How to Multiply and Divide Fractions: Multiply Across, Flip to Divide

Multiplying: just multiply across

Multiplication of fractions is the easy case: no common denominator, no rewriting. Multiply the numerators to get the new top, multiply the denominators to get the new bottom. For 2/3 × 4/5, the numerator is 2 × 4 = 8 and the denominator is 3 × 5 = 15, giving 8/15.

You can cancel common factors before multiplying to keep the numbers small. In 4/9 × 3/8, the 3 cancels into the 9 (leaving 3) and the 4 cancels into the 8 (leaving 2), giving 1/3 × 1/2 = 1/6 directly, with no large product to reduce afterward.

Dividing: multiply by the reciprocal

Dividing by a fraction is the same as multiplying by its reciprocal — its flip. The reciprocal of 4/5 is 5/4. So 2/3 ÷ 4/5 becomes 2/3 × 5/4. Multiply across: 2 × 5 = 10 over 3 × 4 = 12, giving 10/12, which simplifies to 5/6.

Why does flipping work? Dividing by 4/5 asks how many groups of 4/5 fit into the number. Multiplying by 5/4 scales up by 5 and down by 4 to answer exactly that. The reciprocal simply undoes the second fraction, which is what division means.

Whole numbers and simplifying

A whole number is a fraction over 1, which makes mixed problems easy. To compute 6 ÷ 2/3, write 6 as 6/1, flip 2/3 to 3/2, and multiply: 6/1 × 3/2 = 18/2 = 9. Dividing by a fraction smaller than 1 gives a bigger result, which surprises people at first.

Always finish by reducing. After multiplying you often get a product like 10/12 that shares a factor — here 2 — so divide both by it to reach 5/6. Cancelling common factors before you multiply gives the same simplified answer with less arithmetic.

Frequently asked questions

Do I need a common denominator to multiply fractions?

No. Common denominators are only for addition and subtraction. To multiply, you multiply numerators together and denominators together directly.

What is a reciprocal?

The reciprocal of a fraction is that fraction flipped — numerator and denominator swapped. The reciprocal of 4/5 is 5/4, and the reciprocal of 7 (which is 7/1) is 1/7.

Why does dividing sometimes make the number bigger?

When you divide by a fraction smaller than 1, you are asking how many of those small pieces fit — and many do. So 6 ÷ 2/3 = 9, larger than 6.

Should I simplify before or after multiplying?

Either works and gives the same answer. Cancelling common factors before multiplying keeps the numbers smaller, so it is usually easier than reducing a large product afterward.