Adding and Subtracting Fractions

Adding Fractions with Common Denominators

Fraction addition
works almost exactly the same way as normal addition! Let’s go through an example
of fraction addition.
You ate 3/8 of a pizza, and your friend ate 2/8 of the pizza. How much of the pizza
was eaten in all?

The problem would look like this:

=

Notice that we add the numerators (top numbers) but we leave the denominators (bottom
numbers) alone. This is because, when adding fractions with the same (common) denominators,
the denominators stay the same.

Warning! Many people make a common mistake here. Some think that you add the numerators
together, and then add the denominators together. It’s a trap! Don’t fall into this
trick that math is playing on you! You only add the numerators, the denominators
really do stay the same.

Let’s try another one:

Did you get 7/10? You’re right! Great job!

Adding Fractions with Different Denominators

(Note: if you are trying to add fractions with different denominators, please read
the section on
How to Find Common Denominators first. Thanks!)

Adding fractions with different denominators is similar to adding fractions with
the same denominators, but you have to do one important thing before you can add
them . . . you have to find a common denominator.

An addition problem with differing denominators would look like this:

First, find common denominators by finding the least common multiple
between 2 and 3, which is 6. Now, expand each fraction so that they each have denominators
of 6, like this:

Now that you have common denominators, you can set up your fraction addition, like
this:

Check to see if the fraction needs to be reduced (this one does not). If it does
not need to be reduced, you’re done!

Subtracting Fractions with Common Denominators

Subtracting
fractions is very similar to adding fractions, except you’ll be using a different
operation. Keep in mind that you will subtract the two numerators, but the denominator
will stay the same. It will look like this:

Notice here that the numerators subtracted, 7-4 = 3, but the denominator stayed
the same (10). This will happen every time you subtract fractions with the same
denominator.

Subtracting Fractions with Different Denominators

(Note: if you are trying to subtract fractions with different denominators, please
read the section on
How to Find Common Denominators first. Thanks!)

Subtracting fractions with different denominators works very similarly to adding
fractions with different denominators. Let’s say you have a problem that looks like
this:

First, you need to find common denominators. For this problem, we find our common
denominator to be 4, so we change both fractions to have denominators of 4. Then,
our problem looks like this:

Now, you subtract the numerators, so 3 – 2 = 1. Keep the denominator the same: 4.
You do not subtract the denominators.

Thus, your answer is 1/4. Make sure your answer is reduced all the way (this one
doesn’t need to be reduced because it’s in its simplest form) and you’re done!