MM212 Unit 1 Seminar Agenda

• Welcome and Syllabus Review• Classifying Numbers• Operations with Real Numbers• Division and ZERO• Exponents• Order of Operations• Distributive Property

Laura BaggettLbaggett@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

Syllabus Review

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.

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.

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.

Questions?

Examples

• Variables: x, y, z, a

• Algebraic Expression:– a + b– 4x – 7– 6y– x/4– They can be longer, like these:

3x2 – 7y3 + 12z – 2– a + b + c + d + e + f + g

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

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

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

Operations with Real Numbers

• Additive Inverse means oppositeThe additive inverse of-10x is 10x

• Absolute Value is the distance from zero I-4I = 4 and I5I = 5

• Sign Rules for Addition/SubtractionSame sign: add and take that sign -5 + -5 = -10Different 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/DivisionSame sign: positive Different sign: negative

Examples

• -4 + (-3) =

• -5 + 4 =

• 2 – 6 =

• -3 – 7 =

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

EXPONENTS

• How many times you multiply a number times itself …

– Example: 24 = 2*2*2*2 = 16

– Example: x6 = x*x*x*x*x*x

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

ORDER OF OPERATIONS

• PEMDASP: Grouping Symbols – ( ), { }, fraction bars, radicals (like the square

root symbol, absolute value | |. – We will ALWAYS do the arithmetic inside the

grouping symbol first

ORDER OF OPERATIONS

• PEMDASE: Exponents: We will always perform

arithmetic of exponents next.

ORDER OF OPERATIONS

• PEMDASMD: 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

• PEMDASAS: 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)

• 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) + 5 in parentheses, 3 – 5 = -2= 2(4) + 5 in parentheses, -2 + 6 = 4= 8 + 5 got rid of parentheses by multiplying= 13 addition is all that’s left: 8 + 5 = 13

You try it!

1. 6 – 4 * 2 =

2. 52 - 3(4+1) =

3. 5 – 23 + 8*3 – 1 =

Distributive PropertyExamples:

• a(b+c) = ab + ac

• -2(x+2) = -2x-4

• 4(2x-3y) =

• -10(6a-5) =

• (1/2 – 2t+u)(-3/4) =

Questions?