1.8 – Algebraic Proofs Objective: The student will understand real number property definitions in order to justify mathematical processes in the format of an algebraic proof.

REAL NUMBER PROPERTIES Identity: Ex: 3 + 0 = 3 or 3(1) = 3 Inverse: Ex: 3 + (-3) = 0 or 3(0) = 0 Commutative:   Ex: A + B = B = A or AB = BA

Ex: (x + y) + z = x + (y + z) or (xy)z = x(yz) Distributive Practice! Associative: Ex: (x + y) + z = x + (y + z) or (xy)z = x(yz)  Distributive Practice! 3(x – 4) = 3x – 12 7(2•5) = (7•2)5 4(1) = 4 -2 + 2 = 0 5) x + y = y + x 6) (m + n) + o = m + (n + o) 7) 15 – 5x = 5(3 – x)

Equation Properties Addition Property Subtraction Property Multiplication Property Division Property Substitution Property Reflexive Property Property of Opposites

Complete the Algebraic Proof Prove: If a=b, then ca = cb Statements: Reasons: 1. ca = ca 1. ________ 2. a = b 2. ________ 3. ca = cb 3. ________ Prove: If 2x + 3 – 11, then x = 4 Statements: Reasons: 1. 2x + 3 = 11 1. ________ 2. 2x = 8 2. ________ 3. x = 4 3. ________

(taken directly from AzMERIT practice test)

Name Date Period 1.8 HW – worksheet