II Chapter 1 1 Real Numbers Properties 2

II Chapter 1. 1 Real Numbers & Properties #2 Pure mathematics is, in its way, the poetry of logical ideas. ~Albert Einstein

Real Numbers • Whole Numbers – Positive numbers that do not have decimals or fractions. • Integers – Positive & negative whole numbers. • Rational Numbers – Any number that can be written as a quotient of two integers. Includes most fractions & decimals. • Irrational Numbers – Non-ending, non-repeating decimals. Usually Radicals.

Examples of Real Numbers • Whole Numbers- 1 2 3 4 5 6…. . • Integers – -3, 2, 7, -9 -1000 • Rational Numbers –. 75, ½, • Irrational Numbers – pie, e,

Real Numbers Rational In te Irr Whole ge r at io na l

Properties • Closure • If a & b are real numbers then a·b is a real number.

Properties • Commutative • Associative • a+b=b+a • (ab)c = a(bc)

Properties • Identity • This will always make something equal to it’s self • a· 1=a & a+0=a

Properties Inverse This will make something go to 1 or zero • a + (-a) = 0 & a · =1

Properties • Closure • If a & b are real numbers then a·b is a real number. • • • Commutative Associative Identity Inverse Distributive a+b=b+a (ab)c = a(bc) a· 1=a & a+0=a a + (-a) = 0 & a · = 1 a(b + c) = ab + ac Lastly

Example: Use properties & definitions to show that the statement is true Assoc. Property Addition

Example: Use properties & definitions to show that the statement is true

Example: Use properties & definitions to show that the statement is true

Rate of Change You work 5 hours and earn $60, what was your rate of pay? You travel at 60 miles per hour for three hours, how far did you go?

Chapter 1. 2 Algebraic Expressions

Exponential Expressions • Power – Notation used to represent repeated multiplication. • Base - The first number. Tells what value is to be multiplied. • Exponent (Power) – The superscripted number. Tells how many times the base is multiplied. Power Base

Evaluating Expressions 1. Write the Expression 2. Replace the variable with its value. 3. Simplify

Terms & Coefficients • Term – Each part of an expression that is separated by a (+) or (-) symbol. • Variable Term – Any term that contains one or more variables. • Constant Term – Any term that has only numbers. • Coefficient – The number in front of a variable. Variable Terms Constant Coefficients Term

Simplifying Expressions 1. Get rid of grouping symbols. 2. Collect like terms

Simplifying Expressions 1. Get rid of grouping symbols. 2. Collect like terms

Simplifying Expressions 1. Get rid of grouping symbols. 2. Collect like terms

Assignment • 1. 1 • p 7 4 -34 Even • 1. 2 • p 13 6 -53 X 3