Subject  Explanation  Examples (if available) 
Numbers   Natural numbers: all numbers from numerical one forward
 Whole Numbers: all natural numbers and including zero (a.k.a. "origin)
 Integers: all positive and negative numbers, including zero
 Rational numbers: Fractions
  Natural Numbers: 1, 2, 3, 4, 5, ...
 Whole Numbers: 0, 1, 2, 3, 4, ...
 Integers: ..., 2, 1, 0, 1, 2, ...
 Rational Numbers: 1/2, 2/4, 3/6, 4/8, ...

Absolute Values  Absolute 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 Fractions  Multiply 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 Fractions  To 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/Subtraction  Addition: Adding a negative and a positive is like subtracting the negative number from the positive one.
 Adding two negatives is the same as adding two positives, just with a little dash in front.
Subtraction: Subtracting a positive from a negative is like adding the two numbers and putting a dash in front.
 Subtracting a negative from anything is like adding the negative to what's in front of it.
 Addition: 3 + (1) = 2
 1 + (5) = 6
Subtraction: 8  3 = 11
 3  (3) = 6. Also, 4  (5) = 1


Multiplication  When multiplying signed numbers: neg * pos = neg
 pos * neg = neg
 pos * pos = pos
 neg * neg = pos
 Examples: 3 * 3 = 9
 4 * 5 = 20
 9 * 3 = 27
 2 * 4 = 8

Division  When dividing signed numbers: pos D neg = neg
 neg D pos= neg
 neg D neg = pos
 pos D pos = pos
 Examples: 5 D 5 = 1
 4 D 2 = 2
 6 D 3 = 2
 20 D 4 = 5

Division by Origin (Zero)  When dividing with the origin (or zero): 0 D x = 0
 x D 0 = infinity/undefined
 Examples: 0 D 3 = 0
 3 D 0 = undefined

Exponential Expressions  Please 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 Equations  When 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(4^36 D 3) = 1+2*3(162) = 1+2*3(14) = 1+2*42 = 1+84 = 85 