Adding Fractions with a Common Denominator

Accompanying Resources:
Printable Study Guide, Fun Activity

What is a Common Denominator?

The denominator of a fraction is the number on the bottom. When we say that fractions have a common denominator, it means they have the same number on the bottom.

Fractions with a common denominator have the same bottom number.

The denominator of a fraction is the number of equal parts that the whole has been split into. When two fractions have a common denominator, that means both wholes have been divided into the same number of equal pieces and each piece is the same size.

Fractions with a common denominator have equal parts that are the same size.

How Do You Add Fractions?

In order to add fractions, the fractions must have a common denominator. We need the pieces of each fraction to be the same size to combine them together.

Let's say we need to add 2/7 and 3/7 together. These two fractions have the same denominator, so the equal parts that the whole has been split into are the same size. Since the pieces are all the same size, we can add these two fractions together.

$Adding fractions with common denominator.$

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$Picture$

We can add 2/7 to the 3/7 by filling in an additional 2 boxes in the diagram. We can see that this gives us a sum of 5/7.

$How do you add fractions with a common denominator?$

If you're adding two fractions with a common denominator, you can combine them together by adding the numerators together (the top numbers). The denominator will always stay the same because the size of the equal pieces does not change when you combine the two fractions together.

$Rule for adding fractions with the same denominator. Add the numerators and keep the denominator the same.$

For example, let's say you have 1/10 + 6/10. They have the same denominator, so they can be combined together. Add the numerators (1 + 6 = 7). Keep the denominator the same (the bottom number stays a 10). Remember, the denominator does not change because the sizes of the pieces stay the same. You're just counting up the total number of pieces between the two fractions.

$Adding fractions with the same denominator.$

Here's a visual way to look at the same problem:

$Using a visual aid to add fractions with same denominator$

Video

Want to see some more examples? Check out the short video below.

Practice Adding Fractions

Think you're ready to try adding fractions on your own? Click the START button below to try a practice quiz.

Ready to learn how to add or subtract fractions with different denominators?
Want to learn how to multiply fractions or divide with fractions?