Adding Fractions

Fractions are types of numbers that represent parts of a whole number. For example, 1/2 of a burger is half of a burger, because the whole burger has been divided into two equal parts. For more information on fractions, please check out: what is a fraction?

In this article, we will be working with these types of numbers – in particular, how to add in various instances.

Adding Fractions With a Common Denominator

To add fractions with a common denominator (if you recall, this is the bottom number), you need to add the numerators without converting the denominator yet. Here are examples of some equations with fractions containing common denominators being added:

1/2 + 1/2 = 2/2 (1)
4/6 + 1/6 = 5/6
4/12 + 1/12 = 5/12

For example, if I have a fraction with a numerator of 6, and the other fraction’s numerator is 2, but both of them have a denominator of 11, then we just have to add them. 6 + 2 = 8, so the numerator of the sum of the two fractions is 8. The denominator of the fractions added in this case is still 11, as we do not have to change anything with the common denominator.

Sometimes, you will need to add more than 2 numbers, perhaps 3, 4, or even 5+. In this case, the method is very similar – you will just have to do it more times.

1/2+3/2+5/2 = 9/2 (convert to mixed number) because 1+3+5=9, and we keep the denominator of 2.
1/5+1/5+2/5 = 4/5 because 1+1+2=4 and we keep the denominator of 5.

Why? This does make sense when thinking deeper. For instance, if you have a bucket of 1/5-sized pieces of something, if you grab a handful of 3 and then one more, you would have 4 total pieces, all the same size at 1/5. Therefore, you would have 4/5.

NOTE: In some cases, when we add fractions we will get improper fractions, where you may need to convert to a mixed number.

Uncommon Denominators: Converting to a Common Denominator

What if you need to convert the denominators, because the two fractions have different denominators?

Coming soon!