Transcript 1.1 Real Numbers & Number Operations

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 Examples
1. 685ft + 225ft =
2.
 60km 
(2.25h)  h 
910ft
=
135km
3.  66 ft  3600s  1mi 
 



 s 
h
 5280 ft  45 mi/h
1.2 Algebraic
Expressions & Models
(p. 11)
4
Base ?
Exponent ?
Power ?
3
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 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. 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