# Fractions & Decimals

# Multiplying Fractions & Mixed Numbers

**Multiplication of fractions** is pretty simple compared to addition and subtraction. And guess what, you don't have to find a common denominator. Just follow these four easy steps:

- Convert all mixed numbers to improper fractions.
- Multiply the numerators.
- Multiply the denominators.
- Reduce your final answer.

### Multiplication Example 1

First convert 3½ to an improper fraction | |

Next multiply the numerators, then multiply the denominators | |

This is your answer | |

If you'd like, you could convert that into a mixed number |

### Multiplication Example 2

Multiply the numerators, then multiply the denominators. | |

Reduce the fraction (12 and 72 have a GCF of 12) | |

## Cross-Canceling

Instead of reducing the fraction at the end of the problem, you can **cross-cancel*** before you multiply*.

Cross-canceling means that when multiplying fractions you can reduce the numerator of one fraction with the denominator of another. In this example, 5 and 10 can both be divided by 5.

Let's look at the three examples again and see how to use this method.

### Cross-Canceling Example 1

In this first example, we cannot use cross-canceling, since 5 and 2 do not share a common factor, and neither do 7 and 6 | |

### Cross-Canceling Example 2

Here we can reduce the 3 and 9 (by 3) and we can also reduce the 4 and 8 (by 4) | |

### Cross-Canceling Example 3

First convert each to an improper fraction | |

14 and 7 can each be reduced by 7 | |

Cross cancel | |

Here's the answer | |

If you'd like, you can turn it back in to a mixed number |

## Multiplying a Whole Number by a Fraction

Well, remember that all real numbers can be written as fractions. With a whole number, all you need to do is place it over a denominator of 1.

Let's look at an example, shall we?