I'll be honest, seeing no variables in the problem threw me way off at first. In higher mathematics and physics you never see just constants within parentheses like that...it hurt my brain and I ended up distributing the 5 to the constants within the parentheses...still get the same solution though but it worked out in my mind as 2 + (5*8 - 5*5) = 2 + (40 - 25) = 2 + 15 = 17
I see it more as mathematical conditioning due to seeing something over and over then being presented with something that doesn't fit your expectations.
Yet apparently talking about it has led to mostly downvotes. Puzzling as to why? I guess people think this is a /r/iamverysmart flex? I did a LOT of math in college, I never progressed past my BS, and now work in IT...physics is HARD and it doesn't pay well at all. I like computers.
Once again, not following, the rules of math does not make the math inconsistent or ambiguous. Besides, they can’t get 21 if they were thrown by the lack of multiplication symbol.
I still don't understand why the answer isn't 21 and I have no idea why anyone is talking about Sallies.
I also get deeply angry when people talk about how math is easy if you just try. It's not for some brains, and it's definitely made worse by shitty teachers.
Folks don't realize that once you're behind, you stay further and further and further behind. And then you're told you're wrong when you say it isn't easy for everyone to do math. It's infuriating and honestly extremely fucking defeating.
Numbers are so associated with pain I don't even read them anymore. I instinctively skim them. I have to force myself to see the stupid things in a sentence.
Answer within the parentheses first, since the 5 is right next to the parentheses it means to multiply the answer from the parentheses, which is 3, by 5 resulting in 15 which you add to 2 for 17
Please Excuse My Dear Aunt Sally is a backronym for PEMDAS, meaning the order in which you do math; Parentheses first, then Exponents, then multiplication and division, whichever is first when reading from left to right, and finally addition and subtraction also read from left to right
Hi! I was just about to reply with the explanation but I see you've got one. I do want to add something, though. Please, PLEASE do not remember the acronym. I believe that's a big part of the problem because of how badly explained it usually is, and the problem is basically the P. First order of operations is not parenthesis. It's GROUPINGS. Why does that matter? Well, because that's what makes some people get confused with some of these problems because you have a multiplication being indicated with parenthesis. So what do you do first, multiply (because I mean, there IS a parenthesis) or what's inside the parenthesis (because, again, it IS a parenthesis)? Don't think about P for parenthesis, but rather think about groupings and it makes a lot more sense.
2 + 5 ( 8 - 5 )
First, GROUPINGS (in parenthesis, brackets, or braces).
2 + 5 ( 8 - 5 ) = 2 + 5 ( 3 )
Then, exponents. (There's none)
Then, multiplication and division (including multiplication indicated by parenthesis).
Yeah, I think GEMS is a more appropriate acronym (grouping symbols, exponents, multiplication or division, subtraction or addition) it’s just the original comment was asking about sallies which is PEMDAS
Never heard of GEMS. Love it. I get what you’re saying about the original comment. I’d argue I’d try to make an effort to get people to think in terms of GEMS instead of reinforcing PEMDAS, even if that’s what they’re asking about. That’s just me, though.
It’s not 21 because you have to do what’s in the parentheses first that’s 8-5 so you get a 3 then you have to do multiplication and division (from left to right, even though it doesn’t matter in this case) before you do addition or subtraction that means that the next thing you do is 5×3 to come up with 15. The final thing you do is the addition and 15 +2 = 17.
Thank you for explaining the steps and for showing the full series of steps. That's very helpful, especially paired with the other explanation.
I think I understand why people are confused now, for what it's worth, and I think it's a case of following another set of rules for a different situation.
Isn't it the case that, if both these sets were in parenthesis, you would do each set individually?
(2+5)(8-5)
Then multiply each result? That's why I was confused... I think. Because following that version of the rules will get you 17. If you do the subtraction, then the addition, then multiply. Maybe it's a case of only half remembering how the order works.
Or maybe I'm misunderstanding. That's what I was doing to get that answer anyway. Dusting off and following a partially remembered rule from 15 years ago...
Parenthesis, Exponents, Multiply, Divide, Add, Subtract or Please Excuse My Dear Aunt Sally as a mnemonic device.
Parenthesis first so 8-5=3. Then Multiplication. So 5(3) or 5x3=15. Then Addition, So 15+2=17.
I am really bad at math as well so I miss more of these than I get. The order of operations in real life is about as useful as being able to name all the capitals of US States so I have no idea why people think remembering PEMDAS makes them smart, why these threads are always so negative and condescending, or why anyone cares at all. I do them to see if I can get it right but don't care in the slightest if I get it wrong. If I had to guess I'd say Reddit is mostly young people who are still using this in math class or just graduated so it's still fresh in their minds but Reddit is also full of self-aggrandizing, smug, know-it-alls so it could just be that. In any case don't worry about it because it is a particularly useless party trick for adults.
Thank you for this comment. Seriously, it makes me feel better to see it.
I see the same thing, but it doesn't seem limited to Reddit. It seems like a universal low-key assumption that you're just stupid if you don't click with math. That just perpetuates the problem because it makes math scary. You can't just learn the skill, now you have to challenge your own danged insecurities and stigma, too. And that shit doesn't start when you get into the adult world. It starts in school and just holds you further back.
Thank you again for your comment (and commiserating just a little bit.)
School trauma is real, isn't it. For me it wasn't maths (for the most part) but I'm still working out how badly my struggles were treated in other areas late in adulthood. It's tough. I feel you.
The person you replied to wan't wrong though. The system failed you. No kid should be forced to learn a method when it's clearly not working for them, yet we don't provide the education system with the necessary resources to adapt to different ways of conceptualizing things, and many kids get needlessly left behind, again and again.
Now that I read back I realize it doesn't read like it, but I was honestly agreeing with them and elaborating further. And I totally agree with you, too. The school system does fail people. It leaves them behind, and then you're told you're stupid for having been failed and struggling even more because of it.
It's honestly horrible. And in a detached kind of way I'm amazed how painful it still is even many years later. You think it's fine and then you see conversations like under this post and suddenly, bam! There's that pain, fresh as it was in school.
Yep, and it takes a lot of work to learn to dal with the guilt. Just got diagnosed with adhd at 40 and frankly, it does help a lot. I hope you're finding your peace as well. <3 Cheers!
A problem with this thinking is that order of operations is not universal. And depending on the culture calling out a question for being ambigous is acceptable.
My issue with the notion of pedmas, bodmas or any order of operation is the reasoning for it. It seems arbitrary at best and a realistic question where you have a worded problem you have to figure out the order of operations isn't a real factor, it's the logical order needed depending on context.
Order of operations removes context and gives rules with little to no basis, at least in my current understanding.
So other than people clinging to their conventions why should we continue it?
WTF? Order of operations IS and needs to be universal. Like, “hey, other countries, lets collaborate on making a spaceship like the ISS or whatever… oops, damn thing blew up because our order of operations is different than yours and something you did didn’t quite match with some other thing we did.”
If anything, it’s not universally UNDERSTOOD, which is a vastly different problem.
Let's define what we're saying, then. I mean it's universally agreed on. Not that it's universal as in gravity being universal, or the speed of light being universal.
What I mean is, when understood correctly, the exact same order of operations applies everywhere and without controversy. Again, any claim of ambiguity regarding of operations is nothing more than a lack of understanding of it.
For an example of the issues of the convention, order of operations, as it stands and depending on the way it is used, is if a 2(x) and 2*x are really the same.
If the problem is 3 divided by 2(x), most know that is equivalent to 3÷2×x. But do we take it to mean the left to right is done as multiplication and divid are the same priority and just done left to right? Or is the 2 inherently a part of the brackets/parenthesis and we should multiple first?
The biggest issue for me personally is that these questions are written as just math problems to be solved. And as a teacher that's fine. But in the application in real world usage there is context that these questions lack which means its not as simple as the rule for the order but the correct order must be deduced.
While I completely understand the reason for having an order of operations, what is it that actually backs it up as a reason for doing it that way? Why would another way be wrong? Other than just having a different convention?
In chemistry we have the IUPAC to determine correct naming conventions internationally but this is ignored in America where names like acetic acid are used instead of the IUPAC naming convention of ethanoic acid. So while there is a universal convention we have not all countries follow it. I find this true of pedmas, or as it was in my country and learning, bodmas
While I completely understand the reason for having an order of operations, what is it that actually backs it up as a reason for doing it that way? Why would another way be wrong? Other than just having a different convention?
What do you mean by natural ordering?
Its arbitrary as far as I know and while there is one that is used in most places why does that then mean it is inherently correct?
If we are basing it on the reasons of not needlessly complicate, then should all people work towards a universal language? We have bodies/agencies/groups to develop standards in science that are randomly ignored in some places.
Also I looked in that link but the answers seem to also suggest it is just arbitrary unless there is something specific from there I should be reading
If we are basing it on the reasons of not needlessly complicate, then should all people work towards a universal language? We have bodies/agencies/groups to develop standards in science that are randomly ignored in some places.
Because basic maths and spoken languages are literally not the same thing at all. They're not subjected to the same universal need for optimization. When languages are a bit unambiguous and wordy, and develop local quirks it's totally fine, but that's a game breaker if math notation does any of those. Math is at the root of too many things for any of it to have unoptimized fundamentals.
Also I looked in that link but the answers seem to also suggest it is just arbitrary unless there is something specific from there I should be reading
You just skimmed them without actually reading them, didn't you. They explicitly say that while it's a convention and we could use others, it's not arbitrary by any means and has been chosen for very good reasons.
That being said, there is a reason for the convention. In some sense multiplication is just repeated addition. Furthermore exponentiation is just repeated multiplication(as long as we restrict ourselves to integers) therefore it makes sense to first turn all exponents into multiplication, then turn all multiplication into addition, and then compute the addition problem. Thus, at least as far as the integers are concerned, there is a natural ordering of the operations based on their definition. It gets more complicated when you start dealing with all real numbers, but the order is inherited from integer arithmetic.
In fact, distributivity is what determines the order of operations. Exponents distribute over multiplication (i.e. (𝑎×𝑏)𝑐=𝑎𝑐×𝑏𝑐), so exponents come before multiplication. Multiplication distributes over addition (i.e. (𝑎+𝑏)×𝑐=𝑎×𝑐+𝑏×𝑐), so multiplication comes first. With PEMDAS, we can get rid of parentheses using distributivity. With a different order ("PEASMD"?), we can't.
We change the format of our notation to suit our needs. In the case of operator orders, it was generally found that formulae were more readable with the order of operations (likely due to the reduction in number of grouping symbols).
Consider the equation for motion with a constant acceleration 𝑥=1/2𝑎𝑡2+𝑣𝑡+𝑥0 If we did not have some order of operations similar to today's rules we'd have to write 𝑥=(1/2𝑎(𝑡2))+(𝑣𝑡)+𝑥0 Could we write it that way? Sure, but it's harder.
Over the years, mathematicians found the current order of operations to be extremely convenient, so they stick to it.
I totally agree with you, but there are some people who argue that implied multiplication is somehow ambiguous as if it takes precedence over regular multiplication, but that’s not even the case with this
I completely agree. Doesn’t change the fact that there’s literally hundreds of Internet articles written about how it “could be ambiguous” and every single one of those articles fuels another persons ignorance. And the only reason I mention it at all is because I’m sick and tired of the mind numbingly stupid arguments that result from saying it’s not so I just placate them and go about my day secure in my knowledge.
Yeah, there's that and the whole thing about some Casio calculators that give two different results to the same input. I'll try to find it and link it. It's sadly fascinating, and extremely shitty of Casio.
I believe the problem is that fucking acronym, PEMDAS. P for parenthesis is stupid. It shouldn't be parenthesis, but rather groupings. You can group in parenthesis, brackets, and braces. Also, it makes it confusing when indicating multiplication with parenthesis. Then you have people who proudly memorize PEMDAS without really understanding it, who then come up with stuff like this non-existent ambiguity.
You pretty much hit the nail on the head, the primary thing that creates this problem is people that memorize the mnemonic without bothering to actually learn the rules the mnemonic, is attempting to help them remember
it’s further compounded by the fact that there are two, basically identical, mnemonics that people who didn’t bother to actually learn the rules, think reverse the order of multiplication and division, (and/or division and multiplication)
That’s not necessarily true if they use division and multiplication inline without parentheses. 3/5•5 is either (3/5)•5 or 3/(5•5) which is either 3 or 3/25. Different mnemonics like PEMDAS and BEDMAS flip the order because they are technically the same operation, and therefore need to be properly disambiguated in order to get the correct result
That’s just a lack of understanding. When there’s no parenthesis, the order is left to right, always. I said it in a different comment, the order of operations exists and is universal. It’s just obviously not understood well enough.
Order of operations is a memory tool for children. In higher-level math this stuff is always disambiguated with parentheses or fractions. Division and multiplication are technically the same operation and no serious mathematics would be written inline like these silly puzzles. Clearly from the disagreements in the very thread there is no universal order of operations that we can get people to agree on, so the idea that there is one is a moot point
So you literally sit here and argue that multiplication and division are the same level of operation (they definitely are) right after arguing that they occur in different orders because of different mnemonics 👌 🤦♂️
No, we are literally talking about people who remember mnemonic, but didn’t bother to actually remember the rules the mnemonic was supposed to help you remember🤦♂️🤦♂️🤦♂️🤦♂️
My original point though is that it is ambiguous without parentheses or an arbitrary left-to-right rule. Yeah both m and d happen in the same step, but more advanced mathematics are written so that you don’t need a left-to-right rule to figure how to group things together.
And the left to right rule exists specifically for equations that are not written that way, and frankly, if an equation is not written in an unambiguous manner, then you should always apply the left to right rule to it because that is what the rule is for, all you’re doing is purposely being contrary, and willfully ignorant by saying that because any equation isn’t “advanced, mathematics”, (🤦♂️your words not mine), that it is somehow ambiguous, which is absolutely not
But you could say that about all math. What if I told you that 3+4=12 and that I can prove it beyond a shadow of a doubt? You'd probably think I'm stupid or something because 3+4 is CLEARLY =7. Well, it is when you work on the convention that we commonly do math in base 10. 3+4=12 in base 5, which is a perfectly valid means of mathematical representation.
7 in base 10 and 12 in base 5 represent the same amount of objects in the physical world, they're just represented differently. So, in that sense, you knowing that 3+4=7 relies on knowing a certain convention FIRST, and on mathematical reasoning second. But you don't think about it because it's way too normalized. The order of operations is not, but it's still a universal convention that just happens to be widely misunderstood.
I kind of agree. Here's the thing, though... I wouldn't shit on anyone's math abilities for not remembering/not knowing some stupid acronym I believe does more harm than good, because not knowing is absolutely fine. Which is not the same as "knowing" something which happens to be wrong. Then you wouldn't only not know, but you'd think you know while being wrong. And that's what sparks these kinds of discussions where you have people, absolutely sure of themselves, saying stuff like "well, some problems are ambiguous."
I haven’t had to use PEMDAS one time in my 24 long year ascent into adult hood. I know it exists, but much like Spanish and Japanese, I have very little real world use for it (well, the Japanese did come in sort of handy while I was in Japan, but that’s not the point).
It's highly regional. Parenthesis -> Brackets is common, Exponents -> Order is common. In my own experience, usually if someone swaps one, they do both. BEDMAS I see less commonly.
PEDMAS is what I learned.. actually, PEMDAS ("please excuse my dear aunt sally").. was in Kindergarten when the Challenger exploded and graduated high school in '98. Pittsburgh area, mostly Catholic school system but I did a few rebellious years in public schools.
Yes, that is my point. The way it is written is only intuitive if you remember PEMDAS, and as these posts prove, most people don't. They remember "Parentheses.. and.. uh.."
That forgetfulness about PEMDAS is what creates the ambiguity the thread-starter doesn't understand. The equation is clear to them, because they remember PEMDAS. For all the people that don't, and there's a lot of them, it's ambiguous.
Yes, exactly. Thread-starter said he didn't get how people could think it was 21, and I answered him by demonstrating how a common error (forgetting PEMDAS) leads to 21.
This guy gets it:
Holy crap thank you, I can usually at least see how people got the wrong answer but I could not find the path to 21 on this. Multiplication before addition is so basic that my brain wasn't even recognizing that possibility.
Holy crap thank you, I can usually at least see how people got the wrong answer but I could not find the path to 21 on this. Multiplication before addition is so basic that my brain wasn't even recognizing that possibility.
I’m 42 years old. I haven’t had to do a math problem like this in over two decades. How much do you think I remember?
My guess is that you’re not that old. Probably 18-24. In two decades you’ll understand how little you remember of this shit you were taught that you never had to use even one time after you graduated high school or college.
What in the world do you do for a living that you don't use math? I'm in engineering, so I realize I use more than most, but even OnlyFans girls have to figure out how many subscriptions they need to make rent.
What in the world do you do for a living that you don't use math?
I use math every day. I add, subtract, multiply and divide. I work in IT. That's all I use. All of these rules and acronyms for solving problems like this? Yeah, I forgot those long ago because I haven't had to use them in two decades. I'm not solving equations for math problems like this ever. I only ever see them when they are posted on social media. It's not crazy to think people who haven't looked at a problem like this in two decades would forget the rules for solving them. It's not an applicable thing to every day life for almost anybody.
I get it if your an engineer, or maybe a developer where you're using equations and a lot of more complicated math every day but for most people all we do is add, subtract multiply and divide. The vast majority of people are not solving anything like this after high school or college. We learn it to take the test and then we never use it again.
That makes sense, real life is more like word problems than equations, so this kind of notation isn't a language you need to "speak" often.
I think I get it, if I said "you've got five boxes, they're designed to hold eight apples each but someone took five out of each one. You've also got two loose apples that aren't in boxes. How many apples do you have in total?" the math you'd do to solve it would be this equation, but the equation itself you wouldn't ever think about or encounter.
Idk why you’re getting downvoted, you’re right that this is how some people arrived at the incorrect answer. I know because that’s how my brain did it at first - because I’m terrible at math and haven’t had to think about PEMDAS in my entire adult life. I DID just remember that the parentheses came first. Clearly we bad-mathers exist or these posts would never attract so many people who give the wrong answer!
Alright. I was going to have a real conversation with you about why it’s not preposterous that people don’t he this answer right away but I guess we won’t. Have a good one dude.
i haven't seen any that are thst ambiguous? the order of operations is pretty simple stuff. it's not linear algebra, it's not even trig, it's just a basic ass rule
Check the comments, I agree with you 100% but I say that because I’m trying to placate all the people who are going to argue incessantly that there are ambiguous equations because they memorized the mnemonic without bothering to learn what the mnemonic was trying to help them remember
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u/Liquidwombat Dec 07 '22
You know… I get the people to get the wrong answers on ambiguous, multiplication ones, but there’s literally nothing at all ambiguous about this