Real numbers and their properties

College Algebra and TrigonometryCollege Algebra and Trigonometry

Dr.Maryam T. Al DossaryDr.Maryam T. Al Dossary

Real Numbers and Their Properties

Real Numbers and Their Properties

OBJECTIVES

At the end of this lesson, you should be able to:

1- Evaluate expressions using order of operations

2- Find absolute values of real numbers

3- Evaluate absolute values using their properties

Order of Operations

If grouping symbols such as parentheses, square brackets,

or fraction bars are present:

Step 1 Work separately above and below each fraction bar

Step 2 use the rules below within each set of parentheses or square

brackets. Start with the innermost set and work outward

Order of Operations

If no grouping are present:

Step 1 simplify all powers and roots, working from left to right

Step 2 do any multiplication or division in order, working from left to

right

Step 3 do any negations, additions or subtractions in order, working

from left to right

USING ORDER OF OPERATIONS

Evaluate each expression

Solution

Example1

(a)

USING ORDER OF OPERATIONS

Evaluate each expression

Solution

Example1

(b)

Absolute Values

ABSOLUTE VALUES

Evaluate each expression

Solution

Example2

(a) (b) (c)

Properties of Absolut Values

For all real numbers a and b

(The triangle inequality)

ABSOLUTE VALUES

Evaluate each expression

Solution

Example2

(a)

ABSOLUTE VALUES

Evaluate each expression

Solution

Example2

(b)

Thank You

Questions