# Common Denominator

This is the easiest method we 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?

When the denominators of two or more fractions are the **same**, they are **Common 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 \frac{20}{32} to \frac{10}{16} , then to \frac{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 \frac{2}{3} + \frac{4}{5} ?

\frac{2}{3} + \frac{4}{5} = \frac{2×5 + 3×4}{3×5} = \frac{10 + 12}{15} = \frac{22}{15 }

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

That is how the experts do it!