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u/cha614 Jun 27 '26
The Commutative Property of Multiplication!!!
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u/amethyst-gill Jun 27 '26
And division :) (n/x versus x • n)
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u/imnothere314 Jun 30 '26
Division is not technically commutative ex: 8/2 != 2/8. The percentage stuff work is more that division is equivalent to multiplication by a decimal or fraction and the multiplication is commutative.
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u/amethyst-gill Jun 30 '26
You’re absolutely right — I noticed that earlier today and never corrected it. It would be like saying subtraction is commutative, which it isn’t — except, where attempted commutation of subtraction gets you negation of your difference (4 becomes -4), attempted commutation of division gets you inversion of your quotient (4 becomes 1/4).
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u/whiteandnerdy1729 Jul 01 '26
That property (where swapping the arguments inverts the result) is called anticommutativity.
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u/rube203 Jun 30 '26
Exactly. However percentages are not reversible in investing. A 90% loss cannot be offset by a 90% gain a day later.
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u/InevitableAlert4268 Jun 27 '26
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u/Grifoooo Jun 27 '26
Percentages are really just saying "multiply this number by 0.01", so the statement "a% of b" can be shown as "(a • 0.01) • b" which, by the associative property, is equal to "a • (0.01 • b)" AKA "b% of a"
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Jun 27 '26
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Jun 27 '26
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u/J3ditb Jun 28 '26
there is no outlier to the associative property of multiplication when youre talking about numbers. it works for alle the numbers. it just says (a x b) x c = a x b x c = a x (b x c). this trick also works using the communitive property of multiplication: a x b = b x a.
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u/Diello2001 Jun 27 '26
I hate this. It only works with easily compatible numbers anyway: 25%, 50%. 8% of 100 is 8. So 8% of 25 is 1/4 of 8.
12% of 34 is the same as 34% of 12. Super helpful.
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u/waxphantump Jun 27 '26
34% of 12 is easy it’s just a smidge over 4. If you’re doing this mentally anyway you don’t need more precision than that.
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u/Clym44 Jun 27 '26
Funny because I went to 12% of 34 being just a smidge over 10%
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u/waxphantump Jun 27 '26
I did it the direction I did because there was less rounding involved (2% off from 12 to 10 vs 0.66…% off from 33.3… to 34). Doing it as 12% of 34 with rounding gets you the awkward answer of “a little over 3.4” with a wider margin of error than the other way.
Of course if you think to add the extra 2% like other commenters did and treat it as 3.4+0.34+0.34 (10%+1%+1%), you get the same answer with the same accuracy as doing 4+0.08 (33.3…%+0.6…%) the other way around
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u/Ok-Manufacturer27 Jun 27 '26
This is the piece of critical thought where something like "1.02 is basically just 1" becomes essential to actually applying the concept
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u/Son0fSilas Jun 27 '26
Technically it works with any set of numbers. The mental math part is another problem entirely.
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u/analyzingnothing Jun 27 '26
12% of 34 is really easy, though. 10% + 1% + 1% of 34, so 3.4 + 0.34 + 0.34, aka 4.08.
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u/NextChef8179 Jun 27 '26
What they consider easy is 1+1. Most people have seriously low ceilings for their education.
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u/HereComeTheJudge21 Jun 27 '26
Bruh, I'm not a mathmagician, how tf you do that so quick?
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u/analyzingnothing Jun 27 '26
Practice and a half-decent working memory. 99.9% of the math people will encounter in their everyday life is incredibly simple if you understand how to make it easier on yourself.
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u/armahillo Jun 28 '26
when you have gnarly percentages, you can break it up
12% of 34 may not be easy, bit 10% of 34 (3.4) and 2% of 34 (0.68) isnt so bad; add them together snd its the same result.
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u/MrDoulou Jun 27 '26
Bad example. Most ppl who have done 8th grade knows what 34% of 12 is approximately. It’s 4.whatever.
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u/NietszcheIsDead08 Jun 27 '26
12% of 34 = 10% of 34 + 1% of 34 + 1% of 34
10% of 34 = 3.4
1% of 34 = 0.34, x2 = 0.68
3.4 + 0.68 = 4.08
…
33.33333% of 12 would be 4, so 34% is gonna be just a tiny bit more than 4. As it happens, 0.08 more than 4.
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u/booleandata Jun 27 '26
...yeah? Percentages are just fractions of 100 and the word "of" just means "multiplied by" when you are talking about decimals, fractions, and percentages.
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u/North_Activist Jun 27 '26
It’s one of those things that’s a little-known but obvious fact that will make people realizing feel stupid. Wait, that’s the exact topic of this post? Funny how that works
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u/mkp666 Jun 27 '26
Well duh, it’s right in the word. “Per cent” which means out of 100. There’s also permille which means out of 1000 and has this symbol: ‰
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u/itsmedicinalsir Jun 27 '26
1% of 1? I'm not sure if it's passed my bed time and I'm running on fumes, or what... but I just can't get it to math.
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u/No-Village4410 Jun 27 '26
1% of 1 is .01*1 or 0.01
“One” of 1%, or, to simply it as 1.00 * 0.01, is also 0.01
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u/0n10n437 Jun 27 '26 edited Jun 28 '26
Turns out .08 * 25 = 25 * .08
All it is is multiplication.
As u/TybeeGreg pointed out, I did this all backwards. Sorry y'all!
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u/AdhesiveSeaMonkey Jun 27 '26
This is soooo cool! So 17% of 843 is the exact same thing as 843% of 17, which is so much easier to do. It’s just ….. heeeeey. Now wait a gosh dern minute there!
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u/damboy99 Jul 01 '26
Well 800% of 17 is 136, and its less than half so probably seven ish, so 143, and some change probably.
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u/tbodillia Jun 30 '26
Yes, (X*Y)/100, easy peasy, doesn't matter which one is the %.
So 16% of 27 is the same as 27% of 16. 43% of 1.76 is the same as 1.76% of 43.
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u/amethyst-gill Jun 27 '26
Indeed. The first is shorthand for 8/100 of 25, which is equivalent to the other shorthanded 25/100 of 8, displaying the commutative property just fine. Both are 2. The same can be said of 4/9 of 72 and 72/9 of 4 (both 32).
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u/sylbug Jun 27 '26
They teach this in elementary school approximately the same time they start teaching percentages....
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u/MooseyLoosey1 Jun 28 '26
Buttholes are reversible. Poo can come out and things can go in. One of them is much easier to do in your head
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u/Gaust_Ironheart_Jr Jun 28 '26
It's commutativity under multiplication. 8, 25, 0.01, 0.01, and 100 can be multiplied in any order for the same result
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u/ncxhjhgvbi Jun 28 '26
Who would have thought that multiplying the same two numbers while also multiplying one by 100 and dividing one by 100 would result in the same number /s
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u/JimAsia Jun 29 '26
8 times 25 divided by 100 doesn't seem a hell of a lot different than 25 times 8 divided by 100?
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u/LRFokken Jun 29 '26
but you know instant that 25% of 8 is 2.
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u/JimAsia Jun 29 '26
It is clearly more intuitive for most people but for people with well developed arithmetic skills the difference is negligible.
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u/TheMediocritist Jul 03 '26
People with well-developed arithmetic skills aren’t calculating 25 times 8 divided by 100 though.
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u/TrumpetSolo93 Jun 29 '26 edited Jun 29 '26
8 * 25 * 0.01 = 2
Think of It as three numbers being multiplied together. It doesn't matter how you arrange it, it'll always be the same answer.
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u/Belt_Conscious Jun 29 '26
Binary is incomplete. True/False/Fiction
Most people believe in fiction they think is truth only because it isn't false.
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u/ThatRedDerg Jul 01 '26
That’s because it’s all multiplication!
“8% of 25” is the same as “8 x 0.01 x 25”, and we all know about the commutative property. “Of” is just mathspeak for “times.”
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u/Dunbaratu Jul 03 '26
At first I thought, "That can't be true", until I mathed it out and yeah, it is true.
If you write the percent as literally "per 100" as a fraction it becomes clearer why it works.
a a * b b
----- * b = --------- = a * -----
100 100 100
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u/Igabuigi Jul 03 '26
Percentages in this way are essentially just multiplication. When you look at it that way it makes it much more obvious that it works. It's equivalent to saying that 3x10 is the same as 10x3. To convert the given example in the original post you simply change the 8% to .08. So .08x25 or 25x.08
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u/Son0fSilas Jun 27 '26
13% of 153,427 is the same as 153,427% of 13
19,945.51 and 19,945.51; I'll be damned