34 Chapter 1 Real Numbers and Algebraic Expressions Objective 1 Examples Find the additive inverse (or opposite) and multiplicative inverse (or reciprocal) of each number. Assume any variables are nonzero. Problems Additive Inverse Multiplicative Inverse 1a. -6 -(-6) = 6 1 - 6 =- 1 6 1b. 3 4 -a3 4 b =- 3 4 1 3 4 = 1 · 4 3 = 4 3 1c. 2x -(2 x)=-2x 1 2x = 1 2x 1d. -3y -(-3y) = 3y 1 -3y =- 1 3y 1e. x 7 -a x 7 b =- x 7 1 x 7 = 1 · 7 x = 7 x Student Check 1 Find the additive inverse (or opposite) and multiplicative inverse (or reciprocal) of each number. Assume any variables are nonzero. a. -10 b. 7 8 c. 4y d. -9b e. a 3 The Commutative, Associative, and Distributive Properties Additional properties of the real numbers are ones that relate to how we add and multiply them. These properties form the foundation of how we work with algebraic expressions. • The commutative property of the real numbers states that the order in which we add real numbers or multiply real numbers doesn’t change the result. • The associative property of the real numbers states that the way numbers are grouped when they are added or multiplied doesn’t change the outcome. Commutative Properties Associative Properties Examples (a = 2, b = 3, c = 4) Addition For all real numbers a and b, a + b = b + a For all real numbers a, b, and c, a + (b + c) = (a + b) + c 2 + 3 = 3 + 2 = 5 2 + (3 + 4) = (2 + 3) + 4 2 + (7) = (5) + 4 9 = 9 Multiplication For all real numbers a and b, a · b = b · a For all real numbers a, b, and c, (a · b) · c = a · (b · c) 2 · 3 = 3 · 2 = 6 (2 · 3) · 4 = 2 · (3 · 4) (6) · 4 = 2 · (12) 24 = 24 The distributive property illustrates that a factor can be distributed over a sum of numbers. Objective 2 ▶ Apply the commutative, associative, and distributive properties.
hendricks_intermediate_algebra_1e_ch1_3
To see the actual publication please follow the link above