# 6.13: Differences of Mixed Numbers with Renaming

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

**Practice**Sums of Mixed Numbers with Renaming

### Let's Think About It

Terry is

In this concept, you will learn how to subtract mixed number by borrowing and renaming.

### Guidance

To **rename** a fraction means to take the fractions and write an equivalent fraction. Here is an example.

Sometimes when you subtract mixed numbers, you must rename the mixed numbers in a different way. Here is an example.

To subtract a fraction from a whole number, rename the whole number to a mixed number. It is similar to borrowing when subtracting. Remember that 1 can be written as a fraction.

Rename 6 into a mixed number. Borrow 1 from the whole number and rename it into a fraction with a denominator of 6.

Now rewrite the problem with 6 as a mixed number.

Then, subtract the mixed numbers.

The difference is

Sometimes you will also have to rename a mixed number if the fraction being subtracted is larger than the first fraction. Here is a subtraction problem with mixed numbers.

This problem involves subtracting a larger fraction, four-ninths, from a smaller fraction, one-ninths. To make this work, rename the first mixed number by borrowing from the whole number. Remember to add the fraction to the renamed mixed number.

Rewrite the problem with the new mixed number.

Then, subtract the mixed numbers.

Next, simplify the fraction.

The difference is

### Guided Practice

Subtract the mixed numbers.

First, rename the fractions so they they have a common denominator of 12.

Then, rename

Next, rewrite the problem and subtract the mixed numbers.

The difference is

### Examples

Subtract the mixed numbers. Answer in simplest form.

#### Example 1

First, rename the whole number as a mixed number with a denominator of 5.

Then, subtract the mixed numbers.

The difference is

#### Example 2

Rename 8 as an equivalent mixed number.

Borrow one from the whole number and rename it into a fraction.

8 is equivalent to

#### Example 3

First, rename

Then, subtract the mixed numbers.

Next, simplify the fraction.

The difference is

### Follow Up

Remember Terry five years ago?

Terry is

First, rename the fractions so they have a common denominator.

Then, rename

Next, subtract the mixed numbers.

Five years ago, Terry was

### Video Review

### Explore More

Rename each whole number as a mixed number with a fraction terms of sixths.

1. 4

2. 5

3. 6

4. 10

5. 9

6. 12

Find each difference. Rename mixed numbers as needed. Answer in simplest form.

7.

8.

9.

10.

11.

12. \begin{align*}15-6\frac{2}{10}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

13. \begin{align*}11-4\frac{1}{7}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

14. \begin{align*}18-16\frac{1}{5}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

15. \begin{align*}20-15\frac{2}{6}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

16. \begin{align*}7\frac{1}{6}-4\frac{3}{6}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

17. \begin{align*}9\frac{1}{5}-3\frac{4}{5}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

18. \begin{align*}10\frac{1}{8}-4\frac{3}{8}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

19. \begin{align*}15\frac{1}{9}-8\frac{4}{9}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

20. \begin{align*}17\frac{4}{7}-9\frac{6}{7}=\underline{\;\;\;\;\;\;\;\;\;}\end{align*}

### Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 6.13.

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### Image Attributions

In this concept, you will learn how to subtract mixed number by borrowing and renaming.