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6.13: Differences of Mixed Numbers with Renaming

Difficulty Level: At Grade Created by: CK-12
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Practice Sums of Mixed Numbers with Renaming
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Let's Think About It

Terry is 614 feet tall. Five years ago, she was 113 feet shorter. How tall was Terry five years ago?

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.

13=39

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

6456

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.

1=22 or 33 or 44. . .

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

6=566

Now rewrite the problem with 6 as a mixed number.

  566456

Then, subtract the mixed numbers.

  566456  116

The difference is 116.

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. 

  619349

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. 

6599+19=599=5109

Rewrite the problem with the new mixed number.

  5109349

Then, subtract the mixed numbers.

  5109349  269

Next, simplify the fraction.

269=223

 The difference is 223.

Guided Practice

Subtract the mixed numbers.

813234=

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

 84122912=716122912

Then, rename 8412. You cannot subtract 912 from 412Borrow 1 from the whole number 8 and rename the mixed number. 

 8412=71212+412=71612

Next, rewrite the problem and subtract the mixed numbers.

716122912=5712

The difference is 5712.

Examples

Subtract the mixed numbers. Answer in simplest form.

Example 1

7215=

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

7=655

7215=655215

Then, subtract the mixed numbers.

 655215=445

The difference is 445.

Example 2

Rename 8 as an equivalent mixed number.

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

 8=788

8 is equivalent to 788.

Example 3

914334=

First, rename 914. Borrow 1 from 9 and add it to the fraction.

914=854

914334=854334

Then, subtract the mixed numbers. 

854334=524

Next, simplify the fraction.

 524=512

The difference is 512.

Follow Up

Remember Terry five years ago?

Terry is 614 feet tall, but was 113 feet shorter five years ago. Subtract to find Terry's height five years ago. 

614113=

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

614113=63121412

Then, rename 6312. Borrow 1 from 6 and add it to the fraction.

6312=51512

Next, subtract the mixed numbers.

515121412=41112  

Five years ago, Terry was 41112 feet tall. 

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. 3214=

8. 7226=

9. 10415=

10. 8249=

11. 14623=

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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Sep 24, 2015
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