Common Denominator

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

fraction

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
in two (or more) fractions are common, or the same.

 

  Common Denominator

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:

common-factor-explained

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

common-factor-explained2

In One Step!

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

common-factor-formula

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!