To multiply fractions, multiply the tops together, multiply the bottoms together, then simplify if you can. Example: 2/3 times 3/4 is 6/12, which simplifies to 1/2. That's the whole method — no common denominators, no cross anything. Multiplying is the kindest fraction operation there is, and most people don't believe that until they try it.

A Little Vocabulary First

Quick vocabulary, because fraction problems are half vocabulary: the top number is the numerator, the bottom number is the denominator. The denominator tells you how many equal pieces the whole is split into; the numerator tells you how many of those pieces you have. In 2/3, the whole is split into 3 pieces and you have 2 of them. When you multiply fractions, you're really asking "a fraction of a fraction" — and that's why you multiply straight across.

Here's where it shows up in real life. A recipe calls for 3/4 cup of sugar, but you're only making two-thirds of the recipe. How much sugar? Two-thirds of 3/4 cup — that's 2/3 × 3/4. Tops: 2 × 3 = 6. Bottoms: 3 × 4 = 12. So 6/12, and both numbers divide by 6, leaving 1/2 cup. Half a cup of sugar, and you didn't have to find a common anything. My kid once stared at a problem like this for ten minutes because she was hunting for a common denominator she'd been taught to find for adding. For multiplying, you just don't need one. That single fact would have saved her the whole ten minutes.

Simplifying: Making the Answer Look Finished

Simplifying — also called reducing — is the only step people skip, and it's worth doing. 6/12 looks unfinished; 1/2 looks like an answer. To simplify, divide the top and bottom by the same number until they won't divide evenly anymore. 6 and 12 both divide by 6, so 6/12 becomes 1/2. Another one: 1/2 times 2/5 is 2/10, and both divide by 2, so that's 1/5. If the numbers won't simplify — like 2/3 times 1/5 is 2/15, and nothing divides both — then you're already done, and that's fine too.

The Cancel-First Shortcut

One shortcut for the confident: cancel before you multiply, sometimes called cross-cancelling. In 2/3 × 3/4, the 3 on the top and the 3 on the bottom cancel each other out, leaving 2/4, which is 1/2. Same answer, smaller numbers. It's optional — the plain method works every time — but once you see it, you'll use it forever.

Dividing Is Just Flipped Multiplying

Two neighbours of this topic are worth knowing so you don't mix them up. Dividing fractions is just multiplying by the reciprocal — you flip the second fraction and multiply. So 2/3 ÷ 3/4 becomes 2/3 × 4/3 = 8/9. And improper fractions (where the top is bigger than the bottom, like 7/4) multiply exactly the same way; you can convert to a mixed number like 1 3/4 at the end if you like, but the multiplication doesn't care.

If you want to check your work, the fraction calculator here shows each step instead of just the answer, which is how you catch the one mistake everyone makes: multiplying the tops and then adding the bottoms by accident. I did that on a test once and got a beautifully wrong answer with total confidence. The free online calculators are good for that second look, and the math calculators handle the rest of the math homework pile. For anything else with numbers, all calculators are right there.

FAQs

Q: How do you multiply fractions step by step?

A: Multiply the tops, multiply the bottoms, then simplify — 2/3 × 3/4 = 6/12 = 1/2.

Q: Do I need a common denominator to multiply fractions?

A: No. Common denominators are only for adding and subtracting.

Q: What is the numerator and denominator?

A: The numerator is the top number (pieces you have); the denominator is the bottom number (pieces the whole is split into).

Q: How do you divide fractions?

A: Flip the second fraction and multiply — 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9.

Q: Can I cancel before multiplying?

A: Yes — in 2/3 × 3/4, the 3s cancel, leaving 2/4 = 1/2. Same answer, smaller numbers.