The word percent is exactly that per cent, which basically means parts of hundred. E.g. 10% are 10 of 100, or 60% are 60 of 100. You can also write this mathematically as 60/100 or 60÷100, which is 0.6.

Now in general: x% are x parts of 100 or x/100 or x÷100. If you want to calculate x% of y you just multiply it: y × x% = y × x ÷ 100.

By what part?

While I get your sentiment, I'm always baffled how people fail to just memorize some basic formulas/equations and then just to plug and play:

1÷kⁿ = k⁻ⁿ

% = 1÷100 = 10⁻²

k×10ⁿ equals k with its floating point shifted by n to the right for positive n, or to the left for negative n

That's really all one needs to know for the "problem" at hand. For your concrete example of "40% of 59" that would just be

59×40×10⁻²

Just solve that whatever way is easiest. I don't get why people get panic-stricken when they see the % sign.