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A Review of Basic Algebra
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Intermediate Algebra by Gustafson and Frisk

Intermediate Algebra by Gustafson and Frisk

Chapter 1

A Review of Basic Algebra

Slide 2

The Real Number System

The Real Number System

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

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

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

Section 1.1: The Real Number System

GRAPHS: plot on the number line.

Intervals not including end points

(

(

)

Slide 6

Arithetic & Properties of Real Numbers

Arithetic & Properties of Real Numbers

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

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

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

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

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

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