1. 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.

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

3. 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
= 0
5) x + y = y + x
6) (m + n) + o = m + (n + o)
7) – 5x = 5(3 – x)

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

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

6. (taken directly from AzMERIT practice test)

7. Name Date Period 1.8 HW – worksheet