Study Guide

Fractions & Decimals - Multiplying Fractions & Mixed Numbers

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Multiplying Fractions & Mixed Numbers

Multiplication of fractions
is pretty simple compared to addition and subtraction. And guess what? We don't need to find a common denominator. We do need to make sure each number is a fraction, though: no mixed numbers or whole numbers allowed. It's an elite fraction club.

Just follow these four easy steps:

  1. Convert all mixed numbers or whole number to improper fractions.
  2. Multiply the numerators.
  3. Multiply the denominators.
  4. Reduce the final answer and convert it back into a mixed number if necessary.

Multiplication Example 1

3/8 x 4/9 =Multiply the numerators, then multiply the denominators.
12/72 =Reduce the fraction. 12 and 72 have a GCF of 12, so divide the top and bottom by 12.
1/6Boom, there's our answer.

Multiplication Example 2

5/6 x 3 1/2First convert that second mixed number to an improper fraction: 3 1/2 = 7/2
5/6 = 7/2Next, multiply the numerators, then multiply the denominators.
35/12 =There's one answer, but we can also turn this into a mixed number.
2 11/12Why hello there, final answer.

Shortcut: Cross-Canceling

Instead of reducing the fraction at the end of the problem, we can cross-cancel before we multiply. It's not required, but it'll save a few steps.

Cross-canceling means that when we're multiplying fractions, we can reduce any numerator with any denominator. In this example, 5 and 10 can both be divided by 5, even though they're not in the same fraction.

5/8 x 3/10 = 3/16

Let's look at Example 1 again and see how to use this method.

Cross-Canceling Example 1

3/8 x 4/9 =Here we can reduce the 3 and 9 (by 3) and we can also reduce the 4 and 8 (by 4). Yeah, let's do that.
1/2 x 1/3Now we multiply the top by the top and the bottom by the bottom, like normal.
1/6Hey, the final answer is the same as in Example 1 from before. Nice.

Here's another example that includes just about everything we've done so far.

Cross-Canceling Example 2

4 2/3 x 1 3/7First convert each to an improper fraction.
14/3 x 10/714 and 7 can each be reduced by 7, so we can cross-cancel.
140/21 =Multiply.
20/3 =Here's the answer.
6 2/3If you'd like, you can turn it back into a mixed number

Multiplying a Whole Number by a Fraction

Just remember that all real numbers can be written as fractions. With a whole number, all we need to do is place it over a denominator of 1.

Let's look at an example, shall we?

5 x 1/3 = 1 2/3

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