Section P1Algebra Expressions

and Real Numbers

Algebraic Expressions

Example:

37 7 7 7

Algebraic Expressions are combinations of variables and numbers using the operations of addition, subtraction, multiplication, or division as well as powers or roots.

Evaluating Algebraic Expressions

22 3( 1) 4 for x =3x

Example

Evaluate an Algebraic Expression

Formulas and Mathematical Models

Mathematical Modeling – the process of finding formulas to describe real-world phenomena.

Example

It takes you 30 minutes to get to your first period class. This includes driving at a rate of .8 miles per minute, and walking from the parking lot to your class at a rate of .07 miles per minute. The total distance of both walking and driving is given by the algebraic expression. Find the distance if it takes you 5 minutes to walk to class.

0.07 .8(30 )D t t

Sets

The Roster Method- lists the elements of the set, with commas in between. The three dots (ellipsis) indicate that the listing continues for ever.

A set is a collection of objects, whose elements can be clearly determined.

If a set has no elements then it is called the null set or empty set, represented by the symbol .

Set Builder Notation – the elements are described, not listed.

If a set has no elements then it is called the null set or empty set, represented by the symbol .

Example

For the following sets of numbers find the Union and the Intersection.

2,4,6,8,10 3,4,5,6,7

2,4,6,8,10 3,4,5,6,7

The Set of Real Numbers

Every Real Number is either rational or irrational. We refer to these sets as subsets of the real numbers, meaning that all elements in each subset are also elements in the set of real numbers.

| is rational or x is irrationalx x

Numbers Examples

Natural Numbers 2,3,4,17

Whole Numbers 0,2,3,4,17

Integers -5,-2,0,2,5

1 5 1 2Rational Numbers , ,.4 ,0,.6

2 1 5 3

Irrational Numbers 2, , 3

25 is a rational number because 25 5.

Example

13, 0, , .95, , 8, 16

2

Consider the following set of numbers.

List the numbers in the set that are:

a. Natural Numbers

b. Whole Numbers

c. Integers

d. Rational Numbers

e. Irrational Numbers

f. Real numbers

Ordering the Real Numbers

The Absolute Value - Distance

Example

Evaluate the following Absolute Value problems.

14

14

Example

Find the distance between -7 and 3 on the number line.

Simplifying Algebraic Expressions

The terms of an algebraic expression are those parts that are separated by addition. There are four terms in the expression below.

An Algebraic Expression is simplified when parentheses have been removed and like terms have been combined. Like terms are terms that have exactly the same variable factors. For example 5x and 7x are like terms.

5 7 12x x x

Example

2 22( 3 ) (5 4) 9x x x x Simplify this Algebraic Expression

Properties of Negatives

39 2 4 1 for x=-3x

Evaluate an Algebraic Expression

(a) 4

(b) 10

(c) 12

(d) 8

Find the distance between -8 and 4 on the number line.

(a) -4

(b) 12

(c) 10

(d) 8

List the numbers in the set below that belong to the set of rational numbers.

(a)

(b)

(c)

(d)

15, , .3, .8, 9, , 13

2

1

5, , .3, .8, 9, 2

15, , .3, .8, 9, 13

2

15, , .3, .8,

2

15, , .8,

2