How to Multiply Fractions Step by Step

Suppose you want to multiply 2/3 by 4/5. Multiply the numerators: 2 times 4 equals 8. Then multiply the denominators: 3 times 5 equals 15. The answer is 8/15. Because 8 and 15 have no common factor greater than 1, the fraction is already in simplest form.

The rule works because multiplication of fractions can represent taking a fraction of another fraction. If you take one half of three quarters, you are finding 1/2 times 3/4. Multiplying gives 3/8. A diagram split into equal parts would show the same result, which is useful if the symbolic rule feels too automatic.

This is the central process for multiplying fractions. Numerator times numerator, denominator times denominator, then simplify. Do not add the denominators, and do not look for a common denominator unless a different operation requires one. Addition and subtraction are different because the pieces must refer to equal-sized parts before their numerators can be combined. Multiplication does not combine two sets of parts in that way, so the denominators can be multiplied directly.

You can often cancel common factors before multiplying. Suppose you have 3/10 times 5/9. The 3 and 9 share a factor of 3, so they reduce to 1 and 3. The 5 and 10 share a factor of 5, so they reduce to 1 and 2. You are left with 1/2 times 1/3, which gives 1/6.

This technique is sometimes called cross-cancelling. It does not change the value of the expression because you are dividing a numerator and a denominator by the same nonzero factor. It simply keeps the numbers smaller and reduces the chance of arithmetic mistakes.

When multiplying fractions, simplifying first is optional but often helpful. You can always multiply first and simplify the final fraction afterward. Both routes should lead to the same result. If the final numbers are large, look for common factors again. Simplifying is not a separate trick attached to the end of the method. It is simply a way to write the same fraction in a cleaner form.

A whole number can be written as a fraction with denominator 1. For example, 3 times 2/5 becomes 3/1 times 2/5, which equals 6/5. You can leave that as an improper fraction or write it as 1 1/5 if the question expects a mixed number.

Mixed numbers should usually be changed into improper fractions before multiplying. For example, 1 1/2 becomes 3/2. If you multiply 1 1/2 by 2/3, you get 3/2 times 2/3. The 3s and 2s cancel, leaving 1.

A quick how to multiply fractions checklist is useful: convert mixed numbers, simplify common factors if convenient, multiply across, and simplify the final answer. Also estimate the size. If you multiply two positive fractions smaller than 1, the result should be smaller than either starting fraction. You can also compare with decimals when a fraction is familiar. One half times one half should be one quarter, not one whole, because you are taking only half of an amount that was already half.

Multiplying fractions comes down to multiplying numerators, multiplying denominators, and simplifying. Common denominators are not needed. Convert whole and mixed numbers into fractions first, cancel common factors when it helps, and use a rough size estimate to catch answers that do not make sense.