# 6.4: Sums of Fractions with Like Denominators

**At Grade**Created by: CK-12

**Practice**Sums of Fractions with Like Denominators

Have you ever had to add small measurements or fractions to put something together?

Having successfully completed the estimation project, Travis is off to do some more measuring for his uncle. Uncle Larry has told Travis that he needs to make some measurements on a wall in what will be the kitchen. Uncle Larry shows Travis which wall to mark on and hands him a ruler and a pencil.

“I need you to make a small mark at \begin{align*}\frac{1}{8}''\end{align*}, another small mark at \begin{align*}\frac{2}{8}''\end{align*} past the first, and a large mark at \begin{align*}\frac{3}{8}''\end{align*} past the second mark,” says Uncle Larry. “Then continue that pattern across the wall. The most important marks are the large ones, please be sure that those marks are in the correct place. The large marks will indicate where I need to put brackets later.”

“Okay,” says Travis, smiling. He is confident that he knows what he is doing.

Uncle Larry goes off to work on another project and leaves Travis to his work. “Hmmm,” thinks Travis to himself. “If I write in all of the large marks first, I will be done a lot quicker. Then I can go back and do the small ones. I can add these fractions to figure out at what measurement I need to draw in the large marks.”

**Travis has a plan, but will his plan work? If Travis adds up the fractions, at what measurement will the large marks be drawn?** **This Concept will teach you all that you need to know to answer each of these questions.**

### Guidance

You have already learned how to add whole numbers and how to add decimals, now you are going to learn how to add fractions. In this Concept, you will learn all about adding fractions with ** like** or

**.**

*common denominators*
**What is a like denominator?**

**A like denominator is a denominator that is the same. This means that the whole has been divided up into the same number of parts.** If the denominator of two fractions is a five, then both of those fractions have been divided into five parts. The numerators may be different, but the denominators are the same.

This picture shows two different fractions with like denominators.

**Now let’s say that we want to add these two fractions. Because the denominators are common, we are adding like parts. We can simply add the numerators and we will have our new fraction.**

\begin{align*}\frac{2}{6} + \frac{4}{6} = \frac{6}{6}\end{align*}

Here it is as a picture.

We combined both of these fractions together to have a fraction we can call six-sixths.

**What about simplifying?**

We must simplify or reduce all of our answers. In this example, when we have six out of six parts, we have one whole. You can see that one whole figure is shaded in. We simplify our answer and then our work is complete.

**Our final answer is** \begin{align*}\frac{6}{6} = 1\end{align*}.

Let’s look at another one. We can work on this one without looking at a picture.

\begin{align*}\frac{2}{8} + \frac{4}{8} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*} **The first step is to make sure that you have like denominators.** In this example, both denominators are 8, so we can add the numerators because the denominators are alike. **Our next step is to add the numerators.**

\begin{align*}2 + 4 = 6\end{align*}

**We put that number over the common denominator.**

\begin{align*}\frac{6}{8}\end{align*}

**Our last step is to see if we can simplify our answer.** In this example, 6 and 8 have the greatest common factor of 2. We divide both the numerator and the denominator by 2 to simplify the fraction.

\begin{align*}\frac{6 \div 2}{8 \div 2} = \frac{3}{4}\end{align*}

**Our final answer is** \begin{align*}\frac{3}{4}\end{align*}.

Now it is time for you to try a few of these on your own. Be sure that your answer is in simplest form.

#### Example A

\begin{align*} \frac{1}{7} + \frac{2}{7} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

**Solution:\begin{align*} \frac{3}{7}\end{align*}**

#### Example B

\begin{align*} \frac{3}{9} + \frac{1}{9} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

**Solution: \begin{align*} \frac{4}{9}\end{align*}**

#### Example C

\begin{align*} \frac{2}{10} + \frac{3}{10} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

**Solution: \begin{align*} \frac{5}{10} = \frac{1}{2}\end{align*}**

Now let's go back and help Travis with his dilemma.

**For Travis to follow his plan, he needs to add up the fractions to figure out what fraction of an inch should be between the large marks for the brackets.**

\begin{align*}\frac{1}{8} + \frac{2}{8} + \frac{3}{8} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

These fractions all have common denominators, so Travis can simply add the numerators.

\begin{align*}1 + 2 + 3 = 6\end{align*}

Next, we can put this answer over the common denominator.

\begin{align*}\frac{6}{8}''\end{align*}

**Travis needs to make a large mark every six-eighths of an inch. It will be a lot simpler to measure the marks if Travis simplifies this fraction.**

\begin{align*}\frac{6}{8} = \frac{3}{4}\end{align*}

**Travis needs to make a large mark every \begin{align*}\frac{3}{4}''\end{align*} of an inch. Confident in his calculations, he gets right to work.**

### Vocabulary

Here are the vocabulary words in this Concept.

- Like Denominators
- when the denominators of fractions being added or subtracted are the same.

- Simplifying
- dividing the numerator and the denominator of a fraction by its greatest common factor. The result is a fraction is simplest form.

### Guided Practice

Here is one for you to try on your own.

\begin{align*}\frac{3}{10} + \frac{2}{10} + \frac{2}{10} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

**Answer**

Our answer is \begin{align*}\frac{7}{10}\end{align*}.

### Video Review

Here are videos for review.

Khan Academy Adding and Subtracting Fractions

### Practice

Directions: Add the following fractions with common denominators. Be sure your answer is in simplest form.

1. \begin{align*}\frac{1}{3} + \frac{1}{3} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

2. \begin{align*}\frac{2}{5} + \frac{2}{5} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

3. \begin{align*}\frac{4}{7} + \frac{2}{7} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

4. \begin{align*}\frac{5}{11} + \frac{4}{11} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

5. \begin{align*}\frac{6}{10} + \frac{1}{10} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

6. \begin{align*}\frac{4}{10} + \frac{1}{10} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

7. \begin{align*}\frac{3}{4} + \frac{1}{4} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

8. \begin{align*}\frac{5}{6} + \frac{3}{6} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

9. \begin{align*}\frac{4}{9} + \frac{2}{9} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

10. \begin{align*}\frac{5}{10} + \frac{1}{10} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

11. \begin{align*}\frac{6}{13} + \frac{4}{13} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

12. \begin{align*}\frac{9}{10} + \frac{1}{10} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

13. \begin{align*}\frac{6}{9} + \frac{1}{9} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

14. \begin{align*}\frac{8}{12} + \frac{1}{12} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

15. \begin{align*}\frac{10}{20} + \frac{4}{20} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

16. \begin{align*}\frac{11}{18} + \frac{5}{18} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

Like Denominators

Two or more fractions have like denominators when their denominators are the same. "Common denominators" is a synonym for "like denominators".Simplify

To simplify means to rewrite an expression to make it as "simple" as possible. You can simplify by removing parentheses, combining like terms, or reducing fractions.### Image Attributions

Here you'll learn to add fractions with like denominators.