fun math hack:
because fractions and decimals are weird, each number has a sort of "partner" number you can use to cheat multiplication and division
i'm bad at explaining this kind of stuff in words, but an example of this is 2 and 5
multiplying stuff by 5 the normal way is kind of a pain, right? if you're doing it in your head, at least. especially for bigger numbers. but because .5 = 1/2, if you divide by two and add a zero you get the same result. and dividing stuff by 2 is easy, since you generally know what half of a given number is off the top of your head anyway, right?
and it works in reverse as well. 12 x 2 = 24, and so does 12/5 x 10, though the latter is way less intuitive to solve so you'd generally only do it the other way around.
or for a bigger number, say you're trying to solve 2384 x 5 without a calculator. not too appealing! sure, you can do 4 x 5 + 80 x 5 + 300 x 5 + 2000 x 5 (or however you choose to handle the zeroes. personally i generally add them after.) but that's a lot of digits to hold in your head and you have to carry on literally all of them. and it just takes longer to do.
2384/2, on the hand, is easy. 1 is half of 2, 1.5 is half of 3, 4 is half of 8 (and add the .5 to make it 9) and 2 is half of 4. 1192. add a zero to get 11920 and bam, easy solve, barely even have to think about it if you're quick with simple calculations. (and if you're not... well, this is still probably easier)
the extra appealing part is that doing it like this lets you work from the biggest digit to the smallest rather than the other way around, which i personally find to be way more intuitive since it's the direction you read the number in.
this happens because we use base 10 for our number system and 2 = 10/5 while 5 = 10/2, so they match.
other number pairs:
4 and 2.5
8 and 1.25
16 and .625
as you can see, it basically only happens with multiples of 2 and 5, so it doesn't work for every situation, but memorizing the ones that show up a lot can let you solve math problems in your head that you'd otherwise have to pull out a calculator for, and in the right situation that can be pretty handy. also makes for a fun party trick to impress people with
(3 and 1/3 are also a pair but since the latter is an infinite decimal it doesn't come up nearly as often. ditto for other multipliers of 3.)
hope someone gets some use out of this. i have no idea to what extent this quirk of fraction/decimal interaction is common knowledge but it was something i figured out myself rather than learning in school so i figure it's probably not completely widespread, and it can make certain problems a lot easier to solve so i figured i'd share it.
