WTF why did no one mention this to me when I was struggling with math as a kid?
They probably did, just not explicitly:
You could write (6*1/100)*50 = 6*(50*1/100)
It only uses the commutative property of multiplication and the fact that % is another way of writing 1/100.
Maybe also worth remembering that “x% of y” is just x/100*y
I’m confused again.
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.
This is one of those “maths is magical” moments, I guess.
Mathemagics.
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By what part?
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.
35x6=180+30=210 at 10% so 21
plus
35x2=60+10=70 at 1% so 0.7
Therefore 62% of 35 = 21.7
While I get your sentiment, I’m always baffled how people fail to just memorize some basic formulas/equations and then just to plug and play:
1÷kⁿ = k⁻ⁿ
% = 1÷100 = 10⁻²
k×10ⁿ equals k with its floating point shifted by n to the right for positive n, or to the left for negative n
That’s really all one needs to know for the “problem” at hand. For your concrete example of “40% of 59” that would just be
59×40×10⁻²
Just solve that whatever way is easiest. I don’t get why people get panic-stricken when they see the % sign.
Seriously, why didn’t anyone?! Would have made my life much easier.
they absolutely taught you the commutative property and transitive property
Yeah but they clearly taught it poorly
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They taught you all the parts. Where they (and I’d agree most math education) failed was to connect the dots.
They taught you about these properties.
They taught you that division is just fractions and vice versa.
They taught you that x/1=x.
They taught you multiplying fractions as (numerator_a • numerator_b) / (denominator_a • denominator_b).
They taught you percentages are just “per centum”, or per hundred, or basically just a fraction “over 100”.
But these tricks, much like many other mental math shortcuts that are useful for everyday life, got glossed over or missed entirely.
Easy way to do %
Say you want 6% of 45
Seems hard right?
1% of 45 is .45
.45 × 6 =
.4 × 6 = 2.4
.05 × 6 = .3
2.4 + .3 = 2.7
So 6% of 45 is 2.7
Extra:
Say you want an item that is 40 dollars and it is 20% off.
10% is 4 dollars.
20% is 8 dollars.
So item would be 32 dollars.
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.
… because multiplication is commutative.
69% of 420 is equal to 420% of 69.
So, is 289.8 the magic, double “nice” number?
Nice^2
Bro that’s actually amazing
Idk if it’s the weed, the adderall, or the ADHD, but this thread is everything I need in my life.
Weed and Adderall sound like a dope ass combo.
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.
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33% of 7 = 7% of 33
Bitch, this only works for certain easy maths.
29% of 29 is 29% of 29
Fuck, this trick sucks.
Which equals 29^2 x .01 => ((28 x 30) +1) X .01
=> (840 + 1) x .01 => 8.4128 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.
((30 x 30)-30-29) x .01, easy
33% is the easy one… 1/3 of 6 is 2, 1/3 of 1 is 0.33… 2.33…
1% of 33 is .33
.33 × 7 =
.3 x 7 = 2.1
.03 x 7 = .21
21 + 2.1 = 2.31
So
7% of 33 = 2.31
You could also do
33% of 7
10% of 7 is .7
1% of 7 is .07
So 11% is .77
.77 × 3 =
.7 × 3 = 2.1
.07 × 3 = .21
2.1 + .21 = 2.31
That’s pretty damned intensive for a trick that’s supposed to make the maths easier.
Who said math will be ever easy?
…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 / 100commutativity 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
/ 100so that can make this easier to figure out in my head”.deleted by creator
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 get0.27.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), becomes27/100, becomes0.27. And that can be simplified asxy/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/100is 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.
I read that now not for the first Time
I still dont believe it
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.
Nah, I prefer to treat my math problems like climate change. With denial.
jiggle it
aljigglebra
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You could also do 6*50 and then divide by 100.
Why would I do that
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.
Yeah, that’s just more math
Woah!
Nice username
Right back at you! :)
Thanks Panzer
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.
Same energy as multiplication with 9, just take 1 from the right side and put it on the left
(09, 18, 27, 36, 45)
Instructions unclear…
09, 108, 1107, 11106, 111105
Keep doing this until you get a binary number and then your pc can do the rest for you
Found the JavaScript developer
You can multiply by 9 on your fingers.
Hold hands out, fingers splayed, thumbs towards each other. 🙌
9*2 put your left ring finger down (the 2nd finger). Left of that is tens place, right of that is the ones place.
So 1 on the left, 8 on the right of the downed finger.
9*5 put the left thumb down (5th finger.) 4, 5. 45.
Instructions unclear, thumb stuck in asshole.
That’s numberwang
Thank god i wasn’t the only one
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.
4 5 therefore 9
9 and 9 therefore 18
18 and 18 therefore 36
4 5 therefore 9
I thought with “reversible” they meant that a number falling 50% and then rising 50% afterwards, it is the same number, which is not true.
10 * 50% = 5
5 * 150% = 7.5
50% of 10 is 5
10% of 50 is 5
Not sure if you’re saying you got it.
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
