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How to find the Hypotenuse or a leg of a right triangle
Pythagorean theorem:


Special Right Triangles
3:4:5
5:12:13
306090
454590

Spot Special Right Triangles
1 2
11

Perimeter of a Rectangle
P = 2 (lenght +width)

Area of a Rectangle
Area = (lenght)(width)

Area of a Square
A =

Area of a Parallelogram
A = (base)(height)

Area of a Trapezoid
A = (average of parallel sides) X (height)

What is the area?
A = 50


 35+45+X = 180
 80+X = 180
 X = 100

PEMDAS order
 P arenthesis
 E xponents (or radicals)
 M ultiplication
 D ivision
 A ddition
 S ubstraction

Solve:
92x(53)^2+6 / 3
= 3

Percent Formula
Part = Percent x Whole

what is 12% of 25?
Part =


15 is % of what number?



The price goes up from $80 to $100. What is the % increase?

How to predict whether a sum, difference, or product will be ODD or EVEN
Just take simple numbers like 2 and 3

If m is even and n is odd, is the product mn odd or even?
m=2 and n=3
is even, so mn is even

How to recognize MULTIPLES of 2
last digit is even

How to recognize MULTIPLES of 3
sum of digits is a multiple of 3

How to recognize MULTIPLES of 4
last two digits are a multiple of 4

How to recognize MULTIPLES of 5
last digit is 5 or 0

How to recognize MULTIPLES of 6
sum of digits is a multiple of 3, and last digit is even

How to recognize MULTIPLES of 9
sum of digits is a multiple of 9

How to recognize MULTIPLES of 10
last digit is 0

How to recognize MULTIPLES of 12
sum of digits is a multiple of 3, and last two digits are a multiple of 4

How to use the AVERAGE to find the SUM

17.5 is the average of 24 numbers. What is the sum of the 24 numbers?
Sum = 17.5 X 24 = 420

Average of consecutive numbers
average of evenly spaced numbers is simply the average of the smallest number and the largest number.

What is the average of all the integers from 13 to 77?

How to count consecutive numbers
the number of integers from A to B inclusive is B  A + 1

How many integers are there from 73 through 419, inclusive?
419  73 + 1= 347

How to find the Sum of Consecutive Numbers
Sum = (Average) X (Number of terms)

What is the sum of the integers from 10 through 50, inclusive?
Average =
 Number of terms = 5010+1 = 41
 Sum =

what is the median of 88, 86, 57, 94, and 73?
86

What is the median of 88, 86, 57, 73, 94, and 100?

Simple Interest
interest = principal X interest rate (decimals) X time (years or fract of year)


If $10000 is invested at 8 percent annual interest, compounded semiannually, what is the balance after 1 year?
= $10816

If $12000 is invested at 6 percent simple annual interest, how much interest is earned after 9 months?
= $540

Permutation Formula
 where n=#in the larger group
 k=#to arrange

Five runners run in a race. The runners who come in first, second, and third place will win gold, silver, and bronze medals respectively. How many possible outcomes for gold, silver, and bronze medal winners are there?

How many different ways are there to choose 3 delegates from 8 possible candidates?

Combination Eq
 n=#in larger group
 k=#we are choosing

