# Simplifying Fractions

*To simplify a fraction, divide the top and bottom by the highest number that
can divide into both numbers exactly.*

## Simplifying Fractions

Simplifying (or *reducing*) fractions means to make the fraction as simple as possible. Why say four-eighths (^{4}/_{8})
when you really mean half (^{1}/_{2}) ?

^{4}/_{8} |
==> | ^{2}/_{4} |
==> | ^{1}/_{2} |
||

(Four-Eighths) | (Two-Quarters) | (One-Half) | ||||

## How do I Simplify a Fraction ?

There are two ways to simplify a fraction:

## Method 1

Try dividing both the top and bottom of the fraction until you can't go any further (try dividing by 2,3,5,7,... etc).### Example: Simplify the fraction ^{24}/_{108} :

÷ 2 | ÷ 2 | ÷ 3 | ||||

24 | = | 12 | = | 6 | = | 2 |

108 | 54 | 27 | 9 | |||

÷ 2 | ÷ 2 | ÷ 3 |

## Method 2

Divide both the top and bottom of the fraction by the Greatest Common Factor, (you have to work it out first!).### Example: Simplify the fraction ^{8}/_{12} :

1. The largest number that goes exactly into both 8 and 12 is 4, so

*the Greatest Common Factor is 4*.

2. Divide both top and bottom by 4:

÷ 4 | ||

8 | = | 2 |

12 | 3 | |

÷ 4 |

And the answer is:

^{2}/_{3}## Simplifying Fractions Automatically

OK, there is a *third* method, use this tool:

## Fractions on the Number LineAlso ... see an animation of Fractions on the Number Line where you can see many common fractions and their simpler version. We also have a chart of fractions with the simplest fraction highlighted. |