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Percentages are reversible. 8% of 25 is the same as 25% of 8, and often one of them is much easier to do in your head.

@ben @fribbledom I sort of knew that but never realized the implications? :blob_dizzy_face:

@fribbledom Wtf, never quite really realized it. I must've known but not this obvious. :D

@fribbledom I have many such tricks. A bunch I use rely on 1/(1+x) ~= 1-x, when x is small (specifically, when x*x can be neglected). So, 18/19 = 18/(18+1) = 1/(1+18) ~= 1-1/18. 1/18 is close to 1/20 or .05. So 18/19 is about .95 (actually .947), and I did it entirely in my head without any actual division! (If you use this trick to approximate 1/18 = 1/(20-2)=1/(20*(1-2/20))=1/(20*(1-1/10)) ~= 1/20 * (1+1/10) = .055, you end up with .945. Again, these are steps one can do in one's head.)

@fribbledom Spot the typo. :) That first bit after 18/(18+1) should be 1/(1+1/18) not 1/(1+18).

@fribbledom !!
That absolutely makes sense and I had absolutely never thought of that.

@funnypanja @fribbledom no. 2 is 8% of 25 because of my decision. Everything else was my stupid neighbors to blame.

@fribbledom I remembered that there was a trick like that, but for the last few days I was trying to remember Perfect timing thanks! (note that I didn't actually look into it, I was just lightly thinking about it)

@fribbledom you mean a*b=b*a or (a/100)*b=a*b/100 .. it sounds very boring stated that way.

@jasper

I think this makes it a bit more readable:

a% of b = (a/100) * b = 0.01 * a * b

equals

b% of a = (b/100) * a = 0.01 * b * a

@fribbledom @jasper

so 25 * 8 = 200 and 8 * 25 = 200, and 200 * 0.01 = 2.

therefore

25 percent of 8 is 2

and

8 percent of 25 is 2

right?

@jasper
Exactly. I don't know why it would be news that 8*5 is the same as 5*8 and just move the decimal place to make sense. People do this all day when out shopping don't they.

@fribbledom did u know? multiplication in the rational numbers is commutative, so 25/100 * 8 = 25 * 1/100 * 8 = 25 * 8 * 1/100 = 25 * 8/100 = 8/100 * 25.

@fribbledom also, it's important that the multiplication is associative, otherwise (25 * 1/100) * 8 = 25 * (1/100 * 8) may not be true.

@fribbledom @puresick it's multiplied, miltiplication is commutative. (Addition is, too. Division or Subtraction are not).

@fribbledom @anarchiv I stumbled across this when I was 8 and learnt the associative rule.

@fribbledom You can really see why this is true if you put it like this: 8% is the same as 8*0.01, so:

8% of 25 is 8*0.01*25, and

25% of 8 is 25*0.01*8

the birthday phenomenon 

@fribbledom

How many random people need to be at a party before there is a 50% chance that two of them share the same birthday?

Hint: it's a lot lower than most people think.

@fribbledom This never occurred to me. Thank you! I'm sad at how many people are explaining your own point to you though 😓

@fribbledom I'm not sure 25*8 is any easier for me to do than 8*25, frankly. Keeping in mind to move the point two places to the left afterwards, of course.

@carcinopithecus @fribbledom what if you need 37% of 7? Multiplying and moving the decimal point is simply more universal than relying on always having nice divisible ratios.

@isagalaev @fribbledom

When I see " * 25%", my mind translate it to "/ 4" without thinking. And the whole thing becomes 8 / 4 :blobsmiley:

@fribbledom I am deeply angry that I wasn't taught this in school.

@fribbledom you can also often do something like 8 * 25 and move the comma two places left

@fribbledom @lotus42 this is STILL blowing my mind hours later. I think this toot has fundamentally and permanently altered the way I see percentages

@fribbledom I never realized that, even though it's really just a simple consequence of the commutativity and associativity of multiplication. Neat!

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