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!