This document discusses real numbers and their properties including order of operations and absolute values. It aims to teach students how to evaluate expressions using order of operations, find absolute values of real numbers, and evaluate absolute values using their properties. Specifically, it outlines the steps for order of operations when grouping symbols are and aren't present. It also provides examples of evaluating absolute value expressions and discusses properties of absolute values like the triangle inequality.

1. College Algebra and Trigonometry
Dr.Maryam T. Al Dossary
Real Numbers
and Their
Properties

2. 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

3. 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

4. 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

5. USING ORDEROFOPERATIONS
Evaluateeach expression
Solution
Example1
)a(

6. USING ORDEROFOPERATIONS
Evaluateeach expression
Solution
Example1
)b(

7. Absolute Values

8. ABSOLUTE VALUES
Evaluateeach expression
Solution
Example2
)a( )b( )c(

9. Properties of Absolut Values
For all real numbers a and b
)The triangle inequality(

10. ABSOLUTEVALUES
Evaluateeach expression
Solution
Example2
)a(

11. ABSOLUTEVALUES
Evaluate each expression
Solution
Example2
)b(

12. thank You
Questions