1-4 Properties of Real Numbers I can identify and use the properties of real numbers

Key Terms Equivalent expressions- two algebraic

expressions are equivalent if they have the same values for all values of the variable(s).

Deductive reasoning- is the process of reasoning logically from given facts to a conclusion.

Counterexample- an example showing that a statement is false.

Properties – Examples Addition Multiplication

Commutative 2+3 = 3+ 2 (2)(3) = (3)(2)

Associative (2+3) + 4 = 2 + (3+ 4)

(23) 4 = 2(34)

Identity Properties 2+0=2 = 2

Property of Zero 2*0 = 0

Property of -1 -1 * 2 = -2

Inverse Property -2 + 2 = 0 2 = 1

Identifying Properties What property is illustrated by each statement?

Writing Equivalent Expressions

Simplify each expression

Using Deductive Reasoning and Counterexamples

Is the statement true or false? If it is false, give a counterexample. o For all real numbers , .

o For all real numbers