Simple proportions

It's easy to remember the steps for quickly solving proportions by using the "cross multiply and divide" mnemonic.

Example:

Suppose I am 5' 10" (70 inches) tall, and one day I happen to measure that my shadow is 56 inches long (without being too obvious about it, of course). At (about) the same time, I notice that the shadow of a nearby street lamp is 16 feet long.
How tall is the street lamp?

Referring to the illustration above, let x = the height of the street lamp

y = the length of the street light shadow (16')

m = my height (70")

n = the length of my shadow (56")

So

x = 70" · 192' / 56" = 20'

Therefore, the street lamp is 20 feet tall. (Notice that it is not even necessary that all numbers use same units so long as units are consistent on each side of the proportion.)

This mnemonic is also useful for inverse proportions. Just invert one of the fractions such that:

x = n · y / m