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Study Guide

**Multiplication of fractions** is pretty simple compared to addition and subtraction. And guess what? We don't need to find a common denominator. We

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.

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. |

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. |

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.

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.

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 |

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?

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