How do you compare and use the properties of real numbers?

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Presentation transcript:

How do you compare and use the properties of real numbers? Section 1-3 & 1-4

Vocabulary Square root Perfect Square- Radical symbol Radicand The square of an integer.

Vocabulary Inequality- Examples: <, >, ≤, or ≥ A mathematical sentence that compares the values of 2 expressions using an inequality symbol. Deductive Reasoning- Process of reasoning logically from given facts to a conclusion. An example showing that a statement is false Counterexample-

Examples

Examples To which subsets of the real numbers does each number belong? 15 -1.4583

Examples Simplify each expression. 5 ( 3n) (4 + 4b) -2

Properties of Real Numbers Commutative Property Addition: a + b = b + a Multiplication: ab = ba Associative Property Addition: (a + b) + c = a + (b + c) Multiplication: (ab) c = a (bc)

Properties of Real Numbers Identity Property Addition: a + 0 = a Multiplication: a * 1 = a Zero Property of Multiplication: a * 0 = 0 Multiplication Property of -1: -1 * a = -a

Example Is the statement true or false? If false, give a counterexample. For all real numbers a and b , a · b = b + a. For all real numbers a, b, and c, (a + b) + c = b + (a+c)