Algebra 1 HS Mathematics Unit: 02 Lesson: 01 Algebraic Properties Equations are composed of two expressions set equal to one another. Although the use of algebra tiles makes it easy to visualize simple equations, the process can get very cumbersome when solving multiple-step equations. The properties of algebra can be used to simplify algebraic expressions much more efficiently and applied to solve multiple-step equations. Properties of Addition and Multiplication Property Rule Example Commutative of Addition a+b=b+a 2+3=3+2 Commutative of Multiplication ab = ba 23=32 Associative of Addition (a+b)+c = a+(b+c) (2+3)+1 = 2+(3+1) Associative of Multiplication (a b)c = a(b c) (2 3)4 = 2(3 4) Distributive a(b+c) = ab + ac or ab + ac = a(b+c) 2(x+5) = 2(x)+2(5) = 2x + 10 or 2x+10 = 2(x +5) The three properties are used to simplify algebraic expressions. The _________________________________________________ is used to expand groups and remove parentheses from expressions. The _________________________________________________ is used to change the order of the numbers so that like terms are together. The _________________________________________________ is used to associate or group like terms. ©2012, TESCCC 05/16/12 page 1 of 4 Algebra 1 HS Mathematics Unit: 02 Lesson: 01 Simplify using the algebraic properties. 1. 3(x – 4) – 2(8 – x) Distributive Commutative Associative Simplified expression 2. 4(m + n) + 3(2m – 5n) Distributive Commutative Associative Simplified expression 3. 5(2a + b) – 2(3a – 5b) Distributive Commutative Associative Simplified expression 4. -2(3p – q) + 5(2p + q) Distributive Commutative Associative Simplified expression ©2012, TESCCC 05/16/12 page 2 of 4 Algebra 1 HS Mathematics Unit: 02 Lesson: 01 5. 3(2x – 7) + 6(10x + 5) Distributive Commutative Associative Simplified expression 6. 4(5x + 1) – (4x – 3) Distributive Commutative Associative Simplified expression Expressions can be evaluated by substituting given values for the variables in the expression and using order of operations. 7. Evaluate the expressions for the given values. a. 2(3a + b) – (a – 3b), a = 3, b = - 2 b. -2(3x – y) + 5(2x + y), x = -2.2, y = 4.6 c. 3.5(2p – 8q) + 6(2.5p + 5q), p = -1, q = 3 ©2012, TESCCC d. 05/16/12 1 1 (12m + 2n) – (5m – 3n), m = 5, n = -10 4 5 page 3 of 4 Algebra 1 HS Mathematics Unit: 02 Lesson: 01 Algebraic Properties Practice Problems 1. Simplify the expressions and justify each step with the appropriate property. a. -5(4x – 3) b. -3x + 5 – 4x – 2 c. (2x + 5) + 7 d. 2(3x + 7) – (x – 4) e. 7(2x + 1) – 3(x – 5) f. 1 3 30( m – 3 5 3 4 n) – 20( m + 2 5 n) 2. Evaluate the expressions for the given values. a. 2p(3m + n) – 3p(5m – 2n); m = 5, p = 1 1 ,n= 3 2 b. 3.5(x – 1.5y) – 5.5(3x + 6y); x = 2.25, y = -1.2 3. Explain how to use the properties of addition and multiplication to perform the indicated addition or multiplication mentally in the simplest way. a. 0.65 + 1.85 + 1.35 b. 425 + 97 + 75 c. 3 3 1 1 6 2 5 8 5 d. 125 798 8 e. 2.5 6.9 4 ©2012, TESCCC 05/16/12 page 4 of 4