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

2. 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

3. 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.

4. 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.

5. Example 1.) Simplify 21 + 3 + 10 24 + 10 21 + 1334

6. Example 2.) 50  9  2  950  9  2  9 450  2  9100  81 900  9 8100 8100

7. Example 3.) 4 + 5y + 3 7 + 5y

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

9. 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

10. Oral Ex Page 46-47 1-12

11. Homework Written Ex Page 47 1-27 even