2-1 Basic Assumptions Objective: To use number properties to simplify expressions.

Closure Property For all real numbers a and b: a + b is a unique real number ab is a unique real number Unique – one exists and it is the only one When you add or multiply real numbers, the result is always a real number

Commutative Property For all real numbers a and b: a + b = b + a ab = ba The order in which you multiply or add numbers does not affect the result.

Associative Property For all real numbers a, b, and c (a + b) + c = a + (b + c) (ab)c = a(bc) When you add or multiply three or more real numbers, the grouping of the numbers does not affect the result.

Example 1.) Simplify

Example 2.) 50  9  2  950  9  2   2  9100  

Example 3.) 4 + 5y y

Example 4.) (5a)(3b)(4c) (5  3  4)(abc) 60abc

Properties of Equality For all real numbers a, b, and c – Reflexive property a = a – Symmetric property If a = b then b = a – Transitive property If a = b and b = c then a = c

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Homework Written Ex Page even