General Math

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  1. Rules and Formulas
  2. Properties

1. Rules and Formulas

Order of Operations

  1. Exponents/Square roots
  2. Parentheses
  3. Multiplication, Division
  4. Addition, Subtraction

Scientific Notation

Scientific notation is a shorthand method for writing very large numbers and very small numbers. An example of a number written in scientific notation is 4.35 ×104. In standard notation, this is equivalent to 43,500. The math is done exactly as shown; the first part is multiplied by the power of 10 indicated. In this example, we are using the 4th power of 10, which means to move the decimal point 4 places to the right, yielding a much larger number than the first part (4.35). If the power of 10 were -4, then we would move the decimal point 4 places to the left (multiplying by 0.0001), making the number smaller. To find the scientific representation of a decimal number, simply move the decimal point so that there is exactly one digit to the left of the decimal point. Count how many digits were moved, and use that number as the power of 10. To find the sign of the exponent, use this general rule: if the original number was less than 1, the exponent is negative; otherwise it is positive. Another example: 0.0012 would be 1.2 ×10-3

Here is a step-by-step version. "e+2" means "× 10 2"

Number               Operation
1536.256             Initial standard representation
153.6256e+1          First step of scientific notation; invalid
15.36256e+2          Second step of scientific notation; invalid
1.563256e+3          Final step; valid scientific notation

Area & Volume Formulas

A = lw (rectangle)
A = s2(square when s=length of one side.)
A = (pi)r2 (circle)
A = (bh) ÷ 2 (triangle; b=base, h=height)
A = ½h(B1+B2) (Trapezoid; h=height, B1=Base1, B2=Base2)
V = lwh (rectangular prism; length × width × height)
V = (pi)r² h (cylindrical solid; r=radius of a base, h=height)
V = [4 r³(pi)] ÷ 3 (sphere; r=radius)

2. Properties

Associative Property

Of Addition: (a + b) + c = a + (b + c)
Of Multiplication: (ab)c = a(bc)

Commutative Property

Of Addition: a + b = b + a
Of Multiplication: ab = ba

Distributive Property

For Adding Fractions(c not equal to 0): (a/c) + (b/c) = (a + c) ÷ c
For Addition or Subtraction: ac + bc = (a+b)c
ac-bc = (a-b)c
c(a+b) = ca + cb
c(a-b) = ca - cb

Means Extremes Property

For all real numbers a, b, c, d: (a/b) = (c/d) then ad = bc

Opposite of Opposites(Op-Op-Prop)

For any real number a: -(-a) = a

Pythagorean Theorem

For a right triangle with legs a and b, and hypotenuse c:
a2 + b2 = c2

Slope-Intercept Form

For any line with slope m and y-intercept b: y = mx + b

Square of a Square Root

For any positive real number n, the square root of n2 is n.