Sadly, this is actually true, people actually don’t know simple math and operation order.
Ajd they ask me why I hold such low expectations for the future 🤦.
You learn these things in 1st, 2nd grade. This is not quantum mechanics, this is simple basic math.
To be fair, it’s completely arbitrary, and all of math would be easier to understand, although slightly more verbose, if the only rule of order of operations is “always use parentheses to denote order, there are no implied parentheses”.
lazy mfs from centuries ago who were mortified by the thought of having to write ( and ) too much (lord what i wouldn’t give to hop in a time machine and show them lisp) should not be dictating our mathematical notation in this century. Explicit grouping is always more obvious to the reader.
It’s also not that hard to just write it in a far less confusing way in many cases.
In this simple case, 4 x 2 + 2 or 2 x 4 + 2 would have been superior choices because both people reading left to right and people following pemdas correctly would get it right, and only people mis-remembering pemdas would be confused.
I would love to watch people who say that diagram a sentence, per 10th grade English class rules.
(For the record, PEMDAS).
To be clear, it’s the standard order of operations (PEMDAS) that is arbitrary. The expression in the post, assuming PEMDAS, is not arbitrary. There’s only one correct answer.
Also, I dunno man. The window from where math is complicated enough to have multiple different operators to where expressions get too complicated to be easily readable with just parentheses to denote order should be passed by like, early to mid highschool, if not junior high. Point being, frankly if you’re struggling with PEMDAS, your either still a high schooler, or you probably should be.
Or we can all learn polish notation
It’s not arbitrary just because you don’t understand the how and why of it. The expression could certainly be written more clearly, but that’s an entirely separate matter.
always use parentheses to denote order, there are no implied parentheses
I completely agree on this, and yes, this is what I always do, cuz… well, we’re human, we make mistakes, parentheses makes things easily visible, thus cutting down on mistakes.
Still, I do know operation order, as a rule I mean. In simple calcs like these, making a mistake is almost impossible. Thus, people that answered 16 probably just don’t know the order… that is something you learn in 1st, 2nd grade, it’s not quantum mechanics we’re talking about here.
lazy mfs from centuries ago who were mortified by the thought of having to write
(and)too much (lord what i wouldn’t give to hop in a time machine and show them lisp) should not be dictating our mathematical notation in this century.
We only do that cuz we’re not sure how the compiler will interpret the operation order, and there’s waaaay too many versions and different languages to actually remember how each of them interprets math operation order. So, we do a safe bet, put parentheses on everything. Hell, I do it as well, I just can’t be bothered to remember if C interprets it like this, Python like that, Rust like… god knows what. They should, in theory, know math operation order, but let’s face it, we all do it cuz we’ve been faced with bugs that are a direct result of the compiler not intepreting things as it should.
That being said, yes, I do agree that prentheses on everything, even math on paper, is the way to go. Plus, even people that don’t know operation order, will learn it a lot qucker if you just show them how easy things become once you start using prentheses.
I will literally commit hate crimes against all of humanity if I had to write brackets around all operations in math. Surely remembering 6 things is easier than writing out brackets 100 times a day
Polish notation ftw. + 2 * 2 4, no parentheses needed and no ambiguity. (Though makes it harder to see at first glance where is the cut between the to terms of the operation.)
Multiplication is a notation which means add some number by itself a number of times.
5 x 3 = 5 +5 + 5
2 * 4 = 2 + 2 + 2 +2
So when you see some like 2 + 4 * 2 it literally means. 2+4+4
By that logic it could just as well be 2 + 4 * 2 = (2 + 4) + (2 + 4) = 12. You still need to know to multiply first, or it’s arbitrary
Edit: a lot of you are missing my point. The expression above is wrong, duh, but my point is that the choice to “expand out” the multiplication first is a convention that the mathematics community agreed on, not a fact that can be proven or measured. That’s why it’s arbitrary. @kogasa put nicely, PEMDAS is just a notation, it’s how we agreed to read and write our math, but the underlying math is no different. If we all agreed to scramble the order of operations, say to add before we multiply, expressions will look different, parentheses may need to be added or removed, but they will still be mathematically consistent if we are consistent in writing and reading in that agreed upon order of operations.
Maybe for very simple calculations like this one, but for more complex ones parenthesis actually make them much harder to read and write. If you’ve ever built a complex functions in Excel you know how difficult it gets because for 90% of the excel operations require parenthesis which means it works exactly like you’d want math to work. Just yesterday I had to do a more complex index match search in excel and excel corrected my parenthesis, because when your function is supposed to end with 5 parenthesis good luck keeping track of how many parenthesis you actually need to write out. Similarly if a week later I would have to change something inside that same function it’s going to take a lot more time to deconstruct the formula because of the abundance of parenthesis.
And the addition of parenthesis in math is entirely unnecessary because the nature of most operators already dictates the order of operations. Exponents are just multiplications and multiplication are just additions. 23 is the same as 2 x 2 x 2 is the same 2 + 2 + 2 + 2. If you take the example in the image then 2 + 2x4 transposed into additions is 2 + (2 + 2 + 2 + 2), parenthesis added to indicate what used to be the multiplication. Why people get it wrong is because they don’t understand the nature of those operators and so they do (2+2)x4 which is how they get (2+2)+(2+2)+(2+2)+(2+2) = 16. The order is clear, you can’t do addition before you do multiplication, because multiplication is a certain form of addition, and you can’t do multiplication before you do exponents, because exponents are a certain form of multiplication. The inverse functions maintain the same order of the function they’re inverting, meaning you can do subtraction before division and you can’t do division before rooting. No need for parenthesis for the natural order of operations. Parenthesis serve a purpose when you need to denote exceptions to the natural order of operations, like (2+2) x 4.
It’s not a “natural” order of operations. Why in the world would you think that we more often add before multiplying instead of vice versa? That’s such a weird claim
I don’t know why you expect the mathematical order of operations to stay fresh in people’s heads. I was taught that in like third grade, and the number of times I’ve needed that information outside of a math class in the 35 years since then is exactly zero. Most people don’t really have occasion to go around solving written equations in their adult lives. I mean, I’m a machinist, I use math every day at my job, the only actual written equations I ever have to deal with are the ones I need to solve to shut off my alarm clock app in the morning. That stuff just doesn’t stick when you never have a reason to use it.
It’s not an equation, it’s simple math, like one used in a grocery store. You have 2 apples and then you pick up 4 more pairs of apples, how many apples you got?
As I said, it’s not quantum mechanics, it’s basic simple math.
I bet your alarm clock app also uses simple math problems like this one. It’s expected for a grown up or a teenager to be able to solve this, that is why they put it on alarm clock app. It’s not something that’s meant to be easily forgotten. That is why you learn these things when you’re very young, so they stick with you for the rest of your life. But from the answers, it’s easy to notice that most have never even learned this in the first place, at all. Why? Your guess is as good as mine 🤷.
Because they grew up in households that would say to them “I don’t know why you’re having to learn this! No one uses it except for the eggheads down at Livermore!” and so they ignored it and now justify their ignorance by repeating the same horseshit anti-intellectual screed
It’s cut off at the bottom. 10 might be there, or even add your own option might be there.
If they wanted the multiplication done first they should have put it first if they wanted it done separately they should have put it in brackets. Not my fault some maths guy invented a specific order to do sums in who the fuck cares oh my god we read left to right fucking hell
Yeah but the way you derive the order of operations is way above the average maths student.
I say that, but its not really that complicated to derive, since you think in terms of the expansion of the naturals to the reals
My brain is fucking dumb
Im sorry, what? The order of operations is completely arbitrary, it just also happens to be the standart. Not having PEMDAS would simply mean we have to write equations differently. PEMDAS et al only exist to avoid ambiguity as in this image.
Except math isn’t real and was entirely made up. Including the order in which the operations are calculated.
Checked with my old basic calculator, the answer is indeed 16 😂
Pemdas isn’t as arbitrary as people in this thread think it is.
I love maths, and I’m going to butcher any attempt to explain why pemdas isnt totally random. But you can look it up if you wanna know more I guess
Besides no one ever uses that notation - by the time you learn about quadratics, you leave multiplication symbols out of the equation entirely and much of the notation changes shape, with division exclusively being expressed as negative powers or fractions.
At that point you aren’t going to make mistakes, since each hyperlevel uses a different style of notation. Pemdas is used to teach 4 year olds, and it’s fucking dumb. What happens with a log, or sine function. Don’t even get me started on integrals and derivatives.
Pemdas is shit, but not because it’s abirtary. In fact it’s shit because it’s a shithole acyromn
Pemdas is mostly just factoring, kinda. That’s how you should think of it.
2x4 is really 2+2+2+2.
That first 2+(anything else) can’t be acted/operated upon until you’ve resolved more nested operations down to a comparable level.
That’s it. It’s not arbitrary. It’s not magic. It’s just doing similar actions at the same time in a meaningful way. It’s just factoring the activities.
It is, in fact, completely arbitrary. There is no reason why we should read 1+2*3 as 1 + (2*3) instead of (1 + 2) * 3 except that it is conventional and having a convention facilitates communication. No, it has nothing to do with set theory or mathematical foundations. It is literally just a notational convention, and not the only one that is still currently used.
Edit: I literally have an MSc in math, but good to see Lemmy is just as much on board with the Dunning-Kruger effect as Reddit.
If you don’t accept adding and subtracting numbers as allowed mathematical transactions, multiplication doesn’t make sense at all. It isn’t arbitrary. It’s fundamental basic accounting.
Yeah I haven no idea what I was saying when I said that, I’ve edited my comment a bit.
On that note though using your example I think I can illistarte the point I was trying to make earlier.
1 + (2*3) by always doing multiplication first we can remove those brackets.
(1 + 2) * 3 can be rewritten as (1 * 3 )+ (2 * 3) so using the first rule again makes a sense. That is a crappy explaination but I think you get my gist.
Please Excuse My Dear Aunt Sally, muthafuckahs!!
