Products of Three Fractions
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 18, 2014
AUTHOR
Jen Kershaw
www.ck12.org
C HAPTER
Chapter 1. Products of Three Fractions
1 Products of Three Fractions
Here you’ll learn to multiply three fractions.
Have you ever become so interested in something that you forgot everything else? Well, this has happened to Julie.
Julie has become so interested in the rainforest that she hasn’t been keeping up on her math homework. Her mom
found out, and as a result, Julie has to stay in until her work is all completed. Julie was moving right along until she
got to a section on multiplying several fractions at one time. Then she got stuck.
Here is the problem Julie was working on.
3
5
× 41 × 56
Julie isn’t sure what to do from here.
This Concept is all about multiplying three fractions. By the end of it, you will know just how to help Julie.
Guidance
How do we multiply three fractions?
Multiplying three fractions is just a bit more complicated than multiplying two fractions. The procedure is the same,
you multiply the numerators and the denominators and up with a new fraction.
The key to multiplying three fractions is to simplify first, like we learned in the last Concept.
This way, you won’t end up with a fraction that is too large when multiplying or is challenging to simplify at the
end.
1 2 4
× × =
4 6 5
To start, let’s only look at the first two fractions.
1 2
×
4 6
We start by simplifying. We can simplify these two fractions in two different ways. We can either cross simplify the
two and the four with the GCF of 2, or we can simplify two-sixths to one-third.
Let’s simplify two-sixths to one-third. Now rewrite the problem with all three fractions.
1
www.ck12.org
1 1 4
× × =
4 3 5
Next, we can multiply and then simplify, or we can look and see if there is anything else to simplify. One-fourth and
one-third are in simplest form, four-fifths is in simplest form. Our final check is to check the diagonals.
1 1 4
× × =
4 3 5
The two fours can be simplified with the greatest common factor of 4. Each one simplifies to one.
1 1 1
1
× × =
1 3 5 15
Our final answer is
1
15 .
Let’s look at another one.
5
7
3
× × =
9 14 5
To start simplifying, look at the fractions themselves and the diagonals. You can see right away that sevenfourteenths can be simplified to one-half. Also, the fives simplify with the GCF of 5. Finally, the 3 and 9
simplify with the GCF of 3.
13
7
×
=
39
1
5
14
1 1 1 1
× × =
3 2 1 6
15
Our final answer is 16 .
2
×
www.ck12.org
Chapter 1. Products of Three Fractions
Practice finding these products. Be sure to simplify.
Example A
1
5
× 65 × 12 =
Solution:
1
12
Example B
8
9
× 43 × 13 =
Solution:
2
9
Example C
6
7
7
2
× 14
× 10
=
Solution:
3
35
Now back to Julie and her homework.
Julie has become so interested in the rainforest that she hasn’t been keeping up on her math homework. Her mom
found out, and as a result, Julie has to stay in until her work is all completed. Julie was moving right along until she
got to a section on multiplying several fractions at one time. Then she got stuck.
Here is the problem Julie was working on.
3
5
× 41 × 56
Julie isn’t sure what to do from here.
First, we can simplify the fives and then look at what we have.
3
1
× 41 × 16
Next, we multiply across.
1
8
This is our answer.
Vocabulary
Product
the answer to a multiplication problem.
3
www.ck12.org
Guided Practice
Here is one for you to do on your own.
Multiply the following fractions. Be sure your answer is in simplest form.
5
6
× 42 × 69
Answer
It makes the most sense to simplify the second two fractions before multiplying.
2
4
6
9
=
=
1
2
2
3
Now we can rewrite the problem.
5
6
× 21 × 23
Next, simplify the twos.
5
6
× 11 × 13
Our answer is
5
18 .
Video Review
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/54816
James Sousa: Ex: Multiplying Three Fractions
Explore More
Directions: Multiply the following fractions. Be sure that your answer is in simplest form.
1
2
1
6
1
9
× 13 × 14 =
× 23 × 18 =
6.
4
5
1
4
3
4
7.
1
4
× 56 × 23 =
8.
3
4
1
2
× 57 × 12 =
1.
2.
3.
4.
5.
9.
10.
4
× 13 × 24 =
× 23 × 34 =
× 23 × 46 =
× 27 × 16 =
4
× 45 × 10
=
9
10
× 56 × 12 =
www.ck12.org
11.
6
7
× 23 × 89 =
12.
3
4
8
× 79 × 11
=
13.
4
5
6
× 12
× 23 =
14.
3
4
8
9
9
× 10
× 56 =
15.
Chapter 1. Products of Three Fractions
1
× 11
12 × 2 =
5