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

	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?