you know them.

Multiplying fractions

Rule: Multiply numerators together and denominators together.

\(\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}\)

Example: ⅔ × ⅘

Answer: ⁸⁄₁₅

Simplify before multiplying (optional but helpful)

You can cancel common factors between numerators and denominators before multiplying.

Example: ⅔ × ⁹⁄₁₀

Answer: ⅗

Multiplying mixed numbers

Convert to improper fractions first, then multiply.

Example: 2½ × 1⅓

Dividing fractions

Rule: Flip the second fraction (reciprocal) and multiply.

\(\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}\)

Example: ⅔ ÷ ⅘

Answer: ⅚

Why "flip and multiply"?

Dividing by a fraction is the same as multiplying by its reciprocal. ½ ÷ ⅓ means "how many thirds fit in a half?" — which is the same as ½ × 3 = 1½.

Quick reference

• Multiply: numerator × numerator, denominator × denominator
• Divide: flip the second fraction, then multiply
• Simplify before or after to keep numbers manageable

Common mistakes

Cross-multiplying instead of straight across: When multiplying fractions, multiply numerator × numerator and denominator × denominator. Don't cross-multiply (that's for solving proportions).

Forgetting to flip: When dividing, you must flip the second fraction (take its reciprocal) before multiplying. 2/3 ÷ 4/5 becomes 2/3 × 5/4.

Not simplifying first: You can cross-cancel before multiplying to keep numbers small. In 4/9 × 3/8, the 4 and 8 share a factor of 4, and the 3 and 9 share a factor of 3.

More examples

Example: 5/6 × 2/3

Example: 3/4 ÷ 1/2

Example (cross-cancelling): 4/9 × 3/8

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