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# 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 just means that the denominators in two (or more) fractions are common, or the same.

## Why is it Important?

### Adding and Subtracting Fractions

Before you 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

If the denominators are not the same, you can either use the Least Common Denominator method to make them the same, or you can:

Multiply each fraction by the denominator of the other

Here is an example (press play button):

This always works, but you will 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 you 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.)