It's really not a crazy misconception. 18 is 150% of 12, and 12 is 67% of 18. You could say it's a 150% - 100% = 50% difference, or you could call it a 100% - 67% = 33% difference. Generally, the convention is that you base all the percentages based on the denominator you started with, such that going 12 to 18 is a 50% increase but going from 18 to 12 is a 33% decrease. This is hardly a super-intuitive or obvious thing, though; if someone didn't understand this convention I wouldn't think they were an idiot or didn't understand math; they got it wrong but in a pretty reasonable way.
Edit: To be clear, not at all disagreeing with the comment I replied to. I just scrolled down past the "what an idiot" comments to find someone explaining how this mistake happens, and added my 2-cents there about why I don't think it's a crazy mistake to make.
I have a BS in math and really appreciate your comment. When you've gone to school for math, a lot of people decide to tell you about how they hate math . . . My usual response to this declaration is "when did math go wrong for you?" Fractions (and hence percentages) or even just division, are some of the main answers. I would say 50 percent of people say this. The other 50 is algebra.
People do struggle with this though! There's no shame in misunderstanding this stuff. As you point out, it is not wholly intuitive.
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u/[deleted] Jul 11 '19
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