Adding Unlike Fractions

Here are some facts to remember before starting to add unlike fractions.

Fractions can only be added if they are like each other.  Fractions are like each other if their denominators are the same.  Fractions with the same denominators have common denominators.  By creating equivalent fractions, denominators of fractions can be changed.  Equivalent fractions are created by multiplying by a special form of one.  The numerator and denominator of any special form of one are the same.  When changing denominators, choose a new denominator that is a multiple of the old one.

To take unlike fractions and change them into like fractions so that they can be added, one or both to the original fractions must be changed into equivalent fractions.  The key to doing this is finding a common multiple for the denominators.  A common multiple is a multiple that matches.  To change unlike fractions into like fractions, it is best to choose a common denominator that is the least common multiple or LCM of the original denominators.  That means it is the smallest common multiple.

To add unlike fractions, follow these steps.

1. Realize that fractions must be like to add them.
2. Choose a common denominator for the fractions using the LCM.
3. Use a special form of one to create equivalent fractions that have the common denominator.
4. Add the equivalent fractions.

Here is an example to study.  You should be able to identify all of the steps.                                  

Do the scratch paper work on this problem then add the equivalent fractions.                                   

There's a little more work on this one for you!

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