Adding and Subtracting Fractions

Adding fractions is probably the skill with fractions that gives people the most trouble! In order to add (and subtract) fractions, you have to follow two steps:

1. Manipulate all of the fractions involved in the addition so that they have a common denominator.
2. Add the numerators (and ONLY the numerators) of the fractions involved.

Before you start this section, you may want to review the sections on multiplying fractions and reducing and enlarging fractions as we will use both of those skills in this lesson.

Adding Fractions Example 1

Add the following fractions:

In this example, both fractions already have a common denominator. A common denominator means that the denominator of each fraction is the same. (In this case, they are both 6). So, move on to step two and add the numerators. 1+4 = 5, so you get the fraction:

Remember, YOU DO NOT ADD THE DENOMINATORS! Adding the denominators is the most common mistake made when adding fractions. Now on to a better example, where the denominators don't start out the same.

Adding Fractions Example 2

Add the following fractions:

In this example, the denominators are different. So, perform step 1. First, we have to figure out a common denominator. The easiest way to do this is to multiply the existing denominators together. (This is BY FAR not the best way, but this is just a review. For more information on common denominators, talk to your teacher.)

3 x 2 = 6, so our common denominator will be 6. Now we must enlarge the fractions (click here for help on enlarging fractions) so that they have a denominator of 6. You must do this separately. Start with 1/3. It becomes 2/6. 1/2 becomes 3/6. Now we have this operation:

Now on to step 2. Add the numerators to arrive at your final answer:

Subtracting Fractions Example 1

Subtracting fractions has the same steps as adding fractions, except you subtract! We'll try subtracting the fractions below:

First, find a common denominator. We could use 27 (9 x 3), but you could also use 9 fairly easily. Let's use 9, since we do not have to do anything to the first fraction. Change 1/3 so that it has a denominator of 9 - you should get 3/9. That leaves us with this operation:

So now subtract the numerators (5 - 3 = 2) to get an answer of:

You can now head back to the fractions main page, or try some sample adding or subtracting questions.