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The panzer has spoken
(sh.itjust.works)
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this post was submitted on 09 Nov 2023
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they absolutely taught you the commutative property and transitive property
Yeah but they clearly taught it poorly
But they didn't teach it in this context.
People don't automatically see the multiplication of a percentage and a whole number for their denominators, because why would they? It's a whole number. You shouldn't be expected to break those things down on your own unless if you spend hours and hours on minor small arithmetics. Yet, that's precisely the explanation even that disaster of a comment above did not do. They overcomplicated by doing a stacked fraction.
For anyone wondering. 6% of 50 is:
(6/100) * (50/1)
and is the same thing if you swap out the 100 and the 1.
They taught you all the parts. Where they (and I’d agree most math education) failed was to connect the dots.
They taught you about these properties.
They taught you that division is just fractions and vice versa.
They taught you that x/1=x.
They taught you multiplying fractions as (numerator_a • numerator_b) / (denominator_a • denominator_b).
They taught you percentages are just “per centum”, or per hundred, or basically just a fraction “over 100”.
But these tricks, much like many other mental math shortcuts that are useful for everyday life, got glossed over or missed entirely.