1.1 & 1.2: Properties of Real Numbers & Algebraic Expressions

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Presentation transcript:

1.1 & 1.2: Properties of Real Numbers & Algebraic Expressions If you would be a real seeker after truth, it is necessary that at least once in your life you doubt, as far as possible, all things.

Exploring Real Numbers Real Numbers: Collection of ALL Rational and Irrational Numbers. Rational Numbers: Any number that can be written in the form Irrational Numbers: Can not be written in the form Integers Whole Numbers Natural Numbers

Ordering and Graphing on a Number Line Ex1) 1 2 3 4 5 -5 -4 -3 -2 -1

Opposite and Reciprocal The opposite of a is –a. the opposite of 2 is -2 The reciprocal of a is . the reciprocal of 5 is the reciprocal of is 2

Properties of Real Numbers: Let a, b, and c represent real numbers Property Addition Multiplication Commutative a + b = b + a ab = ba Associative (a + b) + c = a + (b + c) (ab)c = a(bc) Identity a + 0 = a a·1 = a Inverse a + (-a) = 0 a·(1/a) = 1, a≠ 0 Distributive a(b +c) = ab +ac

Properties of Real Numbers: Ex2) 8 + (-8) = 0 Inverse Property of Addition Ex3) (2·5) ·(-8) = (2)·(5·-8) Associative Property of Multiplication Ex4) (4+1) ·3 = (1+4) ·3 Commutative Property of Addition

Absolute Value A number’s distance from zero. REMEMBER: DISTANCE IS ALWAYS POSITIVE! 7

Algebraic Expressions: Vocabulary 15x2 + 6y Variable: a symbol that represents one or more numbers (x, y) Algebraic Expression: an expression that contains one or more variables (15x2 + 6y) Term: a number, variable, or the product of a number and one or more variables (15x2, 6y) Coefficient: The numerical factor in a term (15, 6) Evaluate: Substituting numbers for variables in an expression and following order of operations 8

Combine Like Terms: Simplify 9

Evaluate 10

Ex14) What is the perimeter of the figure? Challenge Ex14) What is the perimeter of the figure? 11

1.1 & 1.2: Properties of Real Numbers & Algebraic Expressions Homework: 1.1: 1, 2-6 EVEN, 12-16 EVEN, 25-33 ODD, 34, 36 ,37, 48-54 EVEN 1.2: 1-11 odd, 22, 27, 31, 33, 36, 41, 43, 44 If you would be a real seeker after truth, it is necessary that at least once in your life you doubt, as far as possible, all things.