1. Real Numbers, Algebra, and Problem Solving
Chapter 1
Real Numbers, Algebra,
and Problem Solving

2. Real Number Sets Rational Numbers Irrational Numbers
Discuss the difference between equal and approx (including notation)

3. Rational Numbers
Integers
Whole Numbers
Natural Numbers

4. Real Numbers

5. Axioms for real numbers
Closure
For every real number a and b,
a + b is a real number
ab is a real number
Commutative
a + b = b + a
ab = ba
Associative
For any numbers a, b and c,
a + (b + c) = (a + b) + c
a(bc) = (ab)c
Distributive Property For every real number a, b, and c,
a(b + c) = ab + ac
Identity
For any number a,
a + 0 = a
1a = a
Inverse
For each number a, there is one and only one inverse, b, such that a + b = 0
For each nonzero number a, there is one and only one inverse, b, such that ab = 1

6. Unit Analysis Used to convert from one unit to another.
How many seconds are in a week?

7. Computing with a calculator
Use a calculator to evaluate each expression. Round to the nearest thousandth a. b. c. d.
e. 6! – e2

8. Algebraic Expressions and Models
Unit 1.2
Algebraic Expressions and Models

9. Numerical Expressions
Numbers, operations, and grouping symbols
Exponents
____________ ___________________
Order of Operations P E MD AS

10. Math Vocabulary Give an example of each: Variable Algebraic Expression
Term
Coefficient
Like terms
Constant

11. 1.3 and 1.4
Solving Linear Equations and Rewriting Equations and Formulas

12. Examples
3.5x – 2 = 5x - 8
-(x + 2) – 2x = -2(x + 1)

13. Word Problems
You had to take your car to the shop and received a bill for $390. If the cost of parts was $215 and labor is $35/hour, how many hours did the repair take? Write an equation, then solve.
A Retail sales manager earns $40,000 plus 5% of sales. If she earned $71,750 last year, what were her total sales?

14. Example
1. To solve C = 2п(r – 2) for r, what would you do first?

15. Example
2. Solve the formula A = wl for w

16. Example
3. Solve w = 3(x – 2) for x

17. Example
4. Solve the formula A = P + Prt for r

18. 1.5 Problem Solving Using Algebraic models
Understand the Problem
Develop and carry out a Plan
Find the Answer and Check
***Be sure to define any variables you use.

19. Example
1. A carpenter works one third as long after lunch as she worked before lunch. If she works a total of 8 hours, how long did she work before lunch?

20. Example
2. The giant economy size of Wheat Waffles is 25% larger than the regular size. The giant economy size is 500 grams. How large is the regular size?

21. Example
The sum of two consecutive even integers is What are the integers?

22. Useful Tips
If two numbers are consecutive, call one x and the other x + 1
If two numbers are consecutive odd or consecutive even numbers, call one x and the other x + 2
If a number x is increased by n%, the new number is x(100% + n%)
2% increase… x(1.02)