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:
- Convert all mixed numbers or whole number to improper fractions.
- Multiply the numerators.
- Multiply the denominators.
- Reduce the final answer and convert it back into a mixed number if necessary.
Multiplication Example 1
Multiply the numerators, then multiply the denominators. | |
Reduce the fraction. 12 and 72 have a GCF of 12, so divide the top and bottom by 12. | |
Boom, there's our answer. |
Multiplication Example 2
First convert that second mixed number to an improper fraction: | |
Next, multiply the numerators, then multiply the denominators. | |
There's one answer, but we can also turn this into a mixed number. | |
Why 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.
Let's look at Example 1 again and see how to use this method.
Cross-Canceling Example 1
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. | |
Now we multiply the top by the top and the bottom by the bottom, like normal. | |
Hey, 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
First convert each to an improper fraction. | |
14 and 7 can each be reduced by 7, so we can cross-cancel. | |
Multiply. | |
Here's the answer. | |
If 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?