. To find a number that is a common denominator between these two fractions, you have to find a number that 3 and 4 will go into evenly. If you find the smallest number that 3 and 4 go into evenly, this is called the least common denominator.Addition of Fractions
To add fractions, the following steps are:
Note: This is not the only way to add fractions. You do not have to change the mixed numbers to improper fractions but I show this way to make the procedure the same as subtracting fractions (which will be next).
Let's talk about finding a common denominator first.
Take the two fractions: . To find a number that is a common denominator between these two fractions, you have to find a number that 3 and 4 will go into evenly. If you find the smallest number that 3 and 4 go into evenly, this is called the least common denominator.
A common denominator of 3 and 4 is 12, 24, 36, 48, or whatever number that is divisible by 3 and 4 (or 3 and 4 go into 12 evenly, go into 24 evenly, go into 36 evenly, etc...). The least common denominator of 3 and 4 is 12.
To rewrite a fraction so it has a common denominator, you have to multiply the fraction by 1 in fraction form. I will show this for :
. Why multiply 
by 
? So the new fraction has a denominator of 12.
. Why multiply 
by ? So the new fraction has a denominator of 12.
Again, to add fractions, the denominators must be the same. That is, the denominators must have a common denominator.
The new fractions, 
, which are equivalent to can now be added .
Example 1.
Add: 
Solution:
Does the final answer reduce? No, 
, does not reduce.
Example 2.
Add: 
Solution:
To practice adding fractions, go to the Addition of Fractions Worksheet.