## 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:

- 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?