The panzer has spoken

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....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?
- x% × y = x × y ÷ 100 This helps you out much more.
  
  Its easier:
  10% of a 100: 100 * 0,1 = 10
  2,5% of 33: 33 * 0,025 = 30 * 0,025 + 3 * 0,025 = 0,75 + 0,075 = 0,825
  Thats how I calculate it mostly in my brain. But being smart I usually just type everything (like 9*9) in the calculator xD
- 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.
  
  I'd.. probably use the calculator app before I do all this mental gymnastics
  
  This is not mental gymnastics.
  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:
  7 × 8% = 0.56
  7 × 8 / 100 = 0.56
  
  Oh, that is actually much more helpful. So, if you know your times tables, you can do percentages. You just have to use communitavatization.
  Jokes aside, I really appreciate it. That made it much more easier to understand. Thank you.
  
  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".
- I'd find 9% of 3 easier for sure. Sometimes it's easier sometimes it's not. Just use it when it's easier.
  
  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).
- Wait are you questioning the wisdom of panzer of the lake?!
- This tip helped me 21%
  
  So you might even say, "21% of you helped the tip"?
  
  21% of 100%?
  
  No. 100% of 21%
- Yes, idiot. Choosing instances of when it's less helpful (arguably) doesn't negate the cases where it is deemed very helpful.

76 comments