1. Real Number and the number Line

2. Number System Real numbers: is number that can be positive or negative and have decimal places after the point. Natural numbers: to count (1,2,3,……) Whole numbers: are the natural numbers and zero (0, 1,2,3……) Integers numbers: are the natural numbers, their appositive and zero (-2, -1, 0, 1,2,3……) Rational numbers: are all numbers you can write as a quotient of integers include terminating (0.125) and repeating (0.3333 )numbers. Irrational numbers: have decimal representation that neither terminate nor repeat

3. Classifying Real Number Example: Which subset of the real numbers does each number belong? 12 – natural number, whole number integers, rational number. -1,3456- rational number (is a terminating number) rational number.Perfect square Irrational number.Is not perfect square The rational and irrational numbers form the set of real number

4. Statement ( true or false) All negative numbers are integers. F All integers are rational numbers. T All square roots are irrational numbers. F No positive number is an integers. F

5. Properties for Simplifying Algebraic Expressions Definition of Subtraction Definition of Division Distributive property Multiplication by 0 Multiplication by 1 Opposite of a Sum Opposite of a Difference Opposite of a product Opposite of a opposite a – b = a + (-b) a : b a(b-c) = ab – ac a.0 = 0 a. 1 = a -(a + b)= -a – b -(a – b)= -a + b = b – a -(ab)= -a. b = a. (-b) -(a) = a

6. Properties Commutative Associative Inverse Distributive a + b is a real numbers (Addition) ab is real number (Multiplication) (a+b) +c =a +(b+c) Add (ab)c = a(bc) Mult a + (-a)=0 Add a. 1/a = 1 Mult a(b + C)= ab + ac

7. Inequality Inequality: is a mathematic sentences that compare two or more sentences The symbols are: Less than< Less than or equal ≤ More than> More than or equal ≥