1-3B Real Numbers & the Number Line Algebra I

Sets – defined collection Element of the set within braces { } Subset – a set consists of elements from the given set

What is a real number? Rational & irrational #’s Real Numbers Rational numbers Integers Whole numbers Natural numbers or counting #’s Irrational numbers

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.

Ex. 1 Classifying Real Numbers To which subsets of real numbers does each number belong? a.) 12 b.) c.) -5.01479 d.)

Ex. 2 What is an inequality that compares the numbers ?

Ex. 3 What is the order of from least to greatest?

Ex. 4 Graph the real #’s

Assignment

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

Ex. 2 Identify the property that the statement illustrates

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

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

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

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?

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

1.2 Evaluate & Simplify Algebraic Expressions Algebra II

Base ? Exponent ? Power ?

Ex. 1: Evaluate the power (-2)6 = (-2)*(-2)*(-2)*(-2)*(-2)*(-2) = 64 2. -26 = -(2*2*2*2*2*2) = -64

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

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

Ex. 2 Evaluate an algebraic expression

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.

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

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.

Assignment

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