## Basic Maths formulaes

Posted by mtwinkle on June 6, 2007

**Arithmetic / Properties of Numbers**

Even/odd (e/o) identities:

- e +/- e = e
- e +/- o = o
- o +/- e = o
- o +/- o = e
- e x e = e
- e x o = e (also: o x e = e)
- o x o = o

Decimal conversions:

- ½ = .5
- 1/3 = .33, 2/3 = .67
- ¼ = .25, ¾ = .75
- 1/5 = .2, 2/5 = .4, 3/5 = .6, 4/5 = .8
- 1/9 = .11 (repeating), 2/9 = .22 (repeating), etc.
- It’s handy to know 6ths, 7ths, and 8
^{th}s, but they require more memorization and don’t come up as often.

Percent conversions:

- 37% = 0.37 = 37/100
- 0.2% = 0.002 = 0.2/100 = 2/1000

Exponents: (note: x^y = “x raised to the y power”)

- x^-y = 1/x^y
- (x^y)(x^z) = x^(y+z)
- (x^y)^z = x^(yz)
- x^1/2 = radical (square root of) x.

Radicals (roots): (note: r2 = “radical 2” or “square root of 2”)

- r2 = approximately 1.4
- r3 = approximately 1.7
- Know the square of every integer up to 13.
- r(xy) = r(x) times r(y)

**Geometry**

Area

- Triangle: ½ times base times height
- Rectangle: length times width
- Circle: pi(r^2)

Circumference:

- Circle: 2pi(r)
- All other figures: the sum of the lengths of all sides

Right triangles:

- a^2 + b^2 = c^2, where a and b are two sides of the triangle and c is the hypotenuse (Pythagorean theorem)2.Common integer solutions to the Pythagorean Theorem, including 3 : 4 : 5, 6 : 8 : 10 (and all other multiples of 3 : 4 : 5), and 5 : 12 : 13
- The ratio of sides in a triangle with angles 30 : 60 : 90 is x : x(r3) : 2x
- The ratio of sides in a triangle with angles 45 : 45 : 90 is x : x : x(r2)

Solids:

- Volume: area of the base times height
- Surface area: the sum of the areas of all faces of the solid

Coordinate Geometry:

- Slope of a line = (change in y)/(change in x)
- Equation of a line: y = mx + b, where m = slope and b = y-intercept (the point at which x = 0)

**Miscellaneous**

- Rate = distance/time
- Combined work: 1/a + 1/b = 1/t, where a and b are the amount of time it takes two entities working alone to complete a task and t is the amount of time it would take them to complete the task working together. (I’ll go into this in more detail, including some shortcuts, in a future Tip.)
- Average = sum of terms / number of terms
- Probability = number of desired outcomes / number of possible outcomes

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