1. Aim #P. 1 How do we evaluate algebraic expressions
Aim #P.1 How do we evaluate algebraic expressions? What are Real Numbers?

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

3. Example:

4. How do we evaluate Algebraic Expressions?

6. Example
Evaluate an Algebraic Expression

7. Now your turn:

8. Formulas and Mathematical Models

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

10. 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.

11. What are Sets?
A set is a collection of objects, whose elements can be clearly determined.

12. The Roster Method- lists the elements of the set, with commas in between. The three dots (ellipsis) indicate that the listing continues for ever.
If a set has no elements then it is called the null set or empty set, represented by the symbol

13. 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

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

17. Now your turn:

18. What is the Set of Real Numbers?

19. Every Real Number is either rational or irrational
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.

20. Numbers
Examples
What are some other examples we can add?

21. Consider the following set of numbers.
Example
Consider the following set of numbers.
List the numbers in the set that are:
Natural Numbers
Whole Numbers
Integers
Rational Numbers
Irrational Numbers
Real numbers

22. Now your turn:

23. How do we Order Real Numbers?

24. What does The Absolute Value measure?

26. Example
Evaluate the following Absolute Value problems.

27. Now your turn:

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

29. How do we Simplify Algebraic Expressions?

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

31. 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.

32. Example
Simplify this Algebraic Expression

33. Now your turn:

34. What are the Properties of Negatives?

36. Evaluate an Algebraic Expression
Review:
Evaluate an Algebraic Expression
(a) 4
(b) 10
(c) 12
(d) 8

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

38. List the numbers in the set below that belong to the set of rational numbers.
(c)
(d)

39. Simplify the algebraic expression:

40. Summary: Answer in complete sentences.
Explain how to evaluate the algebraic expression. Then evaluate when x = -2.
Given the following number, how would you classify it?