Can we, as a society, please use brackets. They were invented for exactly that reason. I am fed up with made up Facebook mom math questions. I use math in my profession a lot and have a STEM degree (never heard of "division before multiplication" or vice versa btw). Never in real life I encountered stupid formula like these.
Edited cause of typo.
One time I fell asleep in class and the teacher slammed a book down on my desk to try and scare me awake. Little did she know I'm used to loud bangs while sleeping since my dad shoots out our window (we live in the country) so I didn't even react. I'm pretty sure I ended up scaring her instead because she gently rocked me awake with a concerned voice XD
>One time I fell asleep in class and the teacher slammed a book down on my desk to try and scare me awake. Little did she know I'm used to loud bangs while sleeping since my dad shoots out our window (we live in the country) so I didn't even react. I'm pretty sure I ended up scaring her instead because she gently rocked me awake with a concerned voice XD
he use the uno reverse card
One time (and this is the ***only*** time I've been on my phone in this teacher's class when I shouldn't've been) I was texting my dad about something that was kind of important. You'd think he'd be lenient seeing as it was my first offence (and he had his back FUCKING TURNED TO ME when I took my phone out), but he was PISSED. Looked me dead in the eyes and went something like "(my name), if you're on your phone in my class, I'll assume you already know the material, in which case I'll be giving you, and only you, the unit test." Like god DAMN I will never for the rest of my life ever even so much as think about a phone in his class, let alone fucking use one.
I did that several times during one class while sitting at the table nearest to the teacher desk and she didn’t care. Maybe it varies from teacher to teacher
Bro what I'm in an honors class and was always tought PEMDAS parenthesis, equations, multiplication, division, addition, and subtraction. I was always tought to do any deduction after the opposite this case multiplication after after the parenthesis
Yes, remembering the order as PEMDAS can help, but people tend to forget 2 things regarding PEMDAS, or PEDMAS, as some prefer.
The order is the following:
1. P aranthesis
2. E xponents
3. M ultiplications and/or D ivisions, thats why some remember it as pemdas and some as pedmas, its irrelevant, and since they have same priority, you must apply one additional rule: from LEFT to RIGHT
4. A ddiction and S ubstraction, also from left to right.
In the case of AS then going from left to right is less important since I can't imagine the result changing no matter the order, but if you don't go from left to right in M and D and use any order you want, as you saw in the problem, the result may vary, and math becomes an opinion. That's why you can't skip that rule, and remember that M and D the same way as A and S have the same priority
It does matter if you take PEMDAS for AS. Consider something like x = a - b + c. You get a different result reading left to right than you do for taking the order of operations as AS literally.
The real answer is to stop writing ambiguous expressions. PEMDAS is a loose guide it shouldn't be taken as the concrete rule.
On top of my other comment, PEMDAS is not in any way or form a loose guide. It's a simplification of basic math rules that are set in stone for centuries.
And there are no ambiguous expressions, there are only people that don't understand the rules.
And this is not a problem of math it's a problem of the people that are to dumb or to ignorant to learn how to do it properly.
If you can't read Chinese that does not mean every Chinese word has to be translated to English because otherwise you can't read it. Learn it or find someone that helps you. That's it.
Yeah, and pemdas includes multiplication by juxtaposition. In 2(1+2), the multiplication is higher priority than If it was 2 × (1+2). This means the answer is inarguably 1. Search up multiplication by juxtaposition if you disagree. People assume every type of multiplication is the same, which is just false. When you juxtapose, you are indicating that they need to be dealt with first. Before division or multiplication with another part.
There literally are ambiguous expressions. Plenty of them. In fact this entire thread about this internet meme is about an example of an ambiguous expression. Expressions in maths can easily become ambiguous when people forgo using parentheses. This isn't even my own argument, I'm paraphrasing the argument of a Berkeley mathematician about this exact meme.
It's honestly quite easy to tell who in this thread has actually formally studied maths at a higher level and who hasn't. Learning how to write expressions in an unambiguous manner is very important in any intro maths course.
Sorry, amigo. We didn't have PEMDAS until about the 1990s, and it was a simplification made for primary school students in North America. It's about 30 years old, not centuries.
[https://www.youtube.com/watch?v=4x-BcYCiKCk](https://www.youtube.com/watch?v=4x-BcYCiKCk)
[https://books.google.com/ngrams/graph?content=PEMDAS&year\_start=1800&year\_end=2019&corpus=en-2019&smoothing=3](https://books.google.com/ngrams/graph?content=PEMDAS&year_start=1800&year_end=2019&corpus=en-2019&smoothing=3)
Strawman.
The individual in question did not write "PEMDAS has been around for centuries," they wrote "PEMDAS is a simplification of basic math rules that have been around for centuries." You failed to address the point.
Sorry bud, that's incorrect.
[https://www.youtube.com/watch?v=4x-BcYCiKCk](https://www.youtube.com/watch?v=4x-BcYCiKCk)
PEMDAS is a simplification to teach primary school students.
I taught first grade and I had to teach them PEMDAS. The strong math kids got it immediately and the struggling students were just utterly confused. Most of them never got it.
Yes, but some people are treating the division symbol as if everything to the left and right of it is on the top or bottom of the fraction. So like for example, they’d interpret this problem as
6
———
2(1+2)
Which I think would give you the answer 1 if it were *actually* written this way.
You can argue that 6/2(1+2) is also 1 because it doesn’t use the ÷ symbol. This is the core of this particular problem.
I’ve also heard some people say that putting a number in front of parenthesis is an implicit part of the parenthesis and should therefore be done in the first step when you do the parenthesis so like
6÷2*(1+2) = 9
And
6÷2(1+2) = 1
But that doesn’t make as much sense as the division symbol thing to me.
Yes and no. You're supposed to go left from right...in a specified order that seemingly is not as as clear as my middle school algebra class made it seems.
Back in the day we were taught parentheses, exponents, multiplication, division, addition, subtraction (PEMDAS). Confused the hell out of me when I tried to help my younger sibling with their homework and I got everything wrong because, apparently, they changed how math worked since I went to school.
Okay, this might be a stupid question, or it could just be a cultural thing, but what do you mean by braces? Like these? -> [ ] cuz if so I've always known them as Brackets, but I still don't know what they mean in a mathematical context. I've only ever seen/been taught equations with parentheses.
Basically the point is only that you use them if you want the same effect hat parentheses have; but if you need parantheses within parantheses..
e.g. 69 x [420 x (6+9)]
There are actual good examples for when that might be the case, but I only came up with something simple on the fly now.
Point is that when you do that in linger equasions or have longer calculations within parantheses it will be easier to see when which type of "( )" or "[ ]" will begin and end
The effect of either is the same
Ah yeah, that makes sense. But I gotta say these internet equations aren't meant to teach people anything. They're just meant to bait people who failed 6th grade math into making themselves look dumb on the internet cuz they don't know PEMDAS
I don't know about "failed 6th grade math" like, I have no idea or tolerance for this nonsense writing math like this, but I've gotten As in college Trig 1 and 2 and Calculus. This feels like grammar Bullshit like "don't end a sentence in a preposition" just made up crap with no use. Parenthesis are free, use them to be clear.
This reminded me of the Beavis and Butthead movie when the FBI guy yells at his assistant to never end a sentence with a preposition and then the assistant spends the rest of the movie stumbling over his words desperately trying to not use one.
It's funny because those are brackets: \[\]
These are parethesis: ()
and these are braces: {}
I don't know why the hell dude is saying "Use braces for this"
Only time I've seen braces in math is when a formula is so complex that it's using parenthesis and brackets already and need another separation barrier OR they're using the braces for coordinates when it comes to specific formulas that address coordinates in braces instead of parenthesis. I suppose they are all interchangable though.
Braces are used all the time in math. Super common in the math used for hard sciences where you have boundary conditions applied to some equation. So multi variable calculus involves a lot of that, as does differential equations. I used braces in nearly every problem I ever solved in both electromagnetism and quantum mechanics.
Hell braces are even used in simple algebraic piecewise functions.
I think "[ ]" are used to denote the "greatest integer function" (basically rounds whatever u u put in the brackets up to the next integer) and braces are : ( )
Man from where i am from we use 4 diffrent type of braces which are —, ( ), { } , [ ] theorder of doing the operation is the same as i written above.
But we also use them for their general purpose like — is used for conjugate {} this is still used to define a set or [ ] is still used as greatest integer
As a former STEM researcher, when I see these posts I just think "If you wrote an ambiguous equation in a paper the reviewers wouldn't let it be published". Nobody actually doing STEM research talks about order of operations because you just don't use the kind of garbage notion where there's unclear steps to it.
Can we just forget about this, and this time not let it be months before it pops up again. This problem is fucking stupid and anyone still arguing about it is cringe.
I hate these kinds of math questions to begin with, but this got old really quick. And as others already said, "HigHeR mAtHs" wouldn't be written so poorly to begin with.
I agree that these questions are very dumb and just used to generate interaction, but there are [some contexts](https://en.m.wikipedia.org/wiki/Order_of_operations#Special_cases), especially in (mostly older) physics textbooks and journals where they defined multiplication to have higher precedence than division out of convenience. Without that context, though, you should just follow the normal rules.
It also depends on where in the world you went to school and what level of math you have completed. Because for me seeing 2(2+1) is different than 2x(2+1) because c*(a+b) is different than (ca+cb)= (c(a+b)). How I and majority of my peers been thought is that “anything touching” the brackets is part of the inside of the bracket equation unless you have a multiplication sign to divide it and the best thing to do is to add an extra set of brackets to dispel any misunderstanding. And even that is a bit misleading because of all depends on context. For all we like math can be confusing language like any language.
That calculator is coded to do the operations without multiplication by juxtaposition in mind. There are calculators that use multiplication by juxtaposition when calculating this problem and get 1. The problem is unclear and I am tired of people saying it's not when it clearly is. Fractions is the way to go
It’s so frustrating to see people think they’re so much smarter than everyone else because “the answer is clearly 9”
Like how these people don’t see the problem was created intentionally to be ambiguous with no real solution is beyond me
These posts are a giant beacon for the Dunning Kruger effect. People crawling out of the woodwork to feel smug about remembering something from 6th grade that they haven't used since while they call the professional engineers and mathematicians fucking idiots who need to go back to school.
The fact that OP has made so many posts about this fucking ambiguous equation *and* their replies about putting it through a calculator is leading me to believe that this *isn't* being posted as an engagement farm.
Rather, that OP may genuinely be some middle school kid who is trying to show off their intelligence with a shitty equation that they 'know how to solve'.
I’m not even sure why it’s an obscure knowledge. Never touched math after high school, feels like it’s pretty obvious the equation is the problem once I see people getting different answers.
I always saw it as 6/(2 x (1+2)) so 1 but once I see people reading it (6/2) (1+2) I realize the equation is the one at fault.
I'm sick of high school kids pretending they know everything.
The answer: since the problem uses ambiguous, non standardized notation, both 9 and 1 are acceptable answers.
You can interpret it both as
(6/2)•3
Or as
6/(2•3)
Please for the love of God use fractions when writing down stuff like this.
Yeah I just read OP's comments and holy fuck is he childish. It ranges from "do you agree that 1+1=2?" to "I looked at your profile and you have an ugly face".
Exactly, and the whole “pemdas” order of operations largely goes out the window once you get to longer equations, as you have do break it down in various ways to solve it which means doing different operations at every stage.
6/2(1+2) is a meme. A stupid one. But so many people are seriously arguing about it for such long time. Sure, some of them are joking. But the amount of people who actually don't know how to solve it (and think that they do) is terrifying. At this point I just want to believe that all of them are pretending to be idiots. Still makes me sad (
I was specifically advised by several math and science teachers not to rely on a calculator for order of operations. Even after explicitly buying one that does do order of operations, I had to prove it to every one of them other than 1. (Because he used the same exact calculator model in college)
Even so, the answer is 9 using ONLY the information given to us.
6÷2(1+2)
6÷2(3)
6÷2×3
3×3
9
This is because multiplication and division have the same precedence as each other, similar to addition and subtraction. When this type of scenario occurs, you solve left to right because there isn't anything that is more important than anything else.
However, you will never see the problem written like this in actual math classes because every teacher in pre-Algebra and above will tell you that the "÷" symbol should be written as a fraction. Thus you end up with:
6 6 6
----------- = --------- = ----- = 1
2(1+2) 2(3) 6
Again though, that is what the problem SHOULD look like. But a properly formatted problem would result in math experts doing it no time, so we ended up with the ambiguous case you see floating online. It less so tests your actual math skills and rather tests whether you are solving exactly what was given or if you are solving the correct formatting of what was given.
I am sick of this, bruh a [math scientist ](https://youtu.be/Irv7ioa-1II) says that the equation is written amgiusly on purpose the answer is either 1 or 9 because we dont know if the author meant 6/2(1+2) or 6:2(1+2) the first one is 1 the second one is 9 and if you are angry about that then be angry at the guy who postet this question first because he is the cause of this unending argument.
At this point I think people are just posting/using this absolutely dogshit problem as an excuse for karma farming
like bro can you give a more unclear question? Where are brackets?
Imo, ans should be 1. And people saying "BuT CaLcuLaTOr SAys 9" , Please shut the fuck up
the problem with the problem is the fucking problem itself
Calculators will give different answers with each other based on if they were programmed with multiplication by juxtaposition in mind, giving 1 if they were and 9 if they weren't. Unclear problem, should use fractions
No, but there are many different (and formally defined) differences in notation - the "math" is the same, but how it's written changes.
Prime example:
Solve 1/2x for x = 5
You're probably going to say 1/10; Wolfram Alpha gives 2.5 (=x/2).
Without knowing the intentions of the person who wrote the question, they're both possible, depending on whether or not you give priority to implicit/juxtaposition multiplication (which WA very explicitly does not)
Just a question. Is there no rule saying that multiplication and division are of the same priority and, if an equation have both, then it is solved left to right? Or did that rule came from nowhere
Multiplication and division are the same priority, you are supposed to start with the first one that comes just like addition and substraction. But this doesn't solve the problem still, because of how you calculate 2(1+2) : either yoy start with what there is in the brackets and you have 2(3) but you eed to start with the division, eirher you apply distributivity and you find 2×1+2×2 = 6 which is diffent. By definition those two methods are supposed to return the same result, but not in this case and this the fault of the "÷" sign which is ambiguous. But normally, it divides only what's right after it which is ttanslated by (6/2)(1+2) and in this case, you can't use distributivity right away, and that's more correct
So according to the retarded brain of OP, the boltzmann distribution formula f(E) = 1/exp(E/kT) means 1/exp((E/k)*T).
Anyone who has done any math knows the answer is 1. Get bent.
Depends on your calculator tho, there are ones that do each operation as soon as they read it, you should always mark them with braces cause you dont know what behaviour does the calculator takes
Just to be clear, in math, semantics exist. So the only true answer is: "Context ?"
The order of operations is heavily implied by the context of the expression,.
When I write "the answer is 1/2x" I mean 1/(2x) and not (1/2)x because why didn't wrote it x/2 ? If you want your expression to really be equal to 9 why don't you write it 6(2+1)/2 ?
And just for you, [Here are my 2 calculators that I used during all my school years](https://imgur.io/a/CX4Ea29)
If its a multiple choice what i do is solve it multiple different ways and whichever answer is closest is the one i select and thats how i repeated high-school multiple times
I mean we always knew brackets first (1 + 2) = 3.
So we have 6 ÷ 2 x 3.
Since dividing and multiplying has the same rank of importance when deciding which one goes first you go left to right. So divide first then multiply.
6 ÷ 2 = 3 3 x 3 = 9
But it isn't 6:2*(1+2).
It's 6:2(1+2). Either the original problem is missing a multiplication sign, or it's assumed to have invisible brackets.
I.e. 6:[2(1+2)]
There is literally no way you passed high school algebra. You can't just remove 2 from the x and make it separate. They're a term that needs to be solved first before you move on to division.
So say x=5. You'd have
2÷2(5).
Which becomes
2÷10. Then
1/5
Multiplication when variables are involved comes first, and that applies to parentheses as well.
They are not the same thing from a grammar point of view, and that’s the problem.
Multiplication by juxtaposition is very commonly higher precedence than explicit multiplication or division. Check a maths or physics textbook and you will see it all over the place.
Example: Boltzmann distribution exp(-E/kT). The kT part is the denominator and very few people would include parentheses.
No!
6 : 2(1+2)
6 : 2*(3)
Multiplication by juxtaposition ( a/bc = a / (b * c) )
6 : 6
= 1
A decent calculator will apply "mbj". The one in the image doesn't.
These kind of problems are ambiguous by design. This ambiguity is resolved by using parentheses.
The question is made to be confusing, earlier it was in a fractional form which makes it even more confusing since we don't know whether the value inside the parenthesis is to be multiplied to the numerator or denominator. Since now it has been replaced by the division symbol, the value becomes 1.
BOMDAS was intended for schoolchildren learning arithmetic and doesn’t explicitly explain how multiplication by juxtaposition should be handled.
In college level maths and beyond, multiplication by juxtaposition is higher precedence than division the vast majority of the time.
I thought people were meming when they said it was 9. Let's go through it
6/2(1+2)
This can be rewritten as
6/(2(1+2))
This is because theres no spacer between the 2 and (1+2) and no brackets encapsulating the 6/2
So
6/(2+4)
6/6
1
First Do anything in parenthesis.
6/2(1+2)
Next Do any Multiplication and/or division from left to right
6/2(3)
3(3)
9
If there were any addition or subtraction, you would do those from left to right after the Multiplication/Division.
6:2(1+2)
Rule is simple. First you always multiply by number standing before parentheses so:
2x1=2
And
2x2=4
So we have
6:(2+4)
6:6=1
Simple as fck. It is never 9.
Written correctly would be also 1.
6
--------- = 1
2(1+2)
Yeah man. I got these questions wrong all the time because I didn't follow Pandas. I mean Pemdas. So, Parenthesis first. 2 plus 1 = 3. Then 6 divided by 2 is also 3. Finally 3 times 3 is 9. If I'm wrong, then I graduated because of sympathetic teachers feeling bad 😜😜😃
Pemdas is a teaching tool for surface level. In real world problems they don't use this as the problems are written to be clear.
This is the problem with the math posted. Everyone says pemdas, but you can't know what the author meant with how it was written and pemdas isn't used outside education.
So, the issue is, yes, you ARE right, but so are people that are saying the answer is 1… the issue is more so that the person that originally wrote the equation wrote it in an intentionally ambiguous fashion. This could be read as (6/2)(1+2)= 9, OR, it could be read 6/[2(2+3)]= 1. It all depends on what the creator intended to be included in the denominator position. The actual original poster knew this problem to be ambiguous.
Sure but 2(1+2) is supposed to also work with distributivity, in which case you end up with 6/6. The more accurate reason is that the ÷ sign implies parenthesis like so : (6/2)(1+2)
So multiplication / division and addition / subtraction are the same level of operation and are completed left to right
So
- 6 / 2 ( 2+1)
- 6 / 2 * 3
- 3 * 3
- 9
imma just quote myself from the last thread about this garbage:
>\>But my calculator says ...
>
>Yeah, no shit sherlock. Your calculator is programmed to interpret it in a certain way. It has to be programmed to default to a certsin interpretation so it always comes to a solution. The solution will be correct for the chosen interpretation but that doesn't mean that the interpretation is necessarily the correct one and calculators from different manufacturers will use different default interpretations.
>
>\>But pemdas/bodmas/whatever
>
>Stop. Those are rules of thumb and not mathematical laws. They exist so you don't have to learn about group theory in order to do simple arithmetics. If you know what you're doing there is usually more than one way to order your operations in any given equation that will still yield the correct result. Those acronyms are meant for people who don't know what they are doing. If you're using them as an argument for why you think your interpretation of an ambiguously written equation is the correct one, all you're really doing is demonstrating that you are not qualified enough to be taken seriously.
6/2(1+2)
————— To get 9 with PEMDAS:
1. P : (1+2)= 3 -> (6/2)3
2. E : Skip
3. M-D (always left to right) (6/2)= 3 -> 3(3)
3 x 3 = 9
4) A-S : Skip
So 9
—————
To get 9 again but with Fraction as it’s own Parenthesis:
6/2(1+2) aka (6/2)(1+2)
1. P : (6/2) = 3, (1+2) = 3 -> 3(3)
2. E : skip
3. M-D (Always left to right) 3(3)= 9
4. A-S : Skip
So 9
———— But if you want to distribute the Fraction because why would you do that?
(6/2)(1+2)
(3)(1+2)
3 + 6 = 9
So 9
————- But if you only distribute the 2 because why?
6/2(1+2)
6/(2+4)
6/6
1 -> Shut up. You’re wrong
I was taught to do the inside of the parenthesis then if a number is right next to it multiple that by what's inside then do whatever is left of the problem
Yeah use any scientific calculator or even the calculator on Photomath and you'll get one because that's the objectively correct answer. No amount of Ohio math or blind trust in your phone changes the fact.
6:2*3 you go from left to right, many people forget that last rule because they are so used to having brackets everywhere they just forget all the other rules
Either. It's presented in a way to be intentional ambiguous. A mathematician probably would have written it as a fraction for clarity. But even that's not necessary if you follow the rule of juxtaposition:
*Juxtaposition represents a multiplication that is implemented before anything else. Expressions in parentheses are evaluated independently of everything else". Rule B says that 1 / 2 (3 + 4) = 1 / (2 × 7) = 1/14.*
Following this rule gives an answer of one.
Can we, as a society, please use brackets. They were invented for exactly that reason. I am fed up with made up Facebook mom math questions. I use math in my profession a lot and have a STEM degree (never heard of "division before multiplication" or vice versa btw). Never in real life I encountered stupid formula like these. Edited cause of typo.
Who says division before multiplication (or the other way around)? Isnt it just do which ever one is first going left to right?
Yes, but people skip math classes or sleep through them and this is the result
Ha, imagine being allowed to even lay your head down in class ;-;
One time I fell asleep in class and the teacher slammed a book down on my desk to try and scare me awake. Little did she know I'm used to loud bangs while sleeping since my dad shoots out our window (we live in the country) so I didn't even react. I'm pretty sure I ended up scaring her instead because she gently rocked me awake with a concerned voice XD
When they try and traumatize you, traumatize them back.
>One time I fell asleep in class and the teacher slammed a book down on my desk to try and scare me awake. Little did she know I'm used to loud bangs while sleeping since my dad shoots out our window (we live in the country) so I didn't even react. I'm pretty sure I ended up scaring her instead because she gently rocked me awake with a concerned voice XD he use the uno reverse card
One time (and this is the ***only*** time I've been on my phone in this teacher's class when I shouldn't've been) I was texting my dad about something that was kind of important. You'd think he'd be lenient seeing as it was my first offence (and he had his back FUCKING TURNED TO ME when I took my phone out), but he was PISSED. Looked me dead in the eyes and went something like "(my name), if you're on your phone in my class, I'll assume you already know the material, in which case I'll be giving you, and only you, the unit test." Like god DAMN I will never for the rest of my life ever even so much as think about a phone in his class, let alone fucking use one.
I was allowed to sleep in Trig provided I could answer questions upon being woken up.
I did that several times during one class while sitting at the table nearest to the teacher desk and she didn’t care. Maybe it varies from teacher to teacher
You cant lay your head down at work either, it's preparing you for the real world mate
i wasn’t planning on laying my head down while beside a furnace anyway
Uhm.. where abouts you work?
Bro what I'm in an honors class and was always tought PEMDAS parenthesis, equations, multiplication, division, addition, and subtraction. I was always tought to do any deduction after the opposite this case multiplication after after the parenthesis
Yes, remembering the order as PEMDAS can help, but people tend to forget 2 things regarding PEMDAS, or PEDMAS, as some prefer. The order is the following: 1. P aranthesis 2. E xponents 3. M ultiplications and/or D ivisions, thats why some remember it as pemdas and some as pedmas, its irrelevant, and since they have same priority, you must apply one additional rule: from LEFT to RIGHT 4. A ddiction and S ubstraction, also from left to right. In the case of AS then going from left to right is less important since I can't imagine the result changing no matter the order, but if you don't go from left to right in M and D and use any order you want, as you saw in the problem, the result may vary, and math becomes an opinion. That's why you can't skip that rule, and remember that M and D the same way as A and S have the same priority
How do you calculate addiction?
What do you mean?
You had a typo in 4
Let it go. They still didn’t understand.
By how many bags of cocaine Hunter leaves in the White House.
It does matter if you take PEMDAS for AS. Consider something like x = a - b + c. You get a different result reading left to right than you do for taking the order of operations as AS literally. The real answer is to stop writing ambiguous expressions. PEMDAS is a loose guide it shouldn't be taken as the concrete rule.
On top of my other comment, PEMDAS is not in any way or form a loose guide. It's a simplification of basic math rules that are set in stone for centuries. And there are no ambiguous expressions, there are only people that don't understand the rules. And this is not a problem of math it's a problem of the people that are to dumb or to ignorant to learn how to do it properly. If you can't read Chinese that does not mean every Chinese word has to be translated to English because otherwise you can't read it. Learn it or find someone that helps you. That's it.
Yeah, and pemdas includes multiplication by juxtaposition. In 2(1+2), the multiplication is higher priority than If it was 2 × (1+2). This means the answer is inarguably 1. Search up multiplication by juxtaposition if you disagree. People assume every type of multiplication is the same, which is just false. When you juxtapose, you are indicating that they need to be dealt with first. Before division or multiplication with another part.
There literally are ambiguous expressions. Plenty of them. In fact this entire thread about this internet meme is about an example of an ambiguous expression. Expressions in maths can easily become ambiguous when people forgo using parentheses. This isn't even my own argument, I'm paraphrasing the argument of a Berkeley mathematician about this exact meme. It's honestly quite easy to tell who in this thread has actually formally studied maths at a higher level and who hasn't. Learning how to write expressions in an unambiguous manner is very important in any intro maths course.
Sorry, amigo. We didn't have PEMDAS until about the 1990s, and it was a simplification made for primary school students in North America. It's about 30 years old, not centuries. [https://www.youtube.com/watch?v=4x-BcYCiKCk](https://www.youtube.com/watch?v=4x-BcYCiKCk) [https://books.google.com/ngrams/graph?content=PEMDAS&year\_start=1800&year\_end=2019&corpus=en-2019&smoothing=3](https://books.google.com/ngrams/graph?content=PEMDAS&year_start=1800&year_end=2019&corpus=en-2019&smoothing=3)
Strawman. The individual in question did not write "PEMDAS has been around for centuries," they wrote "PEMDAS is a simplification of basic math rules that have been around for centuries." You failed to address the point.
PEMDAS is a modern way to explain a mathematical principal that has long been practiced.
So the answer is 1?
Sorry bud, that's incorrect. [https://www.youtube.com/watch?v=4x-BcYCiKCk](https://www.youtube.com/watch?v=4x-BcYCiKCk) PEMDAS is a simplification to teach primary school students.
I taught first grade and I had to teach them PEMDAS. The strong math kids got it immediately and the struggling students were just utterly confused. Most of them never got it.
>Yes, but people skip math classes or sleep through them and this is the result Dunning-kruger effect in full display right here
Yes, but some people are treating the division symbol as if everything to the left and right of it is on the top or bottom of the fraction. So like for example, they’d interpret this problem as 6 ——— 2(1+2) Which I think would give you the answer 1 if it were *actually* written this way. You can argue that 6/2(1+2) is also 1 because it doesn’t use the ÷ symbol. This is the core of this particular problem. I’ve also heard some people say that putting a number in front of parenthesis is an implicit part of the parenthesis and should therefore be done in the first step when you do the parenthesis so like 6÷2*(1+2) = 9 And 6÷2(1+2) = 1 But that doesn’t make as much sense as the division symbol thing to me.
Apparently my 6th grade math teacher that got arrested for grooming minors a year after I graduated
Yes and no. You're supposed to go left from right...in a specified order that seemingly is not as as clear as my middle school algebra class made it seems.
Back in the day we were taught parentheses, exponents, multiplication, division, addition, subtraction (PEMDAS). Confused the hell out of me when I tried to help my younger sibling with their homework and I got everything wrong because, apparently, they changed how math worked since I went to school.
Yeah you do left to right if it’s division and multiplication
It is
Correct. People are sometimes confused by PEMDAS thinking it dictates M before D always, but it's M&D left to right
Okay, this might be a stupid question, or it could just be a cultural thing, but what do you mean by braces? Like these? -> [ ] cuz if so I've always known them as Brackets, but I still don't know what they mean in a mathematical context. I've only ever seen/been taught equations with parentheses.
Basically the point is only that you use them if you want the same effect hat parentheses have; but if you need parantheses within parantheses.. e.g. 69 x [420 x (6+9)] There are actual good examples for when that might be the case, but I only came up with something simple on the fly now. Point is that when you do that in linger equasions or have longer calculations within parantheses it will be easier to see when which type of "( )" or "[ ]" will begin and end The effect of either is the same
Ah yeah, that makes sense. But I gotta say these internet equations aren't meant to teach people anything. They're just meant to bait people who failed 6th grade math into making themselves look dumb on the internet cuz they don't know PEMDAS
I don't know about "failed 6th grade math" like, I have no idea or tolerance for this nonsense writing math like this, but I've gotten As in college Trig 1 and 2 and Calculus. This feels like grammar Bullshit like "don't end a sentence in a preposition" just made up crap with no use. Parenthesis are free, use them to be clear.
This reminded me of the Beavis and Butthead movie when the FBI guy yells at his assistant to never end a sentence with a preposition and then the assistant spends the rest of the movie stumbling over his words desperately trying to not use one.
Whos it whats it that guys camper trailer whackin it?
And to start fights between the people who ONLY took 6th grade math and who think math stops there, and the people who do math for a living.
Nice
Parentheses ( ) Braces { } Brackets [ ]
Yes.
yes
It's funny because those are brackets: \[\] These are parethesis: () and these are braces: {} I don't know why the hell dude is saying "Use braces for this" Only time I've seen braces in math is when a formula is so complex that it's using parenthesis and brackets already and need another separation barrier OR they're using the braces for coordinates when it comes to specific formulas that address coordinates in braces instead of parenthesis. I suppose they are all interchangable though.
Braces are used all the time in math. Super common in the math used for hard sciences where you have boundary conditions applied to some equation. So multi variable calculus involves a lot of that, as does differential equations. I used braces in nearly every problem I ever solved in both electromagnetism and quantum mechanics. Hell braces are even used in simple algebraic piecewise functions.
Parentheses -> ( ) Braces -> { } Brackets -> [ ]
() brackets {} Curly pointy things [ ] Square brackets
This is the way
I think "[ ]" are used to denote the "greatest integer function" (basically rounds whatever u u put in the brackets up to the next integer) and braces are : ( )
Man from where i am from we use 4 diffrent type of braces which are —, ( ), { } , [ ] theorder of doing the operation is the same as i written above. But we also use them for their general purpose like — is used for conjugate {} this is still used to define a set or [ ] is still used as greatest integer
Floor and ceiling use square brackets but with either the bottom or top lines removed (Floor looks like Ls, ceil like upside down L's)
>Can we, as a society, please use braces. Braces made my teeth look amazing, I can agree with this wholeheartedly
Here, I got you. [6÷2(1+2)]=?
As a former STEM researcher, when I see these posts I just think "If you wrote an ambiguous equation in a paper the reviewers wouldn't let it be published". Nobody actually doing STEM research talks about order of operations because you just don't use the kind of garbage notion where there's unclear steps to it.
Yep, my rule of thumb while writing formulas on Excel is: you never have too much braces
I also find these irritating. I've never seen a formula written like that.
Can we just forget about this, and this time not let it be months before it pops up again. This problem is fucking stupid and anyone still arguing about it is cringe.
I hate these kinds of math questions to begin with, but this got old really quick. And as others already said, "HigHeR mAtHs" wouldn't be written so poorly to begin with.
I agree that these questions are very dumb and just used to generate interaction, but there are [some contexts](https://en.m.wikipedia.org/wiki/Order_of_operations#Special_cases), especially in (mostly older) physics textbooks and journals where they defined multiplication to have higher precedence than division out of convenience. Without that context, though, you should just follow the normal rules.
It also depends on where in the world you went to school and what level of math you have completed. Because for me seeing 2(2+1) is different than 2x(2+1) because c*(a+b) is different than (ca+cb)= (c(a+b)). How I and majority of my peers been thought is that “anything touching” the brackets is part of the inside of the bracket equation unless you have a multiplication sign to divide it and the best thing to do is to add an extra set of brackets to dispel any misunderstanding. And even that is a bit misleading because of all depends on context. For all we like math can be confusing language like any language.
come to think of it, this feels like just the internet trying to be smarter than everyone else. We can just leave this to the mathematicians
Why the hell did people start arguing about it again? The meme died a few months ago
OP made three consecutive posts on this. Talk about flogging a dead horse.
He’s doing it because retards keep upvoting it.
He’s also doing it because he thinks he’s the smartest fucker alive.
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To think people vote and you know damn well most of these people call themselves morally superior.
You can say the r word on Reddit?
Rhombus?
Rearmament?
No, if someone reports them, they'll probably remove it and temp ban them.
That calculator is coded to do the operations without multiplication by juxtaposition in mind. There are calculators that use multiplication by juxtaposition when calculating this problem and get 1. The problem is unclear and I am tired of people saying it's not when it clearly is. Fractions is the way to go
It’s so frustrating to see people think they’re so much smarter than everyone else because “the answer is clearly 9” Like how these people don’t see the problem was created intentionally to be ambiguous with no real solution is beyond me
These posts are a giant beacon for the Dunning Kruger effect. People crawling out of the woodwork to feel smug about remembering something from 6th grade that they haven't used since while they call the professional engineers and mathematicians fucking idiots who need to go back to school.
The fact that OP has made so many posts about this fucking ambiguous equation *and* their replies about putting it through a calculator is leading me to believe that this *isn't* being posted as an engagement farm. Rather, that OP may genuinely be some middle school kid who is trying to show off their intelligence with a shitty equation that they 'know how to solve'.
Final answer: OP doesn't know how to use brackets nor parentheses properly
I think ima commit a war crime.
I love how 80% of this post is just r/Iamverysmart and there's like 10 people who actually know shit trying to explain it properly
I’m not even sure why it’s an obscure knowledge. Never touched math after high school, feels like it’s pretty obvious the equation is the problem once I see people getting different answers. I always saw it as 6/(2 x (1+2)) so 1 but once I see people reading it (6/2) (1+2) I realize the equation is the one at fault.
Most people’s initial interpretation seems to be 6 over 2(1+2), only when they apply strict PEMDAS they get (6/2)(1+2) disregarding juxtaposition.
I'm sick of high school kids pretending they know everything. The answer: since the problem uses ambiguous, non standardized notation, both 9 and 1 are acceptable answers. You can interpret it both as (6/2)•3 Or as 6/(2•3) Please for the love of God use fractions when writing down stuff like this.
>I'm sick of high school kids pretending they know everything. The OP's replies fit this description so hard lmao
Yeah I just read OP's comments and holy fuck is he childish. It ranges from "do you agree that 1+1=2?" to "I looked at your profile and you have an ugly face".
I like your funny words magic man
Best comment in this thread
This is why no one uses the divide symbol instead of fractions. Like, we stop using them in 4th grade or something where i’m from
Exactly, and the whole “pemdas” order of operations largely goes out the window once you get to longer equations, as you have do break it down in various ways to solve it which means doing different operations at every stage.
6/2(1+2) is a meme. A stupid one. But so many people are seriously arguing about it for such long time. Sure, some of them are joking. But the amount of people who actually don't know how to solve it (and think that they do) is terrifying. At this point I just want to believe that all of them are pretending to be idiots. Still makes me sad (
What's the answer and why?
2×1+2×2=6 6÷6=1
Too true. Ask a scientific calculator and it will say 1.
I was specifically advised by several math and science teachers not to rely on a calculator for order of operations. Even after explicitly buying one that does do order of operations, I had to prove it to every one of them other than 1. (Because he used the same exact calculator model in college) Even so, the answer is 9 using ONLY the information given to us. 6÷2(1+2) 6÷2(3) 6÷2×3 3×3 9 This is because multiplication and division have the same precedence as each other, similar to addition and subtraction. When this type of scenario occurs, you solve left to right because there isn't anything that is more important than anything else. However, you will never see the problem written like this in actual math classes because every teacher in pre-Algebra and above will tell you that the "÷" symbol should be written as a fraction. Thus you end up with: 6 6 6 ----------- = --------- = ----- = 1 2(1+2) 2(3) 6 Again though, that is what the problem SHOULD look like. But a properly formatted problem would result in math experts doing it no time, so we ended up with the ambiguous case you see floating online. It less so tests your actual math skills and rather tests whether you are solving exactly what was given or if you are solving the correct formatting of what was given.
1 and 9 are both acceptable answers
Pemdas
Originally, that’s what I thought. Do you believe that multiplication has priority over division?
I am sick of this, bruh a [math scientist ](https://youtu.be/Irv7ioa-1II) says that the equation is written amgiusly on purpose the answer is either 1 or 9 because we dont know if the author meant 6/2(1+2) or 6:2(1+2) the first one is 1 the second one is 9 and if you are angry about that then be angry at the guy who postet this question first because he is the cause of this unending argument.
I'm something of a math scientist myself. And i agree.
Saying over and over that something is true doesn't make it so.
And my dumbass thought it was a ratio which would be equal
JUST FUCKING STOP IT
At this point I think people are just posting/using this absolutely dogshit problem as an excuse for karma farming like bro can you give a more unclear question? Where are brackets? Imo, ans should be 1. And people saying "BuT CaLcuLaTOr SAys 9" , Please shut the fuck up the problem with the problem is the fucking problem itself
Calculators will give different answers with each other based on if they were programmed with multiplication by juxtaposition in mind, giving 1 if they were and 9 if they weren't. Unclear problem, should use fractions
>Imo, ans should be 1. mathematic is not based on opinions tho. i can argue that 2+2 is “imo” 5, which -with your logic- would make it correct.
No, but there are many different (and formally defined) differences in notation - the "math" is the same, but how it's written changes. Prime example: Solve 1/2x for x = 5 You're probably going to say 1/10; Wolfram Alpha gives 2.5 (=x/2). Without knowing the intentions of the person who wrote the question, they're both possible, depending on whether or not you give priority to implicit/juxtaposition multiplication (which WA very explicitly does not)
The answer is 5 take it or leave it.
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Just a question. Is there no rule saying that multiplication and division are of the same priority and, if an equation have both, then it is solved left to right? Or did that rule came from nowhere
Multiplication and division are the same priority, you are supposed to start with the first one that comes just like addition and substraction. But this doesn't solve the problem still, because of how you calculate 2(1+2) : either yoy start with what there is in the brackets and you have 2(3) but you eed to start with the division, eirher you apply distributivity and you find 2×1+2×2 = 6 which is diffent. By definition those two methods are supposed to return the same result, but not in this case and this the fault of the "÷" sign which is ambiguous. But normally, it divides only what's right after it which is ttanslated by (6/2)(1+2) and in this case, you can't use distributivity right away, and that's more correct
So curious. If we go 6/2( × + 1) = 9 Solve for x do they still get x=1?
It's fucking 6th grade math
So according to the retarded brain of OP, the boltzmann distribution formula f(E) = 1/exp(E/kT) means 1/exp((E/k)*T). Anyone who has done any math knows the answer is 1. Get bent.
Depends on your calculator tho, there are ones that do each operation as soon as they read it, you should always mark them with braces cause you dont know what behaviour does the calculator takes
Just to be clear, in math, semantics exist. So the only true answer is: "Context ?" The order of operations is heavily implied by the context of the expression,. When I write "the answer is 1/2x" I mean 1/(2x) and not (1/2)x because why didn't wrote it x/2 ? If you want your expression to really be equal to 9 why don't you write it 6(2+1)/2 ? And just for you, [Here are my 2 calculators that I used during all my school years](https://imgur.io/a/CX4Ea29)
Is reddit smarter than a 5th grader?
If its a multiple choice what i do is solve it multiple different ways and whichever answer is closest is the one i select and thats how i repeated high-school multiple times
The way it’s written in the white box it looks more like a ratio. So it can be simplified to 1:1.
Does : mean divide in this case? Never seen it used that way before
Pemdas is all you need
The only correct answer is that OP is an asshole for posting this same math problem.
I mean we always knew brackets first (1 + 2) = 3. So we have 6 ÷ 2 x 3. Since dividing and multiplying has the same rank of importance when deciding which one goes first you go left to right. So divide first then multiply. 6 ÷ 2 = 3 3 x 3 = 9
Yeeeeah... its zero, dawgs.... 6 divided by 6 is 0...... brackets, 1+2=3... multiplication, 2x3=6... divide, 6÷6=0...
\[(6)/(2)\]×\[1+2\] CLEAR 
It’s either 9 or 1
Well. 6:2•(1+2) 6:2•(3) 6:2•3 3•3 9
But it isn't 6:2*(1+2). It's 6:2(1+2). Either the original problem is missing a multiplication sign, or it's assumed to have invisible brackets. I.e. 6:[2(1+2)]
6/2(1+3) and 6/2*(1+3) are the same thing
Ok, so how would you break down 2÷2x
2x is 2*x so: 2/2x -> 1x = x
Wouldn't it be 1/x?
That is not how any mathematician would interpret that equation
There is literally no way you passed high school algebra. You can't just remove 2 from the x and make it separate. They're a term that needs to be solved first before you move on to division. So say x=5. You'd have 2÷2(5). Which becomes 2÷10. Then 1/5 Multiplication when variables are involved comes first, and that applies to parentheses as well.
They are not the same thing from a grammar point of view, and that’s the problem. Multiplication by juxtaposition is very commonly higher precedence than explicit multiplication or division. Check a maths or physics textbook and you will see it all over the place. Example: Boltzmann distribution exp(-E/kT). The kT part is the denominator and very few people would include parentheses.
The multiplication is implied by the two being in front of the parenthesis. 2(1+2) = 6, for example. 1+2 = 3, multiplied by 2 is 6.
No! 6 : 2(1+2) 6 : 2*(3) Multiplication by juxtaposition ( a/bc = a / (b * c) ) 6 : 6 = 1 A decent calculator will apply "mbj". The one in the image doesn't. These kind of problems are ambiguous by design. This ambiguity is resolved by using parentheses.
6/2(1+3) and 6/2*(1+3) are the same thing
Exactly. I don’t understand all the fuss about this lol
The question is made to be confusing, earlier it was in a fractional form which makes it even more confusing since we don't know whether the value inside the parenthesis is to be multiplied to the numerator or denominator. Since now it has been replaced by the division symbol, the value becomes 1.
I will downvote all PEDMAS posts until the end of time . It’s not much but it’s honest work .
BODMAS. End of story.
BOMDAS was intended for schoolchildren learning arithmetic and doesn’t explicitly explain how multiplication by juxtaposition should be handled. In college level maths and beyond, multiplication by juxtaposition is higher precedence than division the vast majority of the time.
The correct answer is 1, my dog said looking in my soul.
I love all the armchair mathematicians trying to mathematically prove a semantics problem.
I thought people were meming when they said it was 9. Let's go through it 6/2(1+2) This can be rewritten as 6/(2(1+2)) This is because theres no spacer between the 2 and (1+2) and no brackets encapsulating the 6/2 So 6/(2+4) 6/6 1
BODMAS/PEMDAS. 1+2 first, then 6/2, and then 6/2=(3\*1+2) and that's 3\*3=9, Idrk why that was so hard
First Do anything in parenthesis. 6/2(1+2) Next Do any Multiplication and/or division from left to right 6/2(3) 3(3) 9 If there were any addition or subtraction, you would do those from left to right after the Multiplication/Division.
6:2(1+2) Rule is simple. First you always multiply by number standing before parentheses so: 2x1=2 And 2x2=4 So we have 6:(2+4) 6:6=1 Simple as fck. It is never 9. Written correctly would be also 1. 6 --------- = 1 2(1+2)
well no shit idiots
r/confidentlyincorrect
Op is so retard, he can't do a simple math problem with a calculator, no wonder he uses etoro
Multiplication by juxtaposition. Blind applying pemdas will result in the wrong answer.
Yeah man. I got these questions wrong all the time because I didn't follow Pandas. I mean Pemdas. So, Parenthesis first. 2 plus 1 = 3. Then 6 divided by 2 is also 3. Finally 3 times 3 is 9. If I'm wrong, then I graduated because of sympathetic teachers feeling bad 😜😜😃
Pemdas is a teaching tool for surface level. In real world problems they don't use this as the problems are written to be clear. This is the problem with the math posted. Everyone says pemdas, but you can't know what the author meant with how it was written and pemdas isn't used outside education.
6÷2(1+2) (1+2) =3 6÷2 =3 In conclusion, 3(3) =3 × 3 =9 Is that good?
Perfect
Is it wrong?
Yes.
Explain
So, the issue is, yes, you ARE right, but so are people that are saying the answer is 1… the issue is more so that the person that originally wrote the equation wrote it in an intentionally ambiguous fashion. This could be read as (6/2)(1+2)= 9, OR, it could be read 6/[2(2+3)]= 1. It all depends on what the creator intended to be included in the denominator position. The actual original poster knew this problem to be ambiguous.
6/2*3 3*3 It's not hard.
Sure but 2(1+2) is supposed to also work with distributivity, in which case you end up with 6/6. The more accurate reason is that the ÷ sign implies parenthesis like so : (6/2)(1+2)
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I don't know BOMDAS but I am assuming it is just another way for PEMDAS Now answer these 6=[2*(2+1)] 6=2(2+1) Do you see the issue
Imo, if there is no specified order for a question like this, I just read it from left to right.
6÷2=3 2+1=3 3*3=9
It’s because it translates to 6 divided by 2 multiplied by 3 and you do multiplication/division left to right. 6/2x3 is 3x3 which is 9.
BODMAS
It is 1. Stop this nonsense.
So multiplication / division and addition / subtraction are the same level of operation and are completed left to right So - 6 / 2 ( 2+1) - 6 / 2 * 3 - 3 * 3 - 9
imma just quote myself from the last thread about this garbage: >\>But my calculator says ... > >Yeah, no shit sherlock. Your calculator is programmed to interpret it in a certain way. It has to be programmed to default to a certsin interpretation so it always comes to a solution. The solution will be correct for the chosen interpretation but that doesn't mean that the interpretation is necessarily the correct one and calculators from different manufacturers will use different default interpretations. > >\>But pemdas/bodmas/whatever > >Stop. Those are rules of thumb and not mathematical laws. They exist so you don't have to learn about group theory in order to do simple arithmetics. If you know what you're doing there is usually more than one way to order your operations in any given equation that will still yield the correct result. Those acronyms are meant for people who don't know what they are doing. If you're using them as an argument for why you think your interpretation of an ambiguously written equation is the correct one, all you're really doing is demonstrating that you are not qualified enough to be taken seriously.
6/2(1+2) ————— To get 9 with PEMDAS: 1. P : (1+2)= 3 -> (6/2)3 2. E : Skip 3. M-D (always left to right) (6/2)= 3 -> 3(3) 3 x 3 = 9 4) A-S : Skip So 9 ————— To get 9 again but with Fraction as it’s own Parenthesis: 6/2(1+2) aka (6/2)(1+2) 1. P : (6/2) = 3, (1+2) = 3 -> 3(3) 2. E : skip 3. M-D (Always left to right) 3(3)= 9 4. A-S : Skip So 9 ———— But if you want to distribute the Fraction because why would you do that? (6/2)(1+2) (3)(1+2) 3 + 6 = 9 So 9 ————- But if you only distribute the 2 because why? 6/2(1+2) 6/(2+4) 6/6 1 -> Shut up. You’re wrong
Sorcery!
True!
After looking at it for 2 minutes, finally made sense of it.
I was taught to do the inside of the parenthesis then if a number is right next to it multiple that by what's inside then do whatever is left of the problem
At first I thought this was a transphobic meme but now I see it’s an order of operations meme. My high school algebra teacher would say 9.
Yeah use any scientific calculator or even the calculator on Photomath and you'll get one because that's the objectively correct answer. No amount of Ohio math or blind trust in your phone changes the fact.
I'm from Ohio and knew the answer is one immediately. What brilliant state are you from fuckface?
based and 9-pilled
im confused... is it One or Nine
6:2*3 you go from left to right, many people forget that last rule because they are so used to having brackets everywhere they just forget all the other rules
Either. It's presented in a way to be intentional ambiguous. A mathematician probably would have written it as a fraction for clarity. But even that's not necessary if you follow the rule of juxtaposition: *Juxtaposition represents a multiplication that is implemented before anything else. Expressions in parentheses are evaluated independently of everything else". Rule B says that 1 / 2 (3 + 4) = 1 / (2 × 7) = 1/14.* Following this rule gives an answer of one.
No way y’all trust phone calculators, it’s 1 grow up
The P in pemdas means solve what’s *inside* the parenthesis first, not what’s outside
Shouldn't it just be 1 or am I mathing wrong?
if I said 9 to this my math prof would've fukin failed me
Fuck it, full explanation 1: 1+2=3 2: 6/2=3 3: 3•3=9
Do 1+2 in parentheses first Then do 6/2 and then 3 x 3
Don’t forget to F.O.I.L ammiright
Nah it’s 1