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Perimeter of a square
P = 4s
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Area of a rectangle
A = L x W
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Perimeter of a rectangle
P = 2L + 2W
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Cirumference of a circle
C=2πr or C=πd
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Diameter of a Circle
D = 2r
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Area of a triangle
A=1/2(b)(h)
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Pythagorean Theorem
C2 = A2 + B2
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Volume of a Rectangle
V = LWH
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Anything divided by zero is undefined
#/0 = undefined
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Simple Fractions
- divide out common factor
- 15/3 (divide by 5)
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Prime Numbers
- only divisable by 1 & itself
- 2,3,5,7,11,13
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Composite Numbers
- can be divided by several numbers(even numbers except 2)
- 10,15,20,100,42,66....
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Improper Fraction to Mixed Number
- Use long division to make into mixed #
- 7/3 (3 ÷ 7 = 2 r1 = 2 1/3)
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Mixed Number to Improper Fraction
- Divided demoninator by whole number , add numerator, use same demoniator
- 5 2/3 = (3÷5 + 2= 17/3)
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Multiplying Fractions
- multiply across (a/b * c/d)
- 5/8 * 3/4 (5*3/8*4) = 15/32
*Simplify when possible*
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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 = 26r1 = 26 1/10
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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 = 2r1 2 1/2
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Equivalent Fractions
- divide by same fraction on top & bottom with the same number
- 2/5 ( divide by 7) = 14/35
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Adding & Subtracting Fractions
- need to have the same denominator before adding or subtracting (GCF)
- a/b + c/d = a+c/b or a/b-c/d = a-c/b
- 2/3 + 4/5 (divide all by 5) = 10/15 + 12/15 = 22/15*improper*
- 15
÷22 = 1 7/15
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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*
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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*
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Multiplying Fractions w/ unknown veriable
- 1/4x = 3/4
- divide both sides by 4/1 = 1x=3 x=3
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Fraction to Decimal
- convert fraction to division
- 1/3 (3÷1 = 0.333)
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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
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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
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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
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Solving Equations
- 4(2x-1.45) - 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
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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*
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Proportion
- 4 cups flour is to 12 muffins as 8 cups flour is to 24 muffins
- 4/12 = 8/24
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True Proportion
- cross multiply, compare answer
- 1/3 - 7/21( 21*1 = 21 - 7*3= 21) True
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Solving Proportions
- cross multiply, divide
- 8/x = 12/9
- 8*9
- 72 / 72÷12
- x = 6
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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
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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%
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Percent as a fraction or mixed number
- make percent a fraction over 100, simplify
- 15% = 15/100(divide by 5) = 3/20
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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%)
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Solving of equation or porportoion
is/of x/100
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Simple Interest
I = p*r*t
- p = principle
- r = rate of interest (write as decimal)
- t = time in years
- I = interest
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Tax
- tax = tax rate * subtotal (write as decimal)
- subtotal = cost + total
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Commission
commission = total sales * commission rate (decimal)
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Discount
- discount = price * discount rate (decimal)
- sale price = original price - discount
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Graphing
pick point to plug into equation, (stick w/ 0,1,2,3), plot points
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Complement
- angle equaling to 90
- 75o = 75+15 = 90
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Supplement
- sum of angle is 180
- 125o = 125 +75 = 180
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Triangle
sum of all sides are equal to 180
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Acute angle
less than 90o
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Obtuse angle
greater than 90o
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Equations with exponents
- add like terms with similar exponents
- 11y2 - 3y + 7 + 3y2 - 7y -7
- 14y2 (11y2 + 3y2) - 10y(-3y-7y)
- if negative, distrubute negative
- (9b + 2) - (3b2 - 4b + 6)
- 9b + 2 - 3b2 + 4b - 6
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Exponents
- add exponents with the same base, no exponent equals 1
- a3 * a * a7 = a11
- Multiply bases, add exponents
- 2x * 3x2 * 4x3 = 24x6
- exponent being raised is multiplied
- (28)7 = 226
- number with coeffeciant, raise coeff by exponent, multiply exponents
- (2x5)3 = 8x15
- distribute exponents and multiply
- (2x2y)2 (y3y2)3
- 4x4y2 * x9y6
- 4x3y8
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F.O.I.L
First, outside, inside, last
-3x(2x4 - 2x2 + 5) = -6x5 + 6x5 -15x
- (x+6) (x - 2)
- x2 - 2x + 6x - 12
- x2 + 4x - 12
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GCF
smallest number in group or smallest multiple of the group
12, 26, 60 = GCF 12
- smallest of coeff first, then smallest of exponents
- 6m2, 2m2, 12m5 = 2m2
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Factorization
- find smallest or coeff and undo multiplication
- 7y2 = 14y - 28 = 7(y2 + 2y - 4)
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