Add and Subtract Fractions with Different Denominators
Read this text for more examples and guidance. It gives a good review of how to find common denominators. Pay attention to the "How To" section at the beginning for an overview of the process. Do Examples 4.67 – 4.72 and check your answers.
Answers
EXAMPLE 4.67
Solution
Find the LCD of 2, 3. 

Change into equivalent fractions with the LCD 6.  
Simplify the numerators and denominators.  
Add. 
Remember, always check to see if the answer can be simplified. Since and have no common factors, the fraction cannot be reduced.
EXAMPLE 4.68
Solution
Find the LCD of 2 and 4. 

Rewrite as equivalent fractions using the LCD 4.  
Simplify the first fraction.  
Subtract.  
Simplify. 
One of the fractions already had the least common denominator, so we only had to convert the other fraction.
EXAMPLE 4.69
Solution
Find the LCD of 12 and 18. 

Rewrite as equivalent fractions with the LCD.  
Simplify the numerators and denominators.  
Add. 
Because is a prime number, it has no factors in common with . The answer is simplified.
EXAMPLE 4.70
Solution
Find the LCD. 

Rewrite as equivalent fractions with the LCD.  
Simplify each numerator and denominator.  
Subtract.  
Rewrite showing the common factor of 3.  
Remove the common factor to simplify. 
EXAMPLE 4.71
Solution
Find the LCD. 

Rewrite as equivalent fractions with the LCD.  
Simplify each numerator and denominator.  
Add.  
Rewrite showing the common factor of 2.  
Remove the common factor to simplify. 
EXAMPLE 4.72
Solution
The fractions have different denominators.
Find the LCD. 

Rewrite as equivalent fractions with the LCD.  
Simplify the numerators and denominators.  
Add. 
We cannot add and since they are not like terms, so we cannot simplify the expression any further.