1.1 Real Numbers & Number Operations (p. 3)

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 –Irrational numbers –Rational 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.

Properties of Multiplication & Addition (a, b, & c are real #s) Addition Multiplication Closurea+b is reala*b is real Commutativea+b=b+aab=ba Associative (a+b)+c=a+(b+c) (ab)c=a(bc) Identity a+0=a, 0+a=aa*1=a, 1*a=a Inversea+(-a)=0a*(1/a)=1, a≠0 Distributivea(b+c)=ab+ac (a+b)c=ac+bc

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

Unit Analysis Examples 1.685ft + 225ft = 910ft 2.(2.25h)= 135km mi/h

1.2 Algebraic Expressions & Models (p. 11)

Base ? Exponent ? Power ?

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

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

Define: Variable Algebraic expression Coefficient Like terms Constant term

Ex: Simplify the expression. 1.6m 2 – 12m – 7m 2 = -m 2 – 12m 2.3(x-2) – 5(x-8) = 3x – 6 – 5x +40 = -2x + 34

Last example! You want to buy either scented lotion or bath soap for 8 people. The lotions are $6 each and the soaps are $5 each. Using l for the # of lotions, write an expression for the total amount you must spend in terms of l. 6 l + 5(8- l ) 6 l l l +40

Evaluate the expression when 5 people get lotion. l = 45 $45

Assignment