How do I calculate a percentage of something (i.e. 700 is 37.5% of what number)?

The way I was taught to do it in school was as follows. It's not very elegant but it's how I still do it today.

700 ` 37.5
---- = -----
x ` 100

And therefore:

37.5x = 70000
x = 1866.67 or 1867

Halliburton Shill's way is easier.

Divide the number by the percent, but the percent needs to be converted to its standard number form (37.5% = .375).
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A shorthand way to get an approximation is to ask yourself how many times would you multiply the percent to get 100% and then take that number times the number, which in this case you'd say about but under 3, so the answer would be near but under 2100 and more than 1400.
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BTW, "i.e." in this case should be "e.g."

in your example, divide the 700 by the percentage (remember to move the decimal point two places to the left) which would result in the answer 700 is 37.5% of 1866.66.

700 = .375 * x
x = 700 / .375 = 1866.66666...

It makes things infinitely easier if you understand what is being asked before you answer, and math is no exception. In mathspeak, "of" means multiply and "is" means "equals." (Equal, the same. Four is Four, and 4 = 4 = (3+1) = (16/4) etc.)

(Example A)

half of those ten pears = 5 pears
because (50%)(10) = 5

(Example B)

60 is a quarter of what number?
Read the mathspeak: 60 = (1/4)(?)

(But let's be all growed up and substitute a y for the question mark.)

60 = (1/4)y
Welp, let's multiply each side by 4 to get rid of that fraction on the right side.
240 = y
Blammo! Now go back to the question and check your work: Is 60 a quarter of 240? You're damn right it is!