The Number System

The Number System

1. Mathematical Operations

   • There are only four!
   • Dvision
     • Division (÷ or /) is splitting into equal parts or groups. 
     • Ex: 12 ÷ 3 = 4 12 / 3 = 4
     • 12 is the dividend. 3 is the divisor. 4 is the quotient.
   • Multiplication
     • Multiplication (•) is repeated addition.
     • 5 • 3 = 5 + 5 + 5 = 15
     • 5 and 3 are factors. 15 is the product. 
     • Properties of Multiplication
       • Distributive
         • 2(x+4) 2(x) + 2(4) 2x+8
       • Commutative
         • 4 • 2 = 2 • 4
       • Associative
         • (2 • 3) 4 = 2 (3 • 4)
       • Multiplicative Inverse
         • 8 • (1/8) = 1
       • Multiplicative Identity
         •  5 • 1 = 5.
   • Addition
     • Addition (+) is finding the total, or sum, by combining two or more numbers. 
     • Ex: 5 + 3 + 2 = 10
     • 5, 3, 2 are addends 10 is the sum or total
     • Properties of Addition
       • Additive Identity
         • 5 + 0 = 5
       • Associative Property
         • (2 + 3) + 4 = 2 + (3 + 4)
       • Additive Inverse
         • 5 - 5 = 0
       • Commutative
         • 4+2 = 2+4
       • Distributive
         • 2(x+4) 2(x) + 2(4) 2x+8
   • Subtration
     • Subtraction (-) is taking one number away from another.
     • 5 − 2 = 3
     • 5 is the minuend. 2 is the subtrahend.   3 is the difference. 

2. Types of Numbers

   • Complex Numbers
     • A combination of a real and an imaginary number in the form a + bi, where a and b are real numbers and i = √(−1)
     • √(-5) -3i (where a = 0) 1+2i 4 (where b = 0)
     • Real Numbers
       • Can be positive or negative or zero
       • Nearly any number you can think of is a Real Number
       • Represented on a number line
       • Irrational
         • Non-terminating decimals, non-repeating decimals
         • square root of 2 pi
       • Rational
         • A rational number is a number that can be in the form p/q where p and q are integers and q is not equal to zero.
         • Finite or terminating decimals
         • percentage
         • repeating decimals
         • fractions that have numerator and demonimator
         • Integers
           • Whole numbers that include negatives
           • Composites that can be factored as prime numbers
           • Whole Numbers
             • Non-negative, no fractions, includes zero
             • Natural Numbers
               • Counting numbers not including zero
         • Number Line

3. Positive

   • Assets
   • Distance
   • Absolute Value

4. Negative

   • Opposite
   • Temperature below zero
   • Debts

5. Represented as

   • Equations
     • Polynomials
     • Systems of equations
     • Variables and solving unknowns
   • Funtions
     • Derivatives
     • f(x)
     • Inputs and outputs
     • critical numbers
   • Graphs
     • x- and y-axis, input and output, organizes data
   • Tables
     • Input and output, organizes data
   • Number line
     • Includes Fractions and integers
     • Useful to measure, divide, find GCF and LCM 
   • Inequalities
     • Greater than, greater than or equal to, less than, less than or equal to