Did you know?
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.
@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 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)
I think this makes it a bit more readable:
a% of b = (a/100) * b = 0.01 * a * b
b% of a = (b/100) * a = 0.01 * b * a
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 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
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.
@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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