Transcript Document
Welcome to The Wonderful
World of College Algebra
Unit 1 Seminar
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MM212 Unit 1 Seminar Agenda
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Welcome and Syllabus Review
Classifying Numbers
Operations with Real Numbers
Arithmetic and Calculators
Division and ZERO
Exponents
Order of Operations
Items for you to Read
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Items in Doc Sharing
The unit notes in Doc Sharing each week
Syllabus
Announcements
Your email
Things for you to Do
• Familiar yourself with the online site
Seminar
• Although the seminar component is not graded, you will
gain valuable information by your attendance.
• You will gain the most out of seminar by: showing up on
time, staying in the seminar until the end, staying on
topic, and participating
• Have your textbook, something to write with, something
to write on, and your calculator with you at seminar!
• We only have 60 minutes in seminar per week … there
is no way we can cover every single concept
• We will cover more of the concepts in the two hour on
ground session on Tuesdays from 12 – 2 pm
Some General Comments
• The reason you enrolled in this class is
because it is a requirement in order to
graduate with your degree.
• That requirement is not going to change or
disappear.
• If you have never been good at math, or if
you do not like math, or if you have not
had math in a long time does not matter!
General Comments (continued)
• What does matter is this …
#1. You give me a chance to help you
#2. You maintain a POSITIVE ATTITUDE so
you give yourself a chance to be successful
#3. We work TOGETHER as a TEAM so we will
ALL be successful.
#4. NO ONE QUITS OR DISAPPEARS!
General Comments (continued)
• In support of our POSITIVE ATTITUDE, I
have erected a NO NEGATIVE ZONE in
our class
• This means no posts in the Discussion
Board (DB) about you not being good at
math, not liking math, or anything
negative.
• These things are not conducive to our
learning environment and distract us from
our goal of being successful!
Real Number System
The collection or set of numbers we are going to use in
this class are called the Real numbers. There are various
subsets of the real numbers.
1. Natural or Counting Numbers: 1, 2, 3, 4, . . .
2. Whole Numbers: 0, 1, 2, 3, . . .
3. Integers: . . . -3, -2, -1, 0, 1, 2, 3, . . .
4. Positive Integers: 1, 2, 3, 4, . . .
5. Negative Integers: -1, -2, -3, -4, . . .
6. Odd Integers: . . . -5, -3, -1, 1, 3, 5, . . .
7. Even Integers: . . . -6, -4, -2, 0, 2, 4, 6, . . .
RATIONAL NUMBERS:
• Definition 1 – A rational number is a
number that can be expressed as the
quotient of two integers
Examples:
2
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3
25 5
16
; 8
2
36 6
Definition # 2 – a rational number is
a number that can be written as
either a terminating or repeating
decimal.
Examples:
.8, -1.85,
.34
IRRATIONAL NUMBERS:
• Definition # 1 – An irrational number is a
number that cannot be written as the
quotient of two integers
• Definition # 2 – An irrational number is a
number that is a nonterminating and
nonrepeating decimal
Example: .202002000200002 …
Two Famous Irrationals: π, 2
Some Concepts
The ADDITIVE INVERSE or OPPOSITE of a number is the
number that is the same distance from 0 on the number
line, but in the opposite direction.
Example: The opposite of 5 is – 5
The ABSOLUTE VALUE of a number describes
the distance a number is from zero on the number
line.
7 7
5 5
Arithmetic and Calculators
• Calculators are VERY, VERY SMART and
they are VERY, VERY OBEDIENT … they
will do exactly what we ask them to do. It
is important to enter the information
correctly.
• The calculator may only give you an
approximate answer and not and exact
answer
• Most calculators obey the order of
operations
Division and the number ZERO
• THREE TYPES
– 0 in the numerator (dividend) only = 0
– 0 in the denominator (divisor) only =
UNDEFINED
– 0 in both the numerator and denominator =
INDETERMINATE (or cannot be determined)
EXPONENTS
• The exponent tells us how many times the
base is used as a factor.
Example: 43 means we have 3 factors of 4
so 43 = 4 × 4 × 4
-42 means the opposite of 42 or – 16
(-4)2 means two factors of – 4
or (-4)(-4)= 16
SQUARE ROOTS
Examples:
The square root of 9 is 3 because 32 or
3 × 3 is 9
The square root of 100 is 10 because
102 or 10 × 10 = 100
It is the opposite of squaring a number.
ORDER OF OPERATIONS
• PEMDAS
P: Grouping Symbols
a. ( ), { }, fraction bars, radicals (like the square
root symbol), absolute value | |.
b. We will ALWAYS do the arithmetic inside the
grouping symbol first
ORDER OF OPERATIONS
• PEMDAS
E: Exponents: We will always perform
arithmetic of exponents next.
ORDER OF OPERATIONS
• PEMDAS
MD: Multiplication/Division
– Perform these as they occur from left to right.
Do not first do all multiplication and then come
back for division. They are equal-level
operations
ORDER OF OPERATIONS
• PEMDAS
AS: Addition/Subtraction
– By now, this is all you have left to do.
– Perform these as they occur from left to right.
(JUST LIKE multiplication/division)