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

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

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 ExamplesUnit Analysis Examples

1. 685ft + 225ft =

910ft

2. (2.25h) =

135km

3.

45 mi/h

h

km60

ft

mi

h

s

s

ft

5280

1360066

1.2 Algebraic Expressions & Models

(p. 11)

34Base ?

Exponent ?

Power ?

Ex: Evaluate the power

1. (-2)6 =

(-2)*(-2)*(-2)*(-2)*(-2)*(-2) =

64

2. -26 =

-(2*2*2*2*2*2) =

-64

Order of OperationsOrder of OperationsKnow these!!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. 6m2 – 12m – 7m2 =

-m2 – 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.6l + 5(8-l)6l+40-5l

l +40

• Evaluate the expression

when 5 people get lotion.

l + 40

5 + 40 = 45

$45

Assignment