# 6.5: Differences of Fractions with Like Denominators

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

**Practice**Differences of Fractions with Like Denominators

Have you ever had to make something thinner? Well, Travis is spreading some ceiling plaster, and it is too thick. Take a look.

Travis has mixed some plaster and is practicing spreading it. However, the plaster is too thick. When he spreads it out, it measures \begin{align*} \frac{5}{8}\end{align*} of an inch and he needs it to measure \begin{align*} \frac{3}{8}\end{align*} of an inch. Travis needs to subtract to figure out the difference.

Here is his equation.

\begin{align*}\frac{5}{8} - \frac{3}{8} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

The only problem is that he can't remember how to subtract fractions with like denominators.

**This Concept will teach you all about subtracting fractions with like denominators.**

### Guidance

We can also subtract fractions with like denominators to find the ** difference** between the fractions. As long as the denominators are the same, the fractions are alike, and we can simply subtract the numerators.

Here is an example done with pictures.

\begin{align*}\frac{6}{8} - \frac{3}{8} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

To solve this problem, we simply subtract the numerators. The difference between six and three is three. We put that answer over the common denominator.

**Our final answer is** \begin{align*}\frac{3}{8}\end{align*}.

*We don’t need to simplify this fraction because three-eighths is already in simplest form.*

Try a few of these on your own. Simplify the difference if necessary.

#### Example A

\begin{align*}\frac{6}{7} - \frac{2}{7} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

**Solution: \begin{align*} \frac{4}{7}\end{align*}**

#### Example B

\begin{align*}\frac{5}{9} - \frac{2}{9} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

**Solution: \begin{align*} \frac{3}{9}\end{align*} = \begin{align*} \frac{1}{3}\end{align*}**

#### Example C

\begin{align*}\frac{8}{10} - \frac{4}{10} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

**Solution: \begin{align*} \frac{6}{10}\end{align*} = \begin{align*} \frac{3}{5}\end{align*}**

Now back to Travis. Here is the original problem once again.

Travis has mixed some plaster and is practicing spreading it. However, the plaster is too thick. When he spreads it out, it measures \begin{align*} \frac{5}{8}\end{align*} of an inch and he needs it to measure \begin{align*} \frac{3}{8}\end{align*} of an inch. Travis needs to subtract to figure out the difference.

Here is his equation.

\begin{align*}\frac{5}{8} - \frac{3}{8} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

Now let's find the difference. We start by subtracting the numerators and the denominators stay the same.

**The answer is \begin{align*} \frac{2}{8}\end{align*}, which simplified to \begin{align*} \frac{1}{4}\end{align*}.**

### 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.

- Difference
- the answer to a subtraction problem

### Guided Practice

Here is one for you to try on your own.

\begin{align*}\frac{9}{12} - \frac{5}{12} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

**Answer**

To solve this, we subtract the numerators and leave the denominators alone because they are alike.

\begin{align*} \frac{4}{12}\end{align*}

This answer can be simplified.

**Our final answer is \begin{align*} \frac{1}{3}\end{align*}.**

### Video Review

Here is a video for review.

Khan Academy Adding and Subtracting Fractions

### Practice

Directions: Find each difference. Be sure that your answer is in simplest form.

1. \begin{align*}\frac{6}{7} - \frac{3}{7} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

2. \begin{align*}\frac{6}{12} - \frac{4}{12} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

3. \begin{align*}\frac{13}{18} - \frac{3}{18} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

4. \begin{align*}\frac{7}{8} - \frac{6}{8} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

5. \begin{align*}\frac{4}{8} - \frac{2}{8} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

6. \begin{align*}\frac{10}{12} - \frac{6}{12} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

7. \begin{align*}\frac{11}{13} - \frac{6}{13} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

8. \begin{align*}\frac{10}{20} - \frac{5}{20} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

9. \begin{align*}\frac{16}{18} - \frac{5}{18} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

10. \begin{align*}\frac{12}{14} - \frac{2}{14} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

11. \begin{align*}\frac{8}{9} - \frac{3}{9} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

12. \begin{align*}\frac{7}{11} - \frac{3}{11} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

13. \begin{align*}\frac{9}{20} - \frac{7}{20} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

14. \begin{align*}\frac{12}{24} - \frac{8}{24} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

15. \begin{align*}\frac{7}{28} - \frac{2}{28} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

Difference

The result of a subtraction operation is called a difference.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 subtract fractions with like denominators.

Difference

The result of a subtraction operation is called a difference.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.