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Slide 1

Intermediate Algebra by Gustafson and Frisk

Chapter 1

A Review of Basic Algebra

Slide 2

SETS: collections of objects.

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

GRAPHS: plot on the number line.

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

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

MULTIPLICATION:

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

STATISTICS: measures of central tendency

Mean

Median

Mode

Slide 10

Section 1.2: Arithetic & Properties of Real Numbers

Properties:

Associative – addition, multiplication

Commutative – addition, multiplication

Distributive – multiplication is distributed over addition a (b + c) = ab + ac

Slide 11

- The Real Number System
- Arithetic & Properties of Real Numbers
- Definition of Exponents
- Solving Equations
- Solving Problems, Applications
- Basic Algebra Review

- Sound
- Newton's laws of motion
- Friction
- Solar Energy
- Mechanical, Electromagnetic, Electrical, Chemical and Thermal
- Simulation at NASA for the Space Radiation Effort
- Newton’s Law of Gravity

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