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Class Notes

Listen up, Dream Team! This is where all permanent notes will be held (things that aren't included in the "most recent" section on the notes index page and so won't be moved to the DT Blog). Remember, these are notes directly from the Math Lab! All you have to do is highlight, right-click, and print the selection to get the notes you want to study. Or you can just read them online if you want... okay?
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MTH 208 Notes for Week 1

SubjectExplanationExamples (if available)
Numbers
  1. Natural numbers: all numbers from numerical one forward
  2. Whole Numbers: all natural numbers and including zero (a.k.a. "origin)
  3. Integers: all positive and negative numbers, including zero
  4. Rational numbers: Fractions
  1. Natural Numbers: 1, 2, 3, 4, 5, ...
  2. Whole Numbers: 0, 1, 2, 3, 4, ...
  3. Integers: ..., -2, -1, 0, 1, 2, ...
  4. Rational Numbers: 1/2, 2/4, 3/6, 4/8, ...
Absolute ValuesAbsolute values are the values of numbers based on their position from origin (zero)|-3| = 3, because -3 is three places away from zero on the number line. Also, |3| = 3, because it is also three places away from zero.
Fractions  
Multiplying FractionsMultiply straight across on both top and bottom to get your answer.
Formula: a/b * c/d = ac/bd
Problem:
3/6 * 5/6
=(3)(5)/(6)(6)
= 15/32
Dividing FractionsTo divide two fractions, invert (flip!) the second fraction and multiply across. (Please note- I have no division sign, so a capital D will be standing in. :] )
Formula: a/b D c/d = a/b * d/c = ad/bc
Problem:
1/2 D 2/5
= 1/2 * 5/2
= (1)(5)/(2)(2)
= 5/4 OR 1 1/4
Adding Fractions (Must have a common denominator)This one's simple! Just cross multiply and add the products for the top half, then multiply straight across for the bottom half.
Formula: a/b + c/d = ad + bc/bd
Problem:
2/3 + 4/5
= (2)(5) + (3)(4)/(3)(5)
= 10 + 12/15
= 22/15
= 1 7/15
Subtracting Fractions (Must have a common denominator)Same as with addition, only after we cross multiply for the top, we subtract the products!
Formula: a/b - c/d = ad - bc/bd
Problem:
3/5 - 4/3
= (3)(3) - (5)(4)/(5)(3)
= 9 - 20/15
= -11/15
Like/Unlike Signs  
Addition/SubtractionAddition:
  1. Adding a negative and a positive is like subtracting the negative number from the positive one.
  2. Adding two negatives is the same as adding two positives, just with a little dash in front.
Subtraction:
  1. Subtracting a positive from a negative is like adding the two numbers and putting a dash in front.
  2. Subtracting a negative from anything is like adding the negative to what's in front of it.
Addition:
  1. 3 + (-1) = 2
  2. -1 + (-5) = -6
Subtraction:
  1. -8 - 3 = -11
  2. 3 - (-3) = 6. Also, -4 - (-5) = 1
MultiplicationWhen multiplying signed numbers:
  1. neg * pos = neg
  2. pos * neg = neg
  3. pos * pos = pos
  4. neg * neg = pos
Examples:
  1. -3 * 3 = -9
  2. 4 * -5 = -20
  3. 9 * 3 = 27
  4. -2 * -4 = 8
DivisionWhen dividing signed numbers:
  1. pos D neg = neg
  2. neg D pos= neg
  3. neg D neg = pos
  4. pos D pos = pos
Examples:
  1. 5 D -5 = -1
  2. -4 D 2 = -2
  3. -6 D -3 = 2
  4. 20 D 4 = 5
Division by Origin (Zero)When dividing with the origin (or zero):
  1. 0 D x = 0
  2. x D 0 = infinity/undefined
Examples:
  1. 0 D 3 = 0
  2. 3 D 0 = undefined
Exponential ExpressionsPlease note- I can't superscript the text. x^y therefore represents x to the y power.
Exponents are simple! If you have a^4 it is the same as multiplying a four times (i.e. a*a*a*a). a^3 = a*a*a, and so on.
Problems:
3^2 = 3*3 = 9
2^5 = 2*2*2*2*2 = 32
Algebraic EquationsWhen doing algebraic equations, make sure you remember to "Please Excuse My Dear Aunt Sally" -- Parenthesis Exponents Multiplication/Division Addition/Subtraction. That's the order you need to go in to get the right answer!Example: 1+2*3(4^3-6 D 3)
= 1+2*3(16-2)
= 1+2*3(14)
= 1+2*42
= 1+84
= 85

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