Common fractions are most often written in their simplest form. This is also known as expressing or writing fractions using the lowest terms.
Common fractions can be simplified to their lowest terms by applying the concept of equivalent fractions.
This short lesson shows two different methods for simplifying fractions.
The above lesson includes audio (so remember to switch on your speakers). Use the play/ pause button if you need to stop and start the lesson. Related Fractions Lessons 

Introducing Fractions  Equivalent Fractions  Common Denominators  Adding and Subtracting Fractions  Simplifying Fractions  Mixed Numbers and Improper Fractions 
The methods shown in the above lesson are also illustrated below .
Look at the four fractions below. They are all equivalent to each other.
 x 

 x 

 x 


Note how the numerator and denominator both increase by a factor of 2 each time.
Here is another example of equivalent fractions.
 ÷ 


In this case the numerator and denominator both decrease by a factor of 3
To simplify a common fraction we can find the greatest common factor for the numerator and the denominator and then use it to divide both. The steps below show an example of how to do this:
 
1 , 2 , 4 , 8 , 16  
1 , 2 ,4 , 5 , 10 , 20  
1 , 2 , 4  
4  
16 ÷ 4 = 4  
20 ÷ 4 = 5  

When simplifying fractions you can use a trial and error method as an alternative to the greatest common factor one that is shown above .
The following examples show how this trial and error method can be used while simplifying fractions.
Example: Simplifying 16/24
Try  Simplified?  
2  Divide top and bottom by 2 to get 8/12 
Not yet..keep going.. 

2  Divide top and bottom by 2 to get 4/6  Not yet..keep going..  
2  Divide top and bottom by 2 to get 2/3  Yes  
Example: Simplifying 48/60
Try  Simplified?  
6  Divide top and bottom by 6 to get 8/10  Not yet..keep going.. 

2  Divide top and bottom by 2 to get 4/5  Yes 
Example: Simplifying 60/100
Try  Simplified?  
10  Divide top and bottom by 10 to get 6/10  Not yet..keep going.. 

2  Divide top and bottom by 2 to get 3/5  Yes 
The example below shows a fairly common error made by students when showing fractions in their simplest form.
In fairness to those that make the "error" above, if just asked to "simplify a fraction" then the answer above is not wrong  it is just not as good an answer as the correct one!
Use the Simplifying Fractions Worksheet Generator to get as much practice as you need.
The worksheet below will also provide practice on simplifying fractions..
Here is a very nice and simple explanation of simplifying fractions from Math is Fun.