How to Multiply Fractions | Math Review

Multiplying Fractions

Multiplying Fractions

The process for multiplying two fractions is fairly straightforward. All you have to do is multiply the two numerators together and the two denominators together. Your new numerator will be the product of the two numerators, and your new denominator will be the product of the two denominators.

Let’s take a few examples. First, we have 2 over 3 times 4 over 5. Now, what we have to do is multiply 2 by 4 to get 8 and that’s our new numerator. We multiply 3 by 5 to get 15 for a new denominator. That’s your answer.

When you start getting into fractions that have larger numbers, like this one here, it may be beneficial to do what’s called cancelling before you start multiplying your numbers. Let’s take 3 over 22 times 11 over 15.

Now, canceling is taking numbers in the numerator and numbers and denominator of opposite fractions and dividing them by a common factor. For instance, 3 and 15 are both divisible by 3. If we divide 3 by 3 we get 1, and if we divide 15 by 3 we get 5.

11 and 22 are both divisible by 11. We can divide 11 by 11 to get 1, and 22 by 11 to get 2. Now, let’s rewrite this to see what we have left. We have 1 over 2 times 1 over 5. Now, it’s a trivial thing to take the product of these. We have 1 times 1 and 2 times 5.

Lets take one final example 5 over 12 times 9 over 10. Once again, we’re going to cancel. We’ll divided 5 and 10 by 5. 5 over 5 is 1. 10 over 5 is 2. Now with the 9 and the 12, we can’t divide 12 by 9, but we can divide both numbers by 3.

If we divide 9 by 3 we get 3, and if we divide 12 by 3 we get 4. Let’s rewrite this and see where we have left. 1 over 4 times 3 over 2. Now, we can multiply this 1 times 3 is 3 and 4 times 2 is 8.

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by Mometrix Test Preparation | Last Updated: May 8, 2019