# Common Denominator

This is the easiest method I know to add or subtract fractions!

## What is a Denominator?

*The denominator is the bottom number in a fraction.*

*It shows how many equal parts the item is divided into.*

## What is a Common Denominator?"Common" Denominator is when the denominators |

## Why is it Important?

### Adding and Subtracting Fractions

Before we can add or subtract fractions, the fractions need to have a **common** denominator (in other words the denominators **must be the same**).

### Making The Denominators the Same

When the denominators are **not** the same, we can either use the Least Common Denominator method to make them the same, or we can:

Multiply top and bottom of each fraction by the denominator of the other.

Like in this example *(press play button)*:

This always works, but we often need to simplify the fraction afterwards, as in this example *(press play button)*:

We simplified the fraction ^{20}/_{32} to ^{10}/_{16}, then to ^{5}/_{8} by dividing the top and bottom by 2 each time, and that is as simple as it can get!

## What Did We Do?

1. We multiplied each fraction by the denominator of the other. Let's use letters instead of numbers to show it:

2. And because they now have the same denominator, we can add them:

### In One Step!

We could do those two things in one step like this:

Which we can use like this:

### Example: What is ^{2}/_{3} + ^{4}/_{5} ?

2 | + |
4 | = | 2×5 + 3×4 | = | 10 + 12 | = | 22 |

3 | 5 | 3 × 5 | 15 | 15 |

(Note: "a" was 2, "b" was 3, "c" was 4 and "d" was 5.)

That is how the experts do it!