Slide 1
Intermediate Algebra by Gustafson and Frisk
Chapter 1
A Review of Basic Algebra
Slide 2
The Real Number System
Natural Numbers
Whole Numbers
Rational Numbers
Irrational Numbers
Real Numbers
Integers
Positive Numbers
Negative Numbers
Even Numbers
Odd Numbers
Use { } {x | x > 5} is read “the set of all x such that x is greater than 5”
Slide 3
Section 1.1: The Real Number System
Individual numbers are dots
Slide 4
Section 1.1: The Real Number System
GRAPHS: plot on the number line.
Intervals including end points
[
[
]
Slide 5
Section 1.1: The Real Number System
GRAPHS: plot on the number line.
Intervals not including end points
(
(
)
Slide 6
Section 1.2:
OPERATIONS:
Addition
Subtraction (the same as adding a number with the opposite sign)
Multiplication
Division (the same as multiplying by the reciprocal)
Slide 7
Section 1.2: Arithetic & Properties of Real Numbers
ADDITION:
Addends that have opposite signs
Subtract absolute values
Keep the sign of the addend with the largest absolute value
Addends that have the same signs
Add absolute values
Keep the sign of the addends
Slide 8
Section 1.2: Arithetic & Properties of Real Numbers
Multiply absolute values
If the factors have the same signs, the product is positive
If the factors have opposite signs, the product is negative
Slide 9
Section 1.2: Arithetic & Properties of Real Numbers
Mean
Median
Mode
Slide 10
Section 1.2: Arithetic & Properties of Real Numbers
Associative – addition, multiplication
Commutative – addition, multiplication
Distributive – multiplication is distributed over addition a (b + c) = ab + ac
Slide 11