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Perimeter of a square
P = 4s

Area of a rectangle
A = L x W

Perimeter of a rectangle
P = 2L + 2W

Area of a Circle
A=πr^{2}

Cirumference of a circle
C=2πr or C=πd

Diameter of a Circle
D = 2r

Area of a triangle
A=1/2(b)(h)

Pythagorean Theorem
C^{2} = A^{2} + B^{2}


Volume of a Rectangle
V = LWH

Anything divided by zero is undefined
#/0 = undefined

Simple Fractions
 divide out common factor
 15/3 (divide by 5)

Prime Numbers
 only divisable by 1 & itself
 2,3,5,7,11,13

Composite Numbers
 can be divided by several numbers(even numbers except 2)
 10,15,20,100,42,66....

Improper Fraction to Mixed Number
 Use long division to make into mixed #
 7/3 (3 ÷ 7 = 2 r^{1} = 2 1/3)

Mixed Number to Improper Fraction
 Divided demoninator by whole number , add numerator, use same demoniator
 5 2/3 = (3÷5 + 2= 17/3)

Multiplying Fractions
 multiply across (a/b * c/d)
 5/8 * 3/4 (5*3/8*4) = 15/32
*Simplify when possible*

Multiplying Mixed Fractions
 Change to improper fraction, divide denominator by whole number, add numerator, use same denominator
 4 1/2 * 5 4/5 ( 9/2*29/5)
 Cross multiply
 9*29/2*5 = 261/10
 Convert to Mixed Fraction *if answer is improper
 10÷261 = 26r^{1} = 26 1/10

Dividing Fractions
 to divide, flip the reciprocal, multiply
 (a/b÷c/d = a/b÷d/c)
 5/8 ÷1/4 (5/8*4/1 = 20/8) *simplfy*
 20/8 (divide by 4) = 5/2 *improper*
 2 ÷5 = 2r^{1} 2 1/2

Equivalent Fractions
 divide by same fraction on top & bottom with the same number
 2/5 ( divide by 7) = 14/35

Adding & Subtracting Fractions
 need to have the same denominator before adding or subtracting (GCF)
 a/b + c/d = a+c/b or a/bc/d = ac/b
 2/3 + 4/5 (divide all by 5) = 10/15 + 12/15 = 22/15*improper*
 15÷22 = 1 7/15

Adding & Subtracting Mixed Fractions
 find common denominatior, add fraction & whole numbers
 3 1/4 + 5 2/3 (3 3/12 + 5 8/12 = 8 11/12)
* can change to improper fraction & add*

Complex Fraction
 convert to nomal division, flip reciprical and multiply
 a/b/c/d = a/b ÷ c/d = a/b*d/c
5/9/1/3 (5/9÷1/3 = 5/9*3/1 = 15/1
*simplify when needed*

Multiplying Fractions w/ unknown veriable
 1/4x = 3/4
 divide both sides by 4/1 = 1x=3 x=3

Fraction to Decimal
 convert fraction to division
 1/3 (3÷1 = 0.333)

Multiplying decimals
 multiply, add number of decimal points & apply that to answer
 1.235(3 decimal places)
 0.4(1 decimal place)
 4940(move 4 decimal places)
 = 0.494

Dividing decimals
 move decimal places from divisor to make a whole number, move the same number of place in the dividend
 .03÷15.322(move 2 places) = 3÷532.2
 move decimal to same place in the quotent
 3÷532.2 = 177.4

Solving Equations (multiplying)
 move decimals, divide out
 0.4x = 0.24 ( 40x = 24 / 40÷24 = .6)
 or
 .4x = 0.24 / .4÷0.24 = 4÷2.4 = .6
 with like veriables
 2.5x + 1.5x = 5.24
 4.0x = 5.24
 4÷5.24 = 1.31

Solving Equations
 4(2x1.45)  3(x + 8.02) = 24.9
 8x  5.5  3x 24.06 = 24.9 (Distrubte veriable)
 5x  29.86 = 24.9 (add like veriables)
 5x = 54.79 (29.86+24.9)
 5÷54.76
 x = 10.952

Ratios
 write ratio as fraction
 19 to 42 = 19/42
 if number is decimal, move decimal to make number whole, add number of zeros to number of moved spaces
 1.75/25 (2 places in num, add 2 in dem) = 175/2500
* unit rate/ unit cost means divide*

Proportion
 4 cups flour is to 12 muffins as 8 cups flour is to 24 muffins
 4/12 = 8/24

True Proportion
 cross multiply, compare answer
 1/3  7/21( 21*1 = 21  7*3= 21) True

Solving Proportions
 cross multiply, divide
 8/x = 12/9
 8*9
 72 / 72÷12
 x = 6

Percent as Decimal
 Move decimal place 2 times from the right
 526% = 5.26
 if already decimal, move two places from exsisting decimal
 0.78% = 0.078

Decimal to Percent
 move two spaces from the left
 705 = 70,500%
 if already decimal, move two places from the exisiting decimal
 0.954 = 95.4%

Percent as a fraction or mixed number
 make percent a fraction over 100, simplify
 15% = 15/100(divide by 5) = 3/20

Fraction to percent
 long division to decimal, decimal to percent
 6/25 ( 25÷6 = 0.24, move decimal to places = 24%)
 mixed number only change fraction portion
 1 4/5 ( 5/4 = 0.8 = 1.80%)

Solving of equation or porportoion
is/of x/100

Simple Interest
I = p*r*t
 p = principle
 r = rate of interest (write as decimal)
 t = time in years
 I = interest

Tax
 tax = tax rate * subtotal (write as decimal)
 subtotal = cost + total

Commission
commission = total sales * commission rate (decimal)

Discount
 discount = price * discount rate (decimal)
 sale price = original price  discount

Graphing
pick point to plug into equation, (stick w/ 0,1,2,3), plot points

Complement
 angle equaling to 90
 75^{o} = 75+15 = 90

Supplement
 sum of angle is 180
 125^{o }= 125 +75 = 180

Triangle
sum of all sides are equal to 180

Acute angle
less than 90^{o}

Obtuse angle
greater than 90^{o}

Equations with exponents
 add like terms with similar exponents
 11y^{2}  3y + 7 + 3y^{2 } 7y 7
 14y^{2} (11y^{2} + 3y^{2})  10y(3y7y)
 if negative, distrubute negative
 (9b + 2)  (3b^{2}  4b + 6)
 9b + 2  3b^{2} + 4b  6

Exponents
 add exponents with the same base, no exponent equals 1
 a^{3 * }a * a^{7} = a^{11}
 Multiply bases, add exponents
 2x * 3x^{2} * 4x^{3} = 24x^{6}
 exponent being raised is multiplied
 (2^{8})^{7} = 2^{26}
 number with coeffeciant, raise coeff by exponent, multiply exponents
 (2x^{5})^{3 }= 8x^{15}
 distribute exponents and multiply
 (2x^{2}y)^{2} (y^{3}y^{2})^{3}
 4x^{4}y^{2} * x^{9}y^{6}
 4x^{3}y^{8}

F.O.I.L
First, outside, inside, last
3x(2x^{4}  2x^{2} + 5) = 6x^{5} + 6x^{5} 15x
 (x+6) (x  2)
 x^{2 } 2x + 6x  12
 x^{2 }+ 4x  12

GCF
smallest number in group or smallest multiple of the group
12, 26, 60 = GCF 12
 smallest of coeff first, then smallest of exponents
 6m^{2}, 2m^{2}, 12m^{5} = 2m^{2}

Factorization
 find smallest or coeff and undo multiplication
 7y^{2} = 14y  28 = 7(y^{2} + 2y  4)

