(Multiplying by a Common Denominator)
Simplifying Complex Fractions
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Method 1:
This is one of two methods
for simplifying complex fractions.
Also see Method 2. 

Remember ... a complex fraction is just a fraction within a fraction.


                
To Simplify a Complex Fraction by Multiplying by a Common Denominator
1.  Find the least common denominator (LCD) of all fractions appearing within the complex fraction.
2.  Multiply both the numerator and the denominator of the complex fraction by the LCD of the complex fraction from step 1.
3.  Simplify whenever possible.

Let's see Method 1 at work on the following problems:

1.

    

2.

3.

4.

 

5.


Remember ...

Complex Fractions are EASY to simplify
 if you show your work!

 

1.

Solution:  The least common denominator for the ENTIRE problem is 8.  Multiply the top and the bottom by 8.

 

2.

Solution:  The mixed number should be changed to an improper fraction before starting Method 1.  Remember that the unseen denominator for 9 is 1.  The least common denominator for the ENTIRE problem is 3.  Multiply the top and the bottom by 3.

 

3.


 

Solution The least common denominator for the ENTIRE problem is 32.  Multiply the top and the bottom by 32. 

 

Be careful to distribute the 32 through the parentheses.

 



 

Now simplify:  factor the top and the bottom.  Simplify the final answer.

 

 

4.

 
Solution:  The least common denominator for the ENTIRE problem is 12x.  Multiply the top and the bottom by 12x.
 








 

 Be careful to distribute the 12x through the parentheses.
  Now simplify:  factor the top and the bottom. 

 

5.







 

Solution The least common denominator for the ENTIRE problem is 6x2.  Multiply the top and the bottom by 6x2
 

 
 Be careful to distribute the 6x2 through the parentheses.
  Write the final answer. 

 

Don't let these fractions trip you up!

Just work carefully through each problem, showing your work as you progress.