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?

"Common" Denominator is when the

denominators

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

same.

 

 

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.

o simplify a fraction, divide the top and bottom by the highest

number that

can divide into both numbers exactly.

Simplifying Fractions

Simplifying (or reducing) fractions means to make the fraction as simple

as possible.

Why say four-eighths (48) when we really mean half (12) ?

  4/8 ==> 2/4 ==> 1/2  

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

       

How do I Simplify a Fraction ?

There are two ways to simplify a fraction:

Method 1

Try to evenly divide (only whole number answers) both the top and

bottom of the fraction by 2, 3, 5, 7 ,... etc, until we can't go any further.

Example: Simplify the fraction 24/108 :

  ÷ 2   ÷ 2   ÷ 3  

       

24

 = 

12

 = 

6

 = 

2

108 54 27 9

         

  ÷ 2   ÷ 2   ÷ 3  

That is as far as we can go. The fraction simplifies to 29

Example: Simplify the fraction 1035 :

Dividing by 2 doesn't work because 35 can't be evenly divided by

2 (35/2 = 17½)

Likewise we can't divide evenly by 3 (10/3 = 313 and also 35/3=1123)

No need to check 4 (we checked 2 already, and 4 is just 2×2).

But 5 does work!

  ÷ 5  

 

10

 = 

2

35 7

  ÷ 5  

That is as far as we can go. The fraction simplifies to 27

Notice that after checking 2 we didn't need to check 4 (4 is 2×2)?

We also don't need to check 6 when we have checked 2 and 3 (6 is 2x3).

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.)