Distributive Property to
Evaluate Formulas with
Decimals
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 © 2015 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: January 15, 2015
AUTHOR
Jen Kershaw
www.ck12.org
Chapter 1. Distributive Property to Evaluate Formulas with Decimals
C HAPTER
1
Distributive Property to
Evaluate Formulas with Decimals
Here you’ll learn to use the Distributive Property to evaluate formulas using decimal quantities.
Have you ever had to use a formula to figure something out? Well sometimes when you work with properties, it is
necessary.
Let’s say that you had a rectangle that was half as large as this one. That would mean that the side lengths of the
rectangle would be 6 inches and 3.5 inches.
Now what if you had two of them? What would be the area of the two rectangles?
2(6 x 3.5)
Do you know how to figure this out?
This Concept is about the distributive property and formulas. By the end of it, you will know how to tackle
this problem.
Guidance
We can also use and apply the Distributive Property when working with a formula. Let’s think about the formula for
finding the area of a rectangle.
We know that the area of a rectangle can be found by using the formula:
A = lw(length × width)
For this example, we would multiply 12 times 4 and get an area of 48 square inches.
1
www.ck12.org
How can we find the area of both of these rectangles?
You can see that they have the same width. The width is four and a half inches. However, there are two lengths.
We need to find the product of a number and a sum.
Here is our expression.
A = 4.5(12 + 7)
Now we can use the Distributive Property to find the area of these two rectangles.
A = 4.5(12) + 4.5(7)
A = 54 + 31.5
A = 85.5 square inches
Notice that we used what we have already learned about multiplying decimals and whole numbers with the
Distributive Property. When we distributed 4.5 with each length, we were able to find the sum of the products.
This gives us the area of the two rectangles.
Use what you have learned to answer these questions about formulas, area and the distributive property.
Example A
What is the formula for finding the area of a square?
Solution: A = s^2
Example B
Which property is being illustrated: 4(a + b) = 4a + 4b
Solution: The Distributive Property
Example C
What is the formula for finding the area of a rectangle?
Solution: A = length x width
Remember the rectangle from the beginning of the Concept? Now you are ready to work on that problem. Take a
look.
2
www.ck12.org
Chapter 1. Distributive Property to Evaluate Formulas with Decimals
Let’s say that you had a rectangle that was half as large as this one. That would mean that the side lengths of the
rectangle would be 6 inches and 3.5 inches.
Now what if you had two of them? What would be the area of the two rectangles?
2(6 x 3.5)
Do you know how to figure this out?
To figure this out, we have to multiply the value outside the parentheses by both values inside the parentheses.
2(6) × 2(3.5)
12 × 7 = 84
The area of the two rectangles is 84 square inches.
Guided Practice
Here is one for you to try on your own.
Use the Distributive Property to find the area of the rectangles.
Answer
First, we can write an expression to solve it.
A = 2.5(10 + 4)
Next, we can solve it.
A = 2.5(14)
A = 35
The area of the two rectangles is 35mm2 .
3
www.ck12.org
Video Review
MEDIA
Click image to the left or use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/5328
Khan Academy The Distributive Property
MEDIA
Click image to the left or use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/5308
Khan Academy: Area and Perimeter
Explore More
Directions: Practice using the Distributive Property to solve each problem.
1. 3.2(4 + 7)
2. 2.5(6 + 8)
3. 1.5(2 + 3)
4. 3.1(4 + 15)
5. 6.5(2 + 9)
6. 7.5(2 + 3)
7. 8.2(9 + 3)
8. 4(5.5 + 9)
9. 5(3.5 + 7)
10. 2(4.5 + 5)
11. 3.5(2.5 + 3)
12. 2.5(9 + 1.5)
13. 3.2(7 + 8.3)
14. 1.5(8.9 + 2.5)
15. 3.5(2.5 + 8.2)
4