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43 Cards in this Set

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Real Numbers
Any number on the number line (-3 -2 -1 0 1 2 3) Can be a rational or irrational number.
Rational Numbers
Real number that can be written as a fraction, terminating decimal (eg 0.25), or repeating decimal (eg 0.212121...)
Irrational Numbers
Numbers that cannot be written as a fraction. (Square roots, cube roots, and pi, though not ALL square roots are irrational)
Percent Increase
(eg: An amount goes up from 20 to 45... What is the % increase?)
(New Value - Original Value / Original Value ) Multiplied by 100

( 45 - 20 = 25 / 20 = 1.25 x 100 = 12.5% Increase )
Percent Decrease
(eg: An amount of 50 decreases by 5.. What is the %I Decrease?)
(Original Value - New Value / Original Value) Multiplied by 100

( 50 - 45 = 5 / 50 = 0.1 x 100 = 10% decrease)
Convert Fractions to Decimals
(Eg: 3/125)
Divide 3.00 by 125

0.024
Fractions with power of 10 denominators to decimal
1/10 = 0.1
1/100 = 0.01
1/1000 = 0.001
1/10000 = 0.0001
1/100000 = 0.00001
Convert 1/5 to decimal
1/5 --> 2/10 = 0.2
Convert Decimals to Fractions
eg: 0.025 = 25 / 1000

0.25 = 25 / 100
0.0025 = 25 / 10000

Rewrite in simplest form:

25 / 25 = 1
1000 / 25 = 40

= 1/40
Convert Fractions to Percents
eg 5/8 to percents
1) Convert to decimal = 0.625
2) Multiply by 100 and add % sign
= 62.5%
Convert % to Fractions
1) Remove % symbol
2) Write # over 100
3) Simplify
eg: 35% = 35/100
35 divided by 5 = 7
100 divided by 5 = 20
= 7/20
Convert % to Decimals
eg: 78% = 0.78
Roman Numerals
M = 1000
D= 500
C = 100
L= 50
X = 10
V = 5
I = 1
Convert Roman Numeral to Arabic (1)
Begin with largest value then write from left to right.

When I, X, or C is used to to the left of larger value, Subtract it from that value.
eg: IV = 4
Convert Roman Numerals to Arabic (2)
eg: DCCCXXV =
500 + 300 + 20 +5 = 825

MCCXXXIV =
1000
Metric System Prefixes
10^3 = 1000 --- kilo (k)
10^2 = 100 --- hecto (h)
10^1 = 10 --- deka (da)
10^0 = 1
10^-1 = 1/10 --- deci (d)
10^-2 = 1/100 --- centi (c)
10^3 = 1/1000 --- milli (m)
Dependent and Independent Variables
Independent = data put into the set of data --- input

Dependent = output based on input
Algebraic Applications (1)
Addition, Subtraction, Multiplication, and division of polynomial terms.
Constant
A quantity that does not change
Coefficient
The numerical part of a term; the number that is being multiplied to the variable.
Expression
One or more terms consisting of any combination of constants and/or variables.
Algebraic Applications (1)
Addition, Subtraction, Multiplication, and division of polynomial terms.
Constant
A quantity that does not change
Coefficient
The numerical part of a term; the number that is being multiplied to the variable.
Expression
One or more terms consisting of any combination of constants and/or variables.
Variable
An unknown quantity in an expression, usually in the form of x, y, or z.
Like Terms
Terms that have the same variable and with the same exponent.
Degree
The exponent or sum of exponents of the variables of a term.
Divisor
The denominator in a division problem (eg 4/2 . 2 is the divisor)
Dividend
The numerator in a division problem
(eg 14/2 , 14 is the dividend)
Quotient
The answer to the division problem; for example in 14/2 , 7 is the quotient.
Term
A term is a constant, variable, or product of a constant and a variable.

(Terms in an expression are separated by a + or - sign)
Polynomial
Term or combination of terms.
(Monomial or Binomial)
Monomial
Polynomial with 1 term
Binomial
Polynomial with 2 terms
(3x-1) (2x+5)
(3x)(2x) + (3x)(5) - (1)(2x) - 1 (5)

6x^2 +13x - 5
Equations with 1 unknown
Addition principle and Multiplication principle
Addition Principle
Rule that makes it possible to move terms from one side of an equation to the other by adding opposites to each expression.
Multiplication Principle
Rule that makes it possible to isolate the variable in an equation by multiplying both expressions by the reciprocal of the variables coefficient.
Equations with 1 unknown (pt2)

eg: 2(3x -1) = 4x - 14
1) Distributive property to remove parenthesis
2) If there are fractions, remove by multiplying each term by least common denominator
3) Use addition principle to move like terms together on both sides of equation
4) Use multiplication principle to isolate the variable by multiplying both sides of the equation by the reciprocal of the coefficient of the variable
5) Check solution. Substitute the answer into the original equation to make sure both result in the same value.
eg: 2(3x -1) = 4x - 14
2(3x -1) = 4x - 14
6x - 2 = 4x - 14

6x-2 +2 = 4x - 14 +2
6x = 4x - 12

6x - 4x = 4x - 4x - 12
2x = -12

divide both sides by 2
x = - 6
Absolute Value of n = |n|
The distance between the number n and zero on the number line.

|n| = n when n is a positive number
|n| = -(n) when n is a negative number

|x-n| = x-n when x-n is a positive number

|x-n| = -(x-n) when x-n is a negative number
Absolute Value Equations
1) |x-n| = a --- x-n = a or x-n= -a
2) |x-n| < a --- -a < x-n < a
3) |x-n| <_ a --- -a <_ x-n <_ a
4) |x-n| > a ---- x-n > a or x-n < -a
5) |x-n| >_ a --- x-n _> a or x-n _> -a