Section 1.6 Properties of Real Numbers and Simplifying Expressions 97 1. Commutative Properties of Real Numbers When getting dressed in the morning, it makes no difference whether you put on your left shoe first and then your right shoe, or vice versa. This example illustrates a process in which the order does not affect the outcome. Such a process or operation is said to be commutative. In algebra, the operations of addition and multiplication are commutative because the order in which we add or multiply two real numbers does not affect the result. For example: 10 5 5 10 and 10 5 5 10 10 5 5 10 and 10 5 5 10 ⎧⎨⎩ ⎧⎨⎩ ⎧⎨⎩ ⎧⎨⎩ Concepts 1. Commutative Properties of Real Numbers 2. Associative Properties of Real Numbers 3. Identity and Inverse Properties of Real Numbers 4. Distributive Property of Multiplication over Addition 5. Simplifying Algebraic Expressions Answer 1. 9 152 2. x 7y It is important to note that although the operations of addition and multiplication are commutative, subtraction and division are not commutative. For example: 5 2 Applying the Commutative Property of Addition Example 1 Use the commutative property of addition to rewrite each expression. a. 3 172 b. 3x3 5x4 Solution: a. 3 172 7 132 b. 3x3 5x4 5x4 3x3 Recall that subtraction is not a commutative operation. However, if we rewrite a b, a 1b2, as we can apply the commutative property of addition. This is demonstrated in Example 2. 1 2 5 Classroom Example: p. 107, Exercise 16 Commutative Properties of Real Numbers If a and b are real numbers, then 1. a b b a commutative property of addition 2. ab ba commutative property of multiplication Skill Practice Use the commutative property of addition to rewrite each expression. 1. 5 9 2. 7y x Properties of Real Numbers and Simplifying Expressions Section 1.6
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