# 6.11: Differences of Mixed Numbers without Renaming

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

Have you ever had to cut an extra piece off of a board? Well, Travis is doing exactly that. Take a look.

While working with his Uncle, Travis discovered that one of the boards selected was too long for the project. Travis had to take the board and cut it so that it would fit in the place allotted on the floor. First, he measured the board.

Travis discovered that the board was \begin{align*}6 \frac{10}{16}\end{align*} feet long.

Travis needs to cut \begin{align*}3 \frac{2}{16}\end{align*} feet from the board.

To figure this out, Travis knows that he needs to subtract. Here is the problem that he wrote in his notebook.

\begin{align*}6\frac{10}{16} - 3\frac{2}{16}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

Now Travis has to complete the subtract. Then he will know the length of the board.

**To complete this task, you will need to know how to subtract mixed numbers. Pay attention and this Concept will teach you everything that you need to know.**

### Guidance

Just as we can add mixed numbers, we can also subtract mixed numbers.

*The same rule applies, always subtract the fraction parts first then the whole numbers.*

\begin{align*}& \quad \ \ 6\frac{3}{8}\\ & \underline{- \quad 4\frac{1}{8}\;}\end{align*}

We start by subtracting the fractions first, and these fractions have the same denominator so we can simply subtract the numerators. Three-eighths take away one-eighth is two-eighths.

\begin{align*}\frac{3}{8}-\frac{1}{8}=\frac{2}{8}\end{align*}

Next, we subtract the whole numbers. 6 - 4 is 2. **Our answer is** \begin{align*}2\frac{2}{8}\end{align*}. **However, our work is not finished because we can simplify two-eighths.**

\begin{align*}\frac{2}{8}=\frac{1}{4}\end{align*}

**Our final answer is** \begin{align*}2\frac{1}{4}\end{align*}.

Solve a few of these on your own. Be sure that your final answer is in simplest form.

#### Example A

\begin{align*}4\frac{4}{5}-3\frac{1}{5}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

**Solution: \begin{align*}1 \frac{3}{5}\end{align*}**

#### Example B

\begin{align*}6\frac{4}{6}-1\frac{2}{6}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

**Solution: \begin{align*}5 \frac{2}{6} = 5 \frac{1}{3}\end{align*}**

#### Example C

\begin{align*}7\frac{8}{9}-4\frac{4}{9}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

**Solution: \begin{align*}3 \frac{4}{9}\end{align*}**

Have you figured out how to help Travis with the boards? Here is the original problem once again.

While working with his Uncle, Travis discovered that one of the boards selected was too long for the project. Travis had to take the board and cut it so that it would fit in the place allotted on the floor. First, he measured the board.

Travis discovered that the board was \begin{align*}6 \frac{10}{16}\end{align*} feet long.

Travis needs to cut \begin{align*}3 \frac{2}{16}\end{align*} feet from the board.

To figure this out, Travis knows that he needs to subtract. Here is the problem that he wrote in his notebook.

\begin{align*}6\frac{10}{16} - 3\frac{2}{16}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

Now Travis has to complete the subtract. Then he will know the length of the board.

To solve this problem, we can subtract the wholes and the parts separately.

\begin{align*}3 \frac{8}{16}\end{align*}

This is the answer to the subtraction problem.

But wait, our work is not done yet! You can simplify this answer.

**Our final answer is \begin{align*}3 \frac{1}{2}\end{align*} feet.**

### Vocabulary

Here are the vocabulary words in this Concept.

- Mixed Number
- a number that has a whole number and a fraction.

### Guided Practice

Here is one for you to try on your own.

\begin{align*}12\frac{46}{49} - 10\frac{39}{39}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

**Answer**

To find the difference, we have to subtract the wholes and the parts separately.

\begin{align*}2 \frac{7}{49}\end{align*}

But our work is not done because the fraction part of this mixed number can be simplified.

**Our answer is \begin{align*}2 \frac{1}{7}\end{align*}.**

### Video Review

Here are videos for review.

Khan Academy Subtracting Mixed Numbers

James Sousa Subtracting Mixed Numbers

### Practice

Directions: Subtract the following mixed numbers. Be sure that your answer is in simplest form.

1. \begin{align*}6\frac{2}{9}-4\frac{1}{9}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

2. \begin{align*}5\frac{6}{10}-2\frac{1}{10}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

3. \begin{align*}8\frac{2}{8}-4\frac{1}{8}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

4. \begin{align*}12\frac{4}{8}-4\frac{2}{8}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

5. \begin{align*}6\frac{9}{10}-4\frac{2}{10}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

6. \begin{align*}15\frac{6}{15}-5\frac{3}{15}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

7. \begin{align*}18\frac{4}{12}-7\frac{2}{12}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

8. \begin{align*}20\frac{5}{20}-19\frac{1}{20}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

9. \begin{align*}5\frac{2}{5}-1\frac{1}{3}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

10. \begin{align*}8\frac{1}{2}-4\frac{1}{4}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

11. \begin{align*}6\frac{1}{3}-2\frac{1}{6}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

12. \begin{align*}5\frac{1}{4}-3\frac{2}{10}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

13. \begin{align*}8\frac{1}{3}-2\frac{1}{4}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

14. \begin{align*}12\frac{3}{4}-2\frac{1}{3}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

15. \begin{align*}18\frac{6}{9}-12\frac{1}{4}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

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### Image Attributions

Here you'll learn to subtract mixed numbers without renaming them.