Introduction

I’m making this for someone I care about.

Fractions

$ a/b * x/y = (a*x) / (b*y) $

$ a/(b/c) = (a*c) / b $

$ (a/b)/c = a/(b*c) $

$ 1/(1/y) = y $

$ 1/(a/b) = b/a $

Factors

$ (a + b) (a - b) = a^2 - b^2 $

Fractals

$ a^b * a^c = a^(b+c) $

$ (a^b)^x = a^(b*x) $

$ a^0 = 1 $ (when $ a != 0 $)

$ (a^b)/(a^c) = a^(b-c) $

$ a^-b = 1/a^b $

$ (ab)^x = a^x*b^x $

$ (x / y) ^ a = x^a/y^a $

Inequalities

Memorize:

$ x > y $
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$ ax > ay $
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$ -bx < -by $

When you multiply or divide by a negative number, you have to flip the sign. This is because basically when you are adding or subtracting the same number, you are moving both sides in the same direction. When you are multiplying or dividing both sides by a positive number, you are magnifying/reducing both sides. But when you magnify/reduce by a negative number, you are moving the direction the opposite direction.

Geometry

Trapezoid

A trapezoid has four sides, and at least a set of opposing sides needs to be parallel. It’s also possible that both sets of opposing sides are parallel, it’s called a parallelogram. Yes, rectangles and squares are also considered to be trapezoids (and parallelograms).

Area:

$ A = h*(a+b)/2 $

Parameter:

$ P = a+b+x+y $