Real Number and the numberLine
Number System
•Real numbers: is number that can be positive or negative and have decimal places after thepoint.
•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 integersinclude terminating (0.125) and repeating (0.3333 )numbers.
•Irrational numbers: have decimal representation that neither terminate nor repeat
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
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
Properties for Simplifying AlgebraicExpressions
•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
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
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 ≥
