Study Guide

# Fractions & Decimals - Multiplying Fractions & Mixed Numbers

## 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? ## This is a premium product 