Simplifying Fractions

To 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 (4/8) when you really mean half (1/2) ?

  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 dividing both the top and bottom of the fraction until you can't go any further (try dividing by 2,3,5,7,... etc).

Example: Simplify the fraction 24/108 :

  ÷ 2   ÷ 2   ÷ 3  
   
24  =  12  =  6  =  2
108 54 27 9
     
  ÷ 2   ÷ 2   ÷ 3  

Method 2

Divide both the top and bottom of the fraction by the Greatest Common Factor, (you have to work it out first!).

Example: Simplify the fraction 8/12 :


1. The largest number that goes exactly into both 8 and 12 is 4, so the Greatest Common Factor is 4.

2. Divide both top and bottom by 4:
  ÷ 4  
 
8  =  2
12 3
 
  ÷ 4  
And the answer is: 2/3

Simplifying Fractions Automatically

OK, there is a third method, use this tool:

 

 
 

Fractions on the Number Line

Also ... see an animation of Fractions on the Number Line where you can see many common fractions and their simpler version.

We also have a chart of fractions with the simplest fraction highlighted.