Also, a surprising number of people don’t know that precentages are more often than not represented as decimals between 0 and 1 as opposed to actually a number out of 100 when used in calculations (because the concept of a percent doesn’t really exist in math, it’s just a context specific way of formatting a decimal). A lot of people just enter 69 when calculating a formula that operates on a precentage instead of 0.69 which obviously makes the formula useless, or if a formula is supposed to output a precentage, they assume that it output 0.69 percent instead of 69 percent.
Yeah the correct term would be “commutative” as someone already pointed out. Meaning the order doesn’t matter when considering multiple percentages. E.g 50% of 73% of something is the same as 73% of 50% of that same thing
Honestly I recently switched to vyvanse and I don’t actually smoke to get high (at least not until the kids are in bed). I just microdose a bit throughout the day and it balances out the vyvanse. Like, the stimulants alone are just a little bit too much for me. The combo, though, I can dial in just right.
But weed alone always made me fixate on arithmetics. And then stims turn that up to 11.
…I mean, yeah? If the number is 50 or 10 that works out great. But let’s try that with 7% of 13. Now it’s 13% of 7. Just like you said, “much easier to calculate.”
Okay, choosing prime numbers was intentionally mean on my part. But 3% of 9 becomes 9% of 3. 4% of 2 becomes 2% of 4. Can anyone honestly look me in the eye and tell me that this tip has helped them out in any meaningful way?
9% of 3 is easier to estimate because you know it’s “almost 10% of 3”. Or, since 10-1==9, you could think of it as (10% of 3)-(1% of 3) and get the right answer using some other shortcuts. Humans being generally pretty good at base10, this is easy to figure out in your head as (0.3 - 0.03) and get 0.27.
Or, you could do what another commenter suggested and “3% of 9” can broken down as (3/100)•(9/1), becomes, (3•9) / (100•1), becomes 27/100, becomes 0.27. And that can be simplified as xy/100.
Different tools for different jobs. Base10 tricks are good for stuff like figuring out, say, a 15% or 20% tip, because you can easily figure out a 10% tip just by moving the decimal one space to the left, and add half of that (for 15) or double it (for 20). Or half and half again for (almost) 18%. xy/100 is a good trick for figuring out small percentages like sales tax (unless you’re in a place like Mass where it’s 6.25 and you gotta change it now to 625y/10000. At that point I’d just estimate at 6 in my head, or if I had to solve it mentally do (6y100) + ((1y100)/4).
Well, single digit percentages are easy. If it helps, move your decimal to the right so 9% becomes 90%. You can probably calculate 90% of 3 because you can do 10% and subtract it and get 2.7. Now move your decimal back to the left and you get 9% of 3 which is 0.27. You can do the same with higher percentages once you learn to break them in to 10% pieces.
This is a coherent method and makes a lot of sense.
Mental gymnastics is when someone has to lie to themselves to make a point that isn’t correct. Like when people argue that trump was a good president because they can list several good things he did.
Or when people claim something is mental gymnastics when it’s actually called maths.
You’re really asking whether commutativity of multiplication has ever helped anyone? Because that’s what this is.
And yes it has helped me eg. estimate things or whatever along the years – but of course it’s not going to be some sort of magical mathematics trick where just by reversing the numbers it’ll always make things easier to calculate in your head
No, I think we all learned that multiplication is commutative in late elementary school, and obviously that’s an important thing to know.
But I think the original post tried to make it out to be some magical mathematical trick, and I really don’t understand that. Maybe I misunderstood the post.
Edit: wow, “commutative” is a really hard word to spell.
Yeah I think this is more about how you interpreted it, because it doesn’t look like others took it as being an absolute magic trick rule and neither did I.
The Panzer of the Lake didn’t use the word “commutativity” (fuck that really is hard to spell), but it gave out some wisdom that applied that rule by saying that “percentages are reversible”: if the reverse of a percentage would be easier to calculate, you can use it and get the same answer. If it’s not easier, well, then you’re screwed 😁 Oooooor depending on the situation you can use the a × b% = a × b / 100 commutativity trick:
You’re welcome! Glad I could give you an a-ha moment.
Having an intuitive feel for tricks like using the definition of operators or symbols to make your life (well, calculations at least) easier usually means that you either have to just be “naturally” talented at math which is really rare, or you’ve just had to grind grind grind math at eg. university, work or whatever. So unless someone was taught that above trick and they actually remember it from school, they might never come to think that “hmm % just means / 100 so that can make this easier to figure out in my head”.
Which equals 29^2 x .01 => ((28 x 30) +1) X .01
=> (840 + 1) x .01 => 8.41
28 x 30 is an easy mental calculation, as is adding 1, as is moving the decimal place over 2 places. I am teaching this to 4th graders, in two weeks. % to decimal is next week. They can square 2-digit numbers in their heads, already.
The trick that I teach the shorter humanoids is to subtract 1 from the multiplier of 9, put that number in the 10s column, then complete the nine and put that in the 1s column.
Then we spent some time finding the pairs of numbers that make 9. 1+8. 2+7, 3+…7+2, 8+1. I have to be explicit in this part, or they will shortcut to 3, (use fingers to count to 9) uh 6? They usually learn it in a day or two. To get them to flash to instantly know their times tables takes longer.
In the meme example you wouldn’t, but if you were trying to figure out Something like 2% of 5, it’s easier to do (2 * 5)/100=0.1 then to do .02 * 5 or .05 * 2.
My comment was mainly pointing out that you can multiply those numbers in whatever order you want.
You can work it out yourself. 6% is the same as 6/100, so 6% of 50 is (6/100)*50. Then do some algebra and see if you can jiggle it to say (50/100)*6. Then replace 6 and 50 with Greek letters so it looks more convincing.
The word percent is exactly that per cent, which basically means parts of hundred. E.g. 10% are 10 of 100, or 60% are 60 of 100. You can also write this mathematically as 60/100 or 60÷100, which is 0.6.
Now in general: x% are x parts of 100 or x/100 or x÷100. If you want to calculate x% of y you just multiply it: y × x% = y × x ÷ 100.
I totally remember being taught this. It’s just way easier to break down percentages in terms of the nearest 1% or 10% times the number in the percent times the number you’re taking the percentage of. You don’t have to do the math for the 1 or 10 percentage as long as you remember that a 10% means move the decimal left once and 1% means move the decimal left twice. The rest is just basic multiplication.
40% of 59 = 10% of 59 times 4.
So…
4x59=236
or
(4x50=200) + (4x9=36)= 236
10% means move the decimal left once,
Therefore 40% of 59 is 23.6
With that you can easily do more complex percentages mentally like…
62% of 35 = 10% of 35 times 6 plus 1% of 35 times 2.
that’s a shitload of lines of math to write out/work in your head. I learned percentages of x as: 6 * 45 / 100 = x (2.7) If you picture both as fractions, you multiply the opposite and then divide by the other number to get the missing one (x). Hopefully Lemmy renders this well…
6
x
100
45
The way I learned it was multiply diagonally and then divide by whatever is opposite diagonally to x.
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