Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Signal-flow graph wikipedia , lookup
Linear algebra wikipedia , lookup
Polynomial ring wikipedia , lookup
Field (mathematics) wikipedia , lookup
Elementary algebra wikipedia , lookup
System of polynomial equations wikipedia , lookup
System of linear equations wikipedia , lookup
Commutative ring wikipedia , lookup
Homomorphism wikipedia , lookup
Algebraic variety wikipedia , lookup
Algebraic geometry wikipedia , lookup
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. Property Properties of Addition and Multiplication Rule Example Commutative of Addition 2+3=3+2 Commutative of Multiplication Associative of Addition 2•3=3•2 Associative of Multiplication Distributive (a + b)+c = a(b+c) (2 + 3)+1 = 2+(3+1) (a • b)c = a(b • c) (2 • 3)4 = 2(3•4) 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. Sample Problems Simplify using the algebraic properties. 1. 3(x – 4) – 2(8 – x) Distributive Commutative Associative Simplified expression (C) 2012, TESCCC 05/16/12 page 1 of 3 Algebra 1 HS Mathematics Unit: 02 Lesson: 01 Algebraic Properties 2. 4(m + n) + 3(2m – 5n) Distributive Commutative Associative Simplified expression 3. Simplify the expressions and justify each step with the appropriate property. a. 5(2a + b) – 2(3a – 5b) b. -2(3p – q) + 5(2p + q) c. 3(2x – 7) + 6(10x + 5) d. 4(5x + 1) – (4x – 3) Expressions can be evaluated by substituting given values for the variables in the expression and using order of operations. 4. 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 d. 1/4(12m + 2n) – 1/5(5m – 3n), m = 5, n = -10 5. Explain two ways the expressions could be evaluated for the given values. (C) 2012, TESCCC 05/16/12 page 2 of 3 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. 30(1/3m – 3/5n) – 20(3/4m + 2/5n) 2. Evaluate the expressions for the given values. a. 2p(3m + n) – 3p(5m – 2n); m = 5, p = 1/3, n = 1/2 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. 33/5 + 11/8 + 62/5 d. 125 × 798 × 8 e. 2.5 × 6.9 × 4 (C) 2012, TESCCC 05/16/12 page 3 of 3