Why does "of" get converted to multiplication in percentage?

Question

Why is $50$% of $500$ equivalent to $\frac {50}{100} × 500$? Why does "of" get converted to "$×$"?

Answer 1

Because the $\%$ sign designates a special fraction of something.
I say special because $1\%$ is $1/100$th of something.

In general there are other fractions of course (1/3, 1/5, 1/8, etc.)
but these do not have a dedicated sign as $1/100$ has (the % sign).

And $1/100$th of something (e.g. of $A$) is of course $\frac{1}{100} \cdot A$.

Then $n\%$ means $n/100$ ths of something so it's $\frac{n}{100} \cdot A$.

That's where the multiplication comes from.