Differences of Mixed Numbers
without Renaming
Jen Kershaw
Say Thanks to the Authors
Click http://www.ck12.org/saythanks
(No sign in required)
To access a customizable version of this book, as well as other
interactive content, visit www.ck12.org
CK-12 Foundation is a non-profit organization with a mission to
reduce the cost of textbook materials for the K-12 market both
in the U.S. and worldwide. Using an open-content, web-based
collaborative model termed the FlexBook®, CK-12 intends to
pioneer the generation and distribution of high-quality educational
content that will serve both as core text as well as provide an
adaptive environment for learning, powered through the FlexBook
Platform®.
Copyright © 2014 CK-12 Foundation, www.ck12.org
The names “CK-12” and “CK12” and associated logos and the
terms “FlexBook®” and “FlexBook Platform®” (collectively
“CK-12 Marks”) are trademarks and service marks of CK-12
Foundation and are protected by federal, state, and international
laws.
Any form of reproduction of this book in any format or medium,
in whole or in sections must include the referral attribution link
http://www.ck12.org/saythanks (placed in a visible location) in
addition to the following terms.
Except as otherwise noted, all CK-12 Content (including CK-12
Curriculum Material) is made available to Users in accordance
with the Creative Commons Attribution-Non-Commercial 3.0
Unported (CC BY-NC 3.0) License (http://creativecommons.org/
licenses/by-nc/3.0/), as amended and updated by Creative Commons from time to time (the “CC License”), which is incorporated
herein by this reference.
Complete terms can be found at http://www.ck12.org/terms.
Printed: November 11, 2014
AUTHOR
Jen Kershaw
www.ck12.org
C HAPTER
Chapter 1. Differences of Mixed Numbers without Renaming
of Mixed
1 NumbersDifferences
without Renaming
Here you’ll learn to subtract mixed numbers without renaming them.
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 6 10
16 feet long.
2
Travis needs to cut 3 16
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.
2
10
− 3 16
=
6 16
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.
3
8
1
− 4
8
6
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.
3 1 2
− =
8 8 8
Next, we subtract the whole numbers. 6 - 4 is 2. Our answer is 2 28 . However, our work is not finished because
we can simplify two-eighths.
2 1
=
8 4
Our final answer is 2 41 .
Solve a few of these on your own. Be sure that your final answer is in simplest form.
Example A
4 45 − 3 15 =
Solution: 1 35
1
www.ck12.org
Example B
6 46 − 1 26 =
Solution: 5 26 = 5 13
Example C
7 89 − 4 49 =
Solution: 3 49
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 6 10
16 feet long.
2
Travis needs to cut 3 16
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.
2
10
− 3 16
=
6 16
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.
8
3 16
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 3 21 feet.
Vocabulary
Mixed Number
a number that has a whole number and a fraction.
Guided Practice
Here is one for you to try on your own.
39
12 46
49 − 10 39 =
Answer
To find the difference, we have to subtract the wholes and the parts separately.
7
2 49
But our work is not done because the fraction part of this mixed number can be simplified.
Our answer is 2 17 .
Video Review
2
www.ck12.org
Chapter 1. Differences of Mixed Numbers without Renaming
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/5376
Khan Academy Subtracting Mixed Numbers
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/5382
James Sousa Subtracting Mixed Numbers
Explore More
Directions: Subtract the following mixed numbers. Be sure that your answer is in simplest form.
1. 6 29 − 4 91 =
1
6
− 2 10
=
2. 5 10
3. 8 28 − 4 81 =
4. 12 84 − 4 28 =
9
2
5. 6 10
− 4 10
=
3
6
− 5 15
=
6. 15 15
2
4
− 7 12
=
7. 18 12
1
5
− 19 20
=
8. 20 20
9. 5 25 − 1 31 =
10. 8 21 − 4 14 =
11. 6 31 − 2 16 =
2
12. 5 41 − 3 10
=
13. 8 31 − 2 14 =
14. 12 43 − 2 13 =
15. 18 96 − 12 14 =
3