How to Multiply Fractions
Multiply any fractions quickly and correctly
⚡Quick Answer
To multiply fractions, multiply the **numerators** together and the **denominators** together to form a new fraction. Then simplify the result by dividing both parts by their **greatest common divisor (GCD)**.
Step-by-Step Guide
Multiply the Numerators
Multiply the top numbers (numerators) of both fractions together to get the new numerator. For example, in ²⁄₃ × ³⁄₄, multiply 2 × 3 to get 6. This number goes above the fraction bar in your answer.
Multiply the Denominators
Multiply the bottom numbers (denominators) of both fractions together to get the new denominator. Using the same example, multiply 3 × 4 to get 12, so your intermediate answer is ⁶⁄₁₂. Unlike addition, you never need a common denominator — just multiply straight across.
Simplify the Result
Divide both the numerator and denominator by their greatest common divisor (GCD) to reduce the fraction to its simplest form. In the example, the GCD of 6 and 12 is 6, so ⁶⁄₁₂ simplifies to ½. If the GCD is 1, the fraction is already in its simplest form.
Handle Mixed Numbers First
If you have mixed numbers (like 2½), convert them to improper fractions before multiplying — multiply the whole number by the denominator and add the numerator (e.g., 2½ → (2×2+1)/2 = 5/2). Trying to multiply mixed numbers directly is a common source of mistakes. Once converted, proceed with the standard three steps above.
Frequently Asked Questions
Do I need a common denominator to multiply fractions?
No — unlike addition or subtraction, multiplying fractions requires no **common denominator**. You simply multiply the numerators together and the denominators together in one straightforward step. This is one reason fraction multiplication is actually easier than fraction addition.
What is cross-canceling?
**Cross-canceling** (also called cross-simplification) means dividing a numerator of one fraction and a denominator of the other by a shared factor *before* you multiply. For example, in ²⁄₃ × ³⁄₄ you can cancel the 3s first to get ²⁄₁ × ¹⁄₄ = ²⁄₄ = ½. It produces the same result as simplifying at the end but keeps the intermediate numbers smaller and easier to work with.
How do I multiply a fraction by a whole number?
Write the **whole number as a fraction over 1** (e.g., 3 becomes ³⁄₁), then multiply numerator × numerator and denominator × denominator as usual. So ²⁄₅ × 3 becomes ²⁄₅ × ³⁄₁ = ⁶⁄₅, which simplifies to 1⅕. This trick works because any number divided by 1 equals itself.
How do I multiply more than two fractions at once?
When multiplying **three or more fractions**, simply extend the same rule: multiply all the numerators together to get one big numerator, then multiply all the denominators together to get one big denominator. For example, ½ × ²⁄₃ × ³⁄₄ = (1×2×3)/(2×3×4) = ⁶⁄₂₄ = ¼. Using **cross-canceling** across any numerator-denominator pair before multiplying can keep the numbers manageable.