LESSON
2.1 Properties and Operations
2.2
Goal: Use properties of addition and multiplication.
Georgia
Performance
Standard(s)
M8A1b
Commutative and Associative Properties
Commutative Property of
Addition
Commutative Property of
Multiplication
Words In a sum, you can
add the numbers in any
order.
Words In a product, you can
multiply the numbers in any
order.
Numbers 4 (7) 7 4
Numbers 8(5) 5(8)
Algebra a b b a
Algebra ab ba
Associative Property of
Addition
Associative Property of
Multiplication
Words Changing the grouping
of the numbers in a sum does
not change the sum.
Words Changing the grouping
of the numbers in a product
does not change the product.
Numbers
(9 6) 2 9 (6 2)
Numbers
(3 p 10) p 4 3 p (10 p 4)
Algebra
(a b) c a (b c)
Algebra
(a p b) p c a p (b p c)
Example 1
Using Properties of Addition
Distance This week, you rode in a car for 42 miles, rode a bike for
5 miles, and rode in a bus for 23 miles. Find the total distance.
Solution
The total distance is the sum of the three distances.
Use properties of
addition to group
together distances
that are easy to add
mentally.
42 5 23 (42 5) 23
(5
5
) 23
( 42 23)
42
Use order of operations.
Commutative property
of addition
Associative property
of addition
5 65
Add 42 and 23 .
70
Add 5 and 65 .
Answer: The total distance is 70 miles.
50
Georgia Active Learning Textbook, Course 3
Copyright © McDougal Littell/Houghton Mifflin Company
Using Properties of Multiplication
Example 2
Evaluate 4xy when x 8 and y 15.
( )( 15 )
[4( ⫺8 )]( 15 )
[ ⫺8 ( 4 )]( 15 )
⫺8 [( 4 )( 15 )]
⫺8 ( 60 )
Substitute for x and for y.
⫺480
Multiply ⫺8 and 60 .
4xy 4 ⫺8
Use order of operations.
Commutative property of multiplication
Associative property of multiplication
Multiply 4 and 15 .
Checkpoint Evaluate the expression when x 7 and y 25.
1. (2x y) 46
2. 4x 2y
85
4900
Using Properties to Simplify Variable Expressions
Example 3
Simplify the expression.
a. x 5 2 (x 5) 2 Use order of operations.
x (5 2)
x 7
b. 3(9y) (3 p 9)y
27y
Associative property of addition
Add 5 and 2.
Associative property of multiplication
Multiply 3 and 9.
Checkpoint Simplify the expression.
3. n 6 7
n ⫹ 13
Copyright © McDougal Littell/Houghton Mifflin Company
4. (4r)(⫺3)
⫺12r
Georgia Active Learning Textbook, Course 3
51
Identity Properties
Identity Property of
Addition
Identity Property of
Multiplication
Words The sum of a number
and the additive identity, 0,
is the number.
Words The product of a
number and the multiplicative
identity, 1, is the number.
Numbers 6 0 6
Numbers 4 p 1 4
Algebra a 0 a
Algebra a p 1 a
Example 4
Identifying Properties
Statement
Property Illustrated
a. (3 2) 4 3 (2 4)
Associative property of addition
b. 0 b b
Identity property of addition
c. 1(7) 7
Identity property of multiplication
d. cd dc
Commutative property of
multiplication
Checkpoint Identify the property that the statement illustrates.
5. (2 p 6) p 3 2 p (6 p 3)
Associative property
of multiplication
52
Georgia Active Learning Textbook, Course 3
6. q (r) r q
Commutative property
of addition
Copyright © McDougal Littell/Houghton Mifflin Company
Answer Key
Lesson 2.2
1. 21900
5. 3200
9. 248
2. 72
6. 2700
4. 13.37
7. 21600
10. 22400
13. s 1 103
16. 2192r
3. 18.7
11. 0
14. 219 1 j
17. 11.83 1 p
8. 460
12. 50
15. 263t
18. 26.1705x
19. associative property of multiplication
20. identity property of addition
22. 160,000 m
23. 9 minutes
25. 400 square yards
27. 168 cubic inches
26. $240
21. 81 ft
24. 7 lb