[RheingoldRiver]

I don't think the author explained it well. What % means, is, "out of 100" so like X% is X out of 100. % is a unit, just like meter or candela. You can do dimensional analysis with %. To remove a % you do like, X % * 1 / (100%) and then the two % (remember % is a unit) cancel out so you get X % = X / 100.

This dimensional analysis makes more sense with multiple terms, for example X % * Y = X % * 1 / 100% * Y = X * 1 / 100 * Y = X * Y / 100. (And note "of" means "times")

It's the same thing as saying, 5 * 2cm = 10cm = 5cm * 2 (hopefully the statement 5 * 2cm = 5cm * 2 qualifies as "obvious")

If this entire explanation is as automatic to you as breathing (which yes it is if you did a significant amount of technical courses as a student, although admittedly dimensional analysis tends to come up in chemistry not math) then the statement "X% of Y = Y% of X" is vacuously true and I would feel comfortable saying this is more or less "By definition of %" with no further explanation, if I were talking to someone who I know has an equivalent background to me.

Doing the conversion can often be helpful. For example say I'm thinking to myself, "what is 4% of 50" and I'm like ugh idk but half of 4 is 2 so the answer is 2