1. 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.

2. 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

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

4. 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

5. 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

6. 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

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

8. 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

9. Combine Like Terms: Simplify9

10. Evaluate 10

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

12. 1.1 & 1.2: Properties of Real Numbers & Algebraic Expressions
Homework:
1.1: 1, 2-6 EVEN, EVEN, ODD, 34, 36 ,37, 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.