Download The Distributive Property and Common Factors

The Distributive Property
and Common Factors
Name
Chapter 6, Lesson 5A
Objective: To use the Distributive Property to rewrite addition expressions
as multiplication expressions
Sometimes it can be helpful to rewrite an
addition expression as a multiplication
expression.
Rewrite (36 # 16) as a multiple of a sum of
two whole numbers with no common factor.
Distributive Property: Multiplying a sum
by a number is the same as multiplying
each addend by that number and adding
the products.
Example: 2 " (3 # 5) ! (2 " 3) # (2 " 5)
You can use the Distributive Property to rewrite
an expression as a product, if the expression has
addends with a common factor.
1 List all the factors of each number. Find the common factors
and then choose the Greatest Common Factor (GCF) of the two addends.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 16: 1, 2, 4, 8, 16
Common factors: 1, 2, 4
GCF: 4
2 Write each addend as a multiple of the GCF.
Copyright © by William H. Sadlier, Inc. All rights reserved.
36 ! 4 " 9
16 ! 4 " 4
3 Use the Distributive Property to rewrite the expression (36 # 16).
36
#
16
(4 " 9) # (4 " 4)
4 " (9 # 4)
So, (36 # 16) ! 4 " (9 # 4).
Practice
Rewrite as a multiple of a sum of two whole numbers with no common factor.
1. 32 # 12
2. 48 # 6
3. 18 # 27
4"(
#
)
6"(
#
)
9"(
#
)
Discuss and Write
4. Julia and Ryan are measuring two rooms that are 15 feet wide. One room
is 12 feet long and the other is 10 feet long. They need to find the total
area. Julia finds the areas of both rooms and then adds them together.
Ryan multiplies the width by the sum of the lengths of the rooms. Both are
correct. Why?
Grade 6, Lesson 6-5A
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The Distributive Property
and Common Factors
Name
Chapter 6, Lesson 5A
Practice
Rewrite as a multiple of a sum of two whole numbers with no common factor.
6. 21 ! 56
7. 18 ! 66
5. 15 ! 35
"(
!
)
"(
!
)
"(
8. 12 ! 27
9. 28 ! 52
10. 14 ! 40
11. 38 ! 12
12. 55 ! 10
13. 28 ! 24
!
)
Rewrite each product as the sum of two numbers.
14. 3 " (5 ! 8)
15. 7 " (7 ! 4)
16. 6 " (5 ! 6)
Problem Solving
17. Al has a bag of 18 snacks and a bag of
24 snacks. What is the greatest number
of people who can share both kinds of
snacks equally without any left over?
18. Denise wants to rewrite 37 ! 39 as 3 times
a sum of two whole numbers. Can she do
this? Explain why or why not.
19. Rose rewrites a sum of two numbers as
3 " (11 ! 9). What sum did she start with?
How do you know?
20. To find (8 " 28) ! (8 " 72), Edward
rewrites the expression as 8 " 100. Does
this makes sense? Explain why or why not.
Test Preparation
21. Ralph uses the Distributive Property to simplify an addition
expression.
a. The simplified expression is 17 " (2 ! 8). What is the
addition expression?
b. Why is the simplified expression easier to evaluate?
226
Grade 6, Lesson 6-5A
5106-6_WB06_226 226
Copyright © by William H. Sadlier, Inc. All rights reserved.
Solve. Use a strategy that works best for you. Show your work.
For additional Practice, go to page 277 in this Workbook.
Then go to Lesson 6-6, pages 188–189 in the Student Book.
2/12/13 1:10 PM