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134 Chapter 3 Solving Equations Example 2 Solution: a. 6 p p 6 Commutative property of addition b. 5 n n 152 or n 5 Commutative property of addition c. y172 7y Commutative property of multiplication d. xy yx Commutative property of multiplication Recall from Section 1.3 that subtraction is not a commutative operation. However, if we rewrite the difference of two numbers a b as a 1b2, then we can apply the commutative property of addition. For example: Rewrite as addition of the opposite. Apply the commutative property of addition. x 9 x 192 9 x Example 3 demonstrates the associative properties of addition and multiplication. Applying the Associative Properties Example 3 Use the associative property of addition or multiplication to rewrite each expression. Then simplify the expression. a. 12 145 y2 b. 517w2 Solution: a. Apply the associative property of addition. Simplify. 12 145 y2 112 452 y 57 y b. Apply the associative property of multiplication. Simplify. 517w2 15 72w 35w Note that in most cases, a detailed application of the associative properties will not be given. Instead the process will be written in one step, such as: 12 145 y2 57 y, 517w2 35w Example 4 demonstrates the use of the distributive property. Answers 5. 3 x 6. 2z 7. p 1122 or p 12 8. ba 9. 16 142 x; 20 x 10. 12 82w; 16w Example 2 demonstrates the use of the commutative properties. Applying the Commutative Properties Apply the commutative property of addition or multiplication to rewrite the expression. a. 6 p b. 5 n c. y172 d. xy Skill Practice Apply the commutative property of addition or multiplication to rewrite the expression. 5. x 3 6. z 122 7. 12 p 8. ab Skill Practice Use the associative property of addition or multiplication to rewrite the expression. Then simplify the expression. 9. 6 114 x 2 10. 218w2


miller_prealgebra_2e_ch1_3
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