Can we say “commutative” in this case ?
Yeah stuff like that really ain’t it. It works in a few use cases, but is objectively wrong and detracts from understanding the topic properly. That’s why I teach percentages as the fractions they are. By the time you learn percentages, you already know multiplying fractions is commutative, so the trick still works, and you also understand why.
Yeah stuff like that really ain’t it
Yes it is
It works in a few use cases,
It works in every case where you have multiplying and dividing, including fractions and percentages
but is objectively wrong
No it isn’t
detracts from understanding the topic properly
Enhances it actually
That’s why I teach percentages as the fractions they are.
Sounds like you’re only teaching as much as you understand. Try understanding more. Students love the tricks that make Maths easier, including this one.
that’s why I teach percentages as the fractions they are
What about pi%?
That’s pi/100 still. Didn’t say it was a rational number, just that it was a fraction. Though I don’t see a context where it’d make sense.
For real? I’ve never though of this. This may actually be useful!
% really just means
*1/100- it doesn’t matter where you apply that factor:6% of 50 = 6% * 50 = 6/100 * 50 = 6*50/100 = 6 * 50/100Where were you when I failed math 101 4 times?
Thanks!
I was probably on a different continent ^^ Also, the biggest problem explaining math is not making it understandable, but having a motivated learner. Most students that have a bad teacher in school, or are somehow not motivated in school to begin with, will also not be motivated to focus on easier explanations. Technically a basic interest in math should be fostered / encouraged in kids from an early age, and at the latest in elementary school. If that does not work out, many students will have a hard time with it.
You are welcome.
maths is the same in both case but I get it, for small numbers this is useful
Removed by mod
This is blowing my fucking mind like an artillery shell
Yeah, I personally find it a lot easier to compute 13% of 17, rather than 17% of 13.
.2*13=2.6
.03*13=0.39
2.6-0.39=2.21
My brain is maybe a weird place 😂
Same with 375% of 20 rather than 20% of 375.
Actually I disagree.
20% is 1/5
100/5=20
10/5=2
5/5=1
3*20=60
7*2=14
1*1=1
60+14+1=75
Damn, it still worked. Holy shit.
The few times I’ve seen you on Lemmy, it takes me a few seconds to process your username. Today, I had my favorite misreading yet: pronounced Ivana footerall
Thanks, now I can’t unsee that, fartographer
Are you a “silent fartographer”?
No I think they specialise in medium or large format, with various filters… doing their own development with funky chemistry.
I don’t see this person as a black and white character. Very creative. Specialising in avant-garde still life maybe.
Seems pretty vocal to me.
I guess it’s easy to miss that m% just means ×m÷100
6% of 50 means 50 × 6 ÷ 100, and because multiplication and division have the same order of operations you can switch them around. so it is also equal to 6 × 50 ÷ 100, in which you can simplify 50 ÷ 100 into 1 ÷ 2, but you could always do that: 50 × 6 ÷ 100 = 1 × 6 ÷ 2.
this “shortcut” however is of extremely limited use. basically for taking a percentage of anything other than things that can very easily divide or multiply 100 like 50 in this example or maybe 10 or 500 it’s nearly useless.
Hence 90% of 6 is still hard.
Not really tho. If you know 9x6=54 then it’s pretty easy to get to 5.4 from there
8 and 8 fell on the floor, picked it up, it was 74.
It’s because percent just means ×0.01 and multiplication can be rearranged
x/100 * y = x * 1/100 * y = x * y/100
I never would have thought of it myself and still feel like I should have thought of it myself.
So 37 % of 38 is equivalent to (37 * 38 ) / 100 ? Which I can almost do in my head.
37 * 4 is 148 I think, so 37 * 40 is 1480. Subtract 74 we have 1406. So we have 14.06?
You’re hired
For a while I’ve been meaning to memorize all the two digit squares but of course I then fail to practice them, so I’m not very far along. But that would help you with this too, not to mention you can start doing some square roots too.
For quick and dirty I’d probably just go with
37*38 = 40*40 -> 16%which is kinda close to 14% eh?For quick and dirty I’d probably just go with 3738 = 4040 -> 16% which is kinda close to 14% eh?
Quick and dirty and accurate is 38=40-2. So 38x37=(40-2)x37=40x37-2x37=1480-74=1406
Oh absolutely, depends on what you are measuring if that isn’t close enough
This is great. I won’t remember it when I will need it.
Just save the meme in the maths folder!
You clearly don’t have gigs of memes.
(Maths folder is clearly for porn)
(The maths IS the porn)
Ohhh … ‘Seven ate nine’, now I get it.
(As sexy math, not a ST reference.)Meh, either way 😂
You shut your whore mouth
23% of 53
53% of 23, next question
Pretty close to 1/4 of 52, so like 13-ish, but maybe closer to 12.
(13 + 0.25 - 0.53 - 0.53, really. If I had to, I might be able to keep that in my head.)
.5*23=11.5
0.01*23=0.23
3*0.23=0.69
11.5+0.69=12.19
May as well just get out the calculator app to make sure. My point with those numbers is to just use a calculator. Why 2nd guess anything?
May as well just get out the calculator app to make sure
Calculator apps get order of operations questions wrong because of programmers who were too lazy to check they had their Maths correct
My point with those numbers is to just use a calculator.
My point is avoid calculator apps like the plague. Use name brands like Sharp or Casio.
Why 2nd guess anything?
Guess what the programmer of your calculator app did 😂
If “close enough” works, then it’s nice to have the skill. Having the skill requires occasionally using it.
Where accuracy is important, since we almost always have a calculator with us now, that’s a no-brainer.
Maybe more to the point, though, understanding how percentages work is wise. It’s one of the few arithmetic topics that we encounter regularly in life.
In this case, 23% of 53 and 53% of 23 each have their own little trick, depending whether you’d rather overestimate a little with 1/4 of 52 or underestimate a little with half of 24. I find it handy to be able to think that way, especially for example when trying to get out of a taxi and paying cash.
Where accuracy is important, since we almost always have a calculator with us now, that’s a no-brainer.
Unfortunately most calculator apps were written by no-brainers who didn’t check they had their Maths correct. If you need accuracy then get a name brand like Sharp or Casio.
Babagedegaga. Ba.
My dyscalculic ass trying to remember what 50% of 6 is
Probably 5 tbh
is tree fiddy
I’m gonna track down all my HS math teachers and punch each and every one of them in the mouth.
I’m gonna track down all my HS math teachers and punch each and every one of them in the mouth.
Understandable if you’re in the U.S., where Maths teachers don’t have to have any Maths qualifications. Other places, where you do have to have Maths qualifications, we teach this.
Legitimately new knowledge for me that will literally make my work easier. Wish I could give you more than 100% of 1 upvote, OP!
I wish someone told me this trick 30 years ago.
1 of 100% upvote. Yeah, it checks out!
That’s because multiplication is commutative
taking a percentage of something essentially means multiplying it with a hundreath of the percentage
6% of 50 essentially means 50 * 0.06
or 50 * 6 * 0.01and since
50 * 6 * 0.01 = 6 * 50 * 0.01
then of course
50 * 0.06 = 6 * 0.5And we have the above
Yeah my brain just sees 5*6, and then I move the decimal. I never understood how people couldn’t figure out tips when they wanted 20%.
If you live in the U.S. you do them quite often, multiply by 2. Want 10 multiply by .1… Half that and add it if you want 15. Whatever is easiest at that moment
I prefer to keep it technically correct yet evil and confusing. 6% being a fancy way to write 0.06 or 6 * 1/100 means we can take 6 * 50 * 1/100 and simplify to 300 * 1/100 and then represent that as 300%.
Chat is this real
Finally a reasonable way to do percentages! Thank you, I’m stealing this
My life was changed forever when I learned I could say that 6% of 50 was 300%.
… in 1 or 2 dimensional number systems, also known as the real (1-dimension) and the complex (2-dimensions) numbers. With quaternions and higher dimensional systems multiplication is not communicative. In fact, the more dimensions you add, another mathematical property is lost.
… okay? Yes? Nobody thought otherwise? Do we now have to clarify every statement about algebra by specifying that we’re talking about an algebra over the reals or the complex numbers? Or the polynomials or the p-adic integers, whose multiplications are also commutative?
No one would call these “n-dimensional” number systems either. The algebra for each of these operates in R1 and R2, respectively, but, like, you would describe their algebras as being over an n-dimensional vector space. It’s not wrong, but I don’t think “two-dimensional number system” is something you’d hear mathematicians say.
This pedantic aside feels so “I just watched a 3blue1brown video and feel verysmart™” that I don’t know what to do with it. It’s good to be interested in math, but this ain’t it. Everyone knew what they meant.
I don’t think “two-dimensional number system” is something you’d hear mathematicians say
I teach Maths and would’ve thought that was referring to the Cartesian plane.
6*50/100 = 50*6/100 if anyone is curious why this works.
Or, more generally:
Taking X percent of something is the same as multiplying by X/100.
X percent of Y = Y(X/100)=(YX)/100
Y percent of X = X(Y/100)=(XY)/100
(YX)/100=(XY)/100
Percentages are indeed reversible.
6/100 * 50 = 50/100 * 6
6 * 1/100 * 50 = 50 * 1/100 * 66/100 * 50 = 50/100 * 6
=6x5 /10 (2 zeroes cancel out)
it all equals 3
Yes, 47% of 47 is certainly much easier to determine when you look at it as 47% of 47! Genius!
Yes, 47% of 47 is certainly much easier to determine
And your real life example of a 47% discount on a $47 item is… where exactly?
You can also
Multiply one side, divide the other to get the base number to get the base number to 100.
6% of 50 == 3% of 100 == 3
5% of 20 == 1% of 100 == 1
7% of 50 == 3.5℅ of 100 == 3.5
14% of 200 == 7% of 100 == 7Edit* as pointed out below, this one was incorrect.
14% of 200 == 28% of 100 == 28
You don’t have to stop at percentage either.
25 * 16 = 100 * 4
If you’re doing addition, you can add and subtract.
27 + 13 = 20 + 20
Most of the difficulty is in realizing that one number or the other can be brought up to a nice round number, making the equation simple to do in your head. And obviously, just getting to around number on one side doesn’t always make it easy on the other side.
I always loved screwing with math problems to make them easier, which is weird, because overall, I don’t really care for math.
I also do shit like borrowing a couple of numbers to make the equation easy and then pull them back out.
392 / 4 == (400 - 8) / 4 == (100-2) = 98
376 / 4 == (400-24)/4 =100-6=94
Of course it goes up a level when the remainder isn’t evenly divisible. But I still find it’s something I can handle in my head.
371 / 4 == (400-29)/4= 100-7¼ =100-7.25=92.75
14% of 200 == 28% of 100 == 28
You can also do 200% of 14, which I find more straightforward.
I would argue you’re still doing the other side just subliminally. But it is a fair point.
Why do you have to divide on both sides in your example with 14% of 200?
Oh shit, there I go getting along winded and get lost, yep, that should have been multiplied on the other side.
Are you just out here doing common core math on here like it’s just some smart trick to make math easier?! You dirty bastard, some conservative is going to see this and think it’s a good idea, then they’ll just innocently do it in front of their conservative friends and all hell will break loose. Homosexual fornication will suddenly run rampant through the group and those few that can resist the call of the devils numbers will have to cull the rest. You know… Actually… I am not completely against that now that I think about it…
Rofl, I pre-date common core. I’m not exactly sure to what extent they do all that stuff. I do know that they’ve got a fuck of a lot of numberlines, like so many number lines. Like they’re being paid by the number line.
Back in the 80s and 90s, the teachers would do regular scrolling down arithmetic, and they would mention borrowing numbers and shortcuts. And I took that shit seriously because I did not like sitting down and adding/multiplying numbers. I’d probably spend an extra 30 seconds of problem if I thought I could not have to sit down and write equations.
That’s really cool. The borrowing thing is the part of common core that they teach in elementary, and it is the part that enrages conservatives. The point of the homework and practice questions is to repeatedly do the borrowing thing until it becomes automatic and something that they do in their heads all of the time. So, it absolutely enrages the right when kids get the correct answer, but lose points for doing the problem the wrong way.
I was taught to do it the hard way and had to figure out the other tricks for myself much later in life, so now, even after decades of doing it your way, it’s more of a struggle than it should be and I just reach for my calculator instead. So I envy you quite a bit.Keep up the good work with your subversive teaching of common core principles as tips, tricks, cheats and shortcuts. That’s actually how they should have branded it, instead of common core, it should have been cheating core, then they would have been all for it.
There’s nothing wrong with calculators.
I wonder if the next generation is going to be reaching for AI for all their English needs.
There’s nothing wrong with calculators
There is if you’re talking about calculators on phones, etc. Almost all of them give wrong answers to order of operations questions because the programmer didn’t bother checking their Maths first. It’s so bad that the Windows calculator in Standard mode says 2+3x4=20. Stick to name brands like Sharp and Casio. They have money invested in the success of their products, so they take more care to make sure it’s correct!
I haven’t sent anything to anyone that wasn’t spell checked in more than a decade. So, ya it’s going to be a weird future where you just choose the comment you want to respond to and AI fills it out for you.
Ohh man, think of training something on your own corpus of writing over the years.
god we could probably more or less do that now…
