1. MM212 Unit 1 Seminar Agenda Welcome and Syllabus Review Classifying Numbers Operations with Real Numbers Division and ZERO Exponents Order of Operations Distributive Property

2. Laura Baggett Lbaggett@kaplan.edu Office hours by appointment. AIM name: MathTeacherLaura MS in Applied Mathematics from Georgia Tech BS in Mathematics from Auburn University Taught “in the classroom” for 8 years at colleges and universities in Georgia (GTA), Alabama, Washington, Florida, Tennessee, and Arkansas Teaching online since April 2010 for Kaplan and another university

3. Syllabus Review

4. Discussion Boards Make sure to answer the question completely, including all parts. Posts should be written in college-level English, not “text” language. Respond to at least two of your classmates by providing substantive feedback that advances the discussion. No late discussion board posts will be accepted.

5. MML (MyMathLab) Each problem can be worked multiple times for full credit, so it’s always possible to get 100%! (Click Similar Exercise to pull up another problem.) You can leave and come back during the Unit week. Be sure to save your work. Many “helps” available: Help Me Solve This, View an Example, Ask My Instructor, etc.

6. Flex Seminars Three days/times to choose from each week: Wednesdays at 1PM ET, Wednesdays at 7PM ET, and Sundays at 8PM ET. You do not have to attend the same one each week. If you are unable to attend live, please view the archive available within a few hours of the end of the seminar.

7. Questions?

8. Examples Variables: x, y, z, a Algebraic Expression: –a + b –4x – 7 –6y –x/4 –They can be longer, like these: 3x 2 – 7y 3 + 12z – 2 –a + b + c + d + e + f + g

9. Sets of Numbers Natural Numbers: 1, 2, 3, 4, … Whole Numbers: 0, 1, 2,3, … Integers: …-3, -2, -1, 0, 1, 2, 3, … Rational Numbers: ½, 0.5, -6,.333… Irrational Numbers: pi, √[2], √[3] Real Numbers: all rational and irrational numbers

10. RATIONAL NUMBERS: To test if a number is a rational number, there are three things that must be true (not one or two of the things BUT ALL THREE). –The number must be able to written as a fraction (whose denominator ≠ 0) –This fraction must be able to be converted to a decimal number –This decimal number TERMINATES or REPEATS

11. IRRATIONAL NUMBERS: The definition of an irrational number is a number that is NOT RATIONAL. Another way to put this is –The number must not be able to written as a fraction (whose denominator ≠ 0) –This decimal number is NONTERMINATING or NONREPEATING

12. Operations with Real Numbers Additive Inverse means opposite The additive inverse of-10x is 10x Absolute Value is the distance from zero I-4I = 4 and I5I = 5 Sign Rules for Addition/Subtraction Same sign: add and take that sign -5 + -5 = -10 Different sign: subtract and take the sign of the larger -10 + 5 = -5 [if subtracting, change the – to + (-)]: -5 - 2 = -5 + (-2) = -7 Sign Rules for Multiplication/Division Same sign: positive Different sign: negative

13. Examples -4 + (-3) = -5 + 4 = 2 – 6 = -3 – 7 =

14. Division and the number ZERO THREE TYPES –0 in the numerator (dividend) only = 0 Example: 0/6 = 0 –0 in the denominator (divisor) only = UNDEFINED Example: 4/0 = undefined –0 in both the numerator and denominator = INDETERMINATE (or cannot be determined) Example: 0/0 = indeterminate

15. EXPONENTS How many times you multiply a number times itself … –Example: 2 4 = 2*2*2*2 = 16 –Example: x 6 = x*x*x*x*x*x

16. SQUARE ROOTS The square root of a number is the value that you can multiply times itself to get the original number It is the opposite arithmetic of exponents (specifically of squaring a number) –Example: √9 = 3 –Example: √100 = 10

17. ORDER OF OPERATIONS PEMDAS P: Grouping Symbols –( ), { }, fraction bars, radicals (like the square root symbol, absolute value | |. –We will ALWAYS do the arithmetic inside the grouping symbol first

18. ORDER OF OPERATIONS PEMDAS E: Exponents: We will always perform arithmetic of exponents next.

19. 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

20. 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)

21. Order of Operations Mneumonic Device: Please Excuse My Dear Aunt Sally (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction) **Note be careful because multiplication and division are together, and addition and subtraction are together. 2(3 – 5 + 6) + 5 = 2(-2 + 6) + 5in parentheses, 3 – 5 = -2 = 2(4) + 5in parentheses, -2 + 6 = 4 = 8 + 5got rid of parentheses by multiplying = 13addition is all that’s left: 8 + 5 = 13

22. You try it! 1.6 – 4 * 2 = 2.5 2 - 3(4+1) = 3.5 – 2 3 + 8*3 – 1 =

23. Distributive Property Examples: a(b+c) = ab + ac -2(x+2) = -2x-4 4(2x-3y) = -10(6a-5) = (1/2 – 2t+u)(-3/4) =

24. Questions?