# Fractions

*A fraction is a part of a whole*

### Slice a pizza, and we get fractions:

^{1}/_{2} |
^{1}/_{4} |
^{3}/_{8} |

(One-Half) |
(One-Quarter) |
(Three-Eighths) |

The top number says how many slices we have The bottom number says how many slices the pizza is cut into. |

## Equivalent Fractions

Some fractions may look different, but are really the same, for example:

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

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

= | = |

It is usually best to show an answer using the simplest fraction ( ^{1}/_{2} in this case ).
That is called * Simplifying*, or

*the Fraction*

**Reducing**## Numerator / Denominator

We call the top number the **Numerator**, it is the number of parts we have.

We call the bottom number the **Denominator**, it is the number of parts the whole is divided into.

Numerator |

Denominator |

You just have to remember those names! (If you forget just think "Down"-ominator)

## Adding Fractions

It is easy to add fractions with the **same denominator** (same bottom number):

^{1}/_{4} |
+ | ^{1}/_{4} |
= | ^{2}/_{4} |
= | ^{1}/_{2} |

(One-Quarter) | (One-Quarter) | (Two-Quarters) | (One-Half) | |||

+ | = | = |

Another example:

^{5}/_{8} |
+ | ^{1}/_{8} |
= | ^{6}/_{8} |
= | ^{3}/_{4} |

+ | = | = |

## Adding Fractions with Different Denominators

But what about when the **denominators** (the bottom numbers) are not the same?

^{3}/_{8} |
+ | ^{1}/_{4} |
= | ? | ||

+ | = |

We must *somehow* make the denominators the same.

In this case it is easy, because we know that ^{1}/_{4}
is the same as ^{2}/_{8} :

^{3}/_{8} |
+ | ^{2}/_{8} |
= | ^{5}/_{8} |
||

+ | = |

But when it is **hard to make the denominators the same**, use one of these methods (they both work, use the one you prefer):

## Other Things We Can Do With Fractions

We can also:

Visit the Fractions Index to find out even more.