1. 1.1 Real Numbers
Algebra II

2. What is a real number? All the numbers you are used to
using in your previous math classes.
There are 4 types of real numbers:
Whole numbers
Integers
Rational numbers
Irrational numbers

3. Examples of Real numbers
Whole numbers: 0, 1, 2, 3 (counting #s)
Integers: -2, -1, 0, 1, 2 (+ & - whole #s)
Rational numbers: a # that can be written as a fraction. When written as a decimal, they terminate or repeat. ½, 1/3, 4/5, 7/9
Irrational numbers: real #s that are not rational such as π or √3. Decimals that do not terminate or repeat.

4. Ex. 1 Graph the real #’s

5. Properties of Multiplication & Addition
(a, b, & c are real #s)
Addition Multiplication
Closure a+b is real a*b is real
Commutative a+b=b+a ab=ba
Associative (a+b)+c=a+(b+c) (ab)c=a(bc)
Identity a+0=a, 0+a=a a*1=a, 1*a=a
Inverse a+(-a)=0 a*(1/a)=1, a≠0
Distributive a(b+c)=ab+ac
(a+b)c=ac+bc

6. Ex. 2 Identify the property that the statement illustrates

7. Additive Inverse (opposite)
ex: a and –a or -5 and 5
Multiplicative Inverse (reciprocal)
ex: a and 1/a or -1/3 and -3
Remember:
Difference means subtract
Quotient means divide

8. Ex. 3 Use properties & definitions of operations to show that
Justify each step.

9. Unit Analysis Examples
685ft + 225ft =
910ft
(2.25h) =
135km 3.
45 mi/h

10. Ex. 4 a.) You work 8 hours and earn $60. What is your earning rate?
b.)You buy 18 gallons of gasoline at $2.65 per gallon. What is your total cost?

11. Ex. 4
c.) You drive 90 kilometers per hour. What is your speed in meters per second.

12. 1.2 Evaluate & Simplify Algebraic Expressions
Algebra II

13. Base ?
Exponent ?
Power ?

14. Ex. 1: Evaluate the power (-2)6 = (-2)*(-2)*(-2)*(-2)*(-2)*(-2) = 64=
-(2*2*2*2*2*2) =
-64

15. Definitions Variable x Algebraic expression x + 4 Terms Variable term
Constant term
coefficient

16. Order of Operations Know these!!
Please Excuse My Dear Aunt Sally
( )
exponents
multiply/divide (L to R)
add/subtract (L to R)

17. Ex. 2 Evaluate an algebraic expression

18. Ex. 3
You are selling fresh squeezed lemonade at a county fair for $2.50 per glass. You spend $180 to rent the stand and buy the ingredients & supplies you need. Write an expression that shows your profit from selling g glasses of lemonade. Find your profit if you sell 268 glasses of lemonade.

19. Ex. 4 Simplifying by combining like terms
a.)
b.)
c.)
d.)

20. Ex. 5 Simplify a mathematical model
Yesterday, a store sold 60 recordable DVD’s. The Samsung DVD’s sell for $15 each, and the Verbatim DVD’s sell for $12 each. Write and simplify an expression that represents the store’s total income for the DVD sales yesterday if x represents the number of Samsung DVD’s sold. Then find the total income if 38 of the 60 DVD’s were Samsung.

21. Assignment

22. Ex: Simplify the expression.
6m2 – 12m – 7m2 =
-m2 – 12m
3(x-2) – 5(x-8) =
3x – 6 – 5x +40 =
-2x + 34