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 (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 2 9

Example: Simplify the fraction 10 35 :

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 = 3 1 3 and also 35/3=11 2 3 )

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 2 7

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).

In fact, when checking from smallest to largest we use prime numbers:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ...

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 812 :

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

Divide both top and bottom by 4:

  ÷ 4  
 
8  =  2
12 3
 
  ÷ 4  

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