Page 585 - Basic College Mathematics with Early Integers

562 C HAPTE R 8 I INTRODUCTION TO ALGEBRA

Properties of Addition and Multiplication
If a, b, and c are numbers, then
a + b = b + a Commutative property of addition
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a b = b a Commutative property of multiplication
That is, the order of adding or multiplying two numbers can be changed without
changing their sum or product.
(a + b) + c = a + (b + c) Associative property of addition
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(a b) c = a (b c) Associative property of multiplication
That is, the grouping of numbers in addition or multiplication can be changed
without changing their sum or product.

• Examples of these properties are
2 + 3 = 3 + 2 Commutative property of addition
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7 9 = 9 7 Commutative property of multiplication
(1 + 8) + 10 = 1 + (8 + 10) Associative property of addition
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(4 2) 3 = 4 (2 3) Associative property of multiplication
• These properties are not true for subtraction or division.

PRACTICE 6 Example 6 Simplify: 2y - 6 + 4y + 8
Simplify: 8m + 5 + m - 4
Solution: We begin by writing subtraction as the addition of opposites.

2y - 6 + 4y + 8 = 2y + 1-62 + 4y + 8
= 2y + 4y + 1-62 + 8 Apply the commutative property of addition.
= 12 + 42y + 1-62 + 8 Apply the distributive property.
= 6y + 2 Simplify.

Work Practice 6

PRACTICE 7–10 Examples Simplify each expression by combining like terms.
Simplify each expression by
7. 6x + 2x - 5 = 8x - 5
combining like terms.
8. 4x + 3 - 5x + 2x = 4x - 5x + 2x + 3
7. 7y + 11y - 8
= 1x + 3 or x + 3
8. 2y - 6 + y + 7y
9. 1.2y + 10 - 5.7y - 9 = 1.2y - 5.7y + 10 - 9
9. 3.7x + 5 - 4.2x + 15
=-4.5y + 1
10. -9y + 2 - 4y - 8x
+ 12 - x 10. 2x - 5 + 3y + 4x - 10y + 11 = 6x - 7y + 6
Work Practice 7–10

Objective Multiplying Expressions

We can also use properties of numbers to multiply expressions such as 3(2x). By the Copyright 2012 Pearson Education, Inc.
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associative property of multiplication, we can write the product 3(2x) as 13 22x,
which simplifies to 6x.
Answers
6. 9m + 1 7. 18y - 8 8. 10y - 6
9. -0.5x + 20 10. -13y - 9x + 14