Welcome to The Wonderful World of College Algebra Unit 1 Seminar To resize your pods: Place your mouse here. Left mouse click and hold. Drag to the right to enlarge the pod. To maximize chat, minimize roster by clicking here

MM212 Unit 1 Seminar Agenda 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 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:

Definition # 2 – a rational number is a number that can be written as either a terminating or repeating decimal. Examples: .8, -1.85,

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,

Some Concepts Example: The opposite of 5 is – 5 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.

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 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)