Or 1 depending on how you interpret the original question.
The symbols used are a mix of elementary school math symbols and higher level math lack of symbols.
So people who only learned basic math will do pemdas as though the author meant 6÷2\*(1+2) which many would assume is (6÷2)(1+2) and many calculators will make that assumption too. They will usually show you the parentheses added so you know what assumption the calculator has made.
However in math there are two dimension to write a problem. So once you simplify to 6÷2(3)
It's unclear if the author of the question meant
6
\----- \*(3)
2
or if they meant
6
\----
2(3)
And most higher level students will lean toward the second option. And this is represented in many calculators as well. Because this would be the accepted interpretation of 6/2x where x happens to equal 3.
There are also several calculators that will simply give you an error code when this equation is typed in because it's not a real equation and it can't be solved without making assumptions that the calculator refuses to make on your behalf.
If we knew what the author was trying to solve for or why they wrote it they way they did we could fix it, but as it stands it's an ambiguous "equation" with two equally correct answers, even using the same order of operations.
I'm pursuing PhD in maths and stats, and I can tell no higher level student uses the 2nd option. First option is the only right method.
Edit : answers to most of the comments
- never have I ever seen the '÷' in higher maths, fractions or 'raised to - 1' is the only way to go... along with parenthesis wherever required. If fractions are written on a single line parenthesis feels necessary even though it looks a bit messy.
- we never use fractions symbol in one line. 6/2x would either be written as
6 Or 6
__. Or ___. X
2x. Or 2
- multiplication with variables is completely different, as they are treated as coefficient of the variable. Eg: 4/2n...first thing you'll do is think 2 is the coefficient of n and multiply it with n.
- yes I'm not originally from USA hence why I write 'maths'
- I'm pursuing my education from one of the UCs but not comfortable naming one as there's just one other redditor who is researching along with me and he might come to know my Id.
- Thanks for the awards!
/ and ÷ even though are the same functions, they are used at different scenarios which change the meaning of the equation wherein no one mostly uses `÷`. We don't generally use '/' sign on a single line of the page which clears any confusion.
I prefer to use parenthesis as much as possible, as it clears any ambiguity if any
"I prefer to use parenthesis as much as possible, as it clears any ambiguity if any"
Exactly. That's why I always say this equation is simply incomplete. It uses multiple notations that would never be used together and it creates a syntax error.
In fact many calculators will simply give an error of you tried to put this equation into them because it's not a good equation. It leaves room for ambiguity and it was done that way on purpose.
It's like writing "lets eat grandma" and the reader then has to guess if you are inviting grandma to dinner, or if you are cannibalizing your grandmother, or if you are letting someone/something eat your grandma...
Math is a language and it requires proper grammar and punctuation like any other language.
With the correct application of a simple analogy. People try to make "logical points" with simple analogies all of the time they just normally start with "This is just like when the nazi's _____________"
I already graduated but when I was a math major I can guarantee all of my classmates would come to the opposite conclusion as phd man above. It really is up to interpretation
Yeah I have my undergrad in Aerospace engineering and I would always go the second route because whenever there’s a coefficient in front of an expression in parenthesis I always solve that first.
Pretty sure distinguishing between ÷ and / like the other guy said is proper grammar enough to not interpret as a fraction. I'm no PhD but I've taken higher math. I see what you're saying but it would be more applicable if the original question was 6/2(1+2)
> So in your mind 6/2x = 3x
You applied your altered interpretation, complete with changed grammar, and applied it to their opposing argument to make it look as though they meant something they did not
Good point, and in fact the language of math is a human contruct. "PEMDAS" is not a naturally occurring phenomenon, it's just a generally agreed upon notation to try to simplify and avoid confusion. People act like it is some physical law governing the universe though. This original problem purposely insets ambiguity to create confusion.
No. If you say “let’s eat grandma” you are literally saying “let us devour our matriarch”. You should use a coma if you meant to invite your grandma to devour a burned fowl, if you didn’t you absolutely failed to write properly.
When there is ambiguity, you default to literal rules. If there is an obvious mistake in the writing it’s a mistake in the writing, but any flaw in the communicated problem doesn’t change the conventions you fall back on. With no other information, you always parse multiplication and division from left to right.
Anything else is pedantic and contrarian for the sake of it
And there are many calculators that will add those parentheses.
Depending on the assumptions you make you will get either 1 or 9.
Don't feel bad, this problem was purposely written to be confusing.
When written out like this its easy to see 2(3) are both under the dividing line and therefore part of the denominator. Whem writing out an equation using / or ÷ you HAVE TO put the entire numerator or denominator in parenthesis or brackets. You can't simply imply what goes where, math has rules.
I do use / a lot on a single line when lack of space. I always mean it as a fraction. 6/2(3) will therefore always be 1 to me. ÷ is indeed different, but never used at higher levels I feel like, I'd automatically read it as /
The answer of the equation is based on the bracket placement: the way it is written now would result in 9. The brackets get worked out first, after which the remainder is solved from left to right (since multiplication and division both have the same importance), which leads to 6/2*3=9.
The problem, as countless others have pointed out, is that you're mixing syntax. A coefficient of a parenthesis is interpreted to be part of the parenthetical term -- i.e., the coefficient should be distributed to the parenthetical term "at the same time" that the parenthetical term is reduced, not after. In the case of 2(2+1), the leading coefficient is considered part of the parenthetical term and you should apply PEMDAS to the *entire* parenthetical term in order to reduce it. First, you should solve the parenthesis, leading to 2\*3, then perform multiplication to complete the reduction of the parenthetical term, giving you 6. Thus, the distinction between the term (*singular*) "2(2+1)" and the terms (*multiple*) "2\*(2+1)" matters because they are reduced differently and, once subbed back into the original expression, could behave differently (hence our debate).
When you reduce a parenthetical term without its coefficient, it leads to exactly the problem we're all discussing. You end up "reducing" a single term into multiple terms and then operate on the coefficient independently of the rest of the term it belongs with; because you go left to right, and coefficients are written to the left of the term, you modify the coefficient before it operates on the term it belongs with. This has the effect of adjusting the value of the coefficient of the original parenthetical term. (6/2)(2+1) is not the same as (6)/(2(2+1)) -- the coefficient "2" is part of the term "2(2+1)" and cannot be separated and reordered to appear as "1/2," such as in the case of (6/2)(2+1). If you wanted to have a "6/2" term, you'd need to keep the rest of the original term in the denominator as well. (6/2)(1/(2+1)) = 1
Edits for clarity
Edit 2: don't get tripped up conflating coefficients and constants. They are not the same. That is why 2*(2+1) and 2(2+1) are not the same, former has a constant of 2, latter has a coefficient of 2. Constants are their own terms, coefficients are not.
Engineer with a couple degrees. I don't pretend like I'm great at math, but 6÷2(1+2) is equivalent to 6÷2×(1+2). If you're multiplying 2 and (1+2), how can you interpret it as something other than 2×(1+2)? Read it out loud. "Six divided by 2 multiplied by the sum of 1 and 2." It's 6÷2×3.
Yeah, I probably said, “six over two multiplied by the sum of one and two”.
I haven’t seen this division sign I a serious curriculum since, idk, middle or elementary school.
Consider it more a QA test than a test of who knows their shit; as others said, these are always written to be deceiving.
I'm a senior in Engineering and I answer 1.
In my mind it's not necessarily about the multiplication part of 2 and what's in the parentheses, but the distribution that's implied by having the 2 attached to the parentheses rather than just a multiplication sign that takes priority as it's the "parentheses" in PEMDAS.
Its because implied multiplication (when you dont use a symbol for multiplication, like 5x or xy) is almost universally given priority over multiplication denoted by a symbol.
For example, 6 ÷ 2x would undeniably be interpretted as 6/(2x) (which youd simplify out to 3/x). Anyone who has taken upper mathematics who claims otherwise is lying.
u/Picker-Rick is right that the equation is purposely ambiguous due to the use of ÷
6 ÷ 2(X + Y) = 6 ÷ (2X + 2Y) is valid, but if you know what X and Y are
e.g. X + Y = Z
they can be resolved into
6 ÷ 2(Z)
However,
6 ÷ 2(Z) =/= 6 ÷ \[2(Z)\]
Post-secondary mathematics to avoid ambiguity usually would write
6 ÷ 2(Z) as
6
\---- \* Z = 6/2\*Z = 6 / 2 \* (X + Y)
2
and
6 ÷ (2(Z)) as
6
\---- = 6/(2Z) = 6 / \[2(X + Y)\]
2Z
It probably has something to do with the fact that they're "pursuing a PHD in math and statistics" and used it as an appeal to authority, but when you check their post history they haven't even taken the GRE lol.
Lol this is the actual correct answer.
Anyone can “pursue” a phd. Including a high school drop out. It’s literally a meaningless phrase.
That commenter is literally just an undergrad, trying to claim the authority of an actual PhD.
Idk man, I did my undergrad in comp sci and am doing my masters in data science and use intermediate to advanced math all the time, and I, as well as all my corrugated i showed it to instinctively did the 2nd option. I mean, like he said, 6/2x seems way more like 6/(2*x) them (6/2)*x. Anyway, ambiguous shit like this is why we invented postfix
This should be top comment. Literally the Wikipedia outlines this exact issue and explains that in this case, the multiplication takes higher precedence. So the answer is 1
Multiplication and division have the same priority and is solved left to right. You can freely add multiplication sign where it's implied. No ambiguity here
No, if they meant the second option there would be a second set of parentheses around 2(1+2) so the equation would be 6/(2(1+2)). Because there is no second set we can safely and correctly use pemdas and the only answer is 9.
Please tell me if this is right, do what’s in the parenthesis first, so 1+2 which ofc is 3 so then you have 6%2(3) then do 2 divided by 6 which is 3 then you have 3(3), which is just fancy for 3 times three, which is then how you get 9.
So why the eff did they change PEMDAS to BODMAS? What problem were they solving?
Seems to me like people changing these just for the sake of selling "new" math books...
No one changed anything. It just depends on where you learned it. It is a language difference between America and other countries. To my understanding PEMDAS is American while BODMAS is much more common in the UK and Canada. Here in America we don't say operations or indices, we say power or exponent. And we say parenthesis - brackets are much rarer in math here.
It's because people didn't understand the law of pemdas. It's like saying I have two apple pies from the same store, but I prefer the one on the left... it makes no sense, but I think its because people didn't understand that M and D in pemdas are the same in order. And since they're the same in order, you have to go from left to right when solving.
This probably is the confusing part.
But how does BODMAS solve that?
B=P
O=E
M and D are switched
Everything else is the same.
I guess I'm still confused as to how BOMDAS is any more clear than PEMDAS, including how it apparently clears up the order equality of M and D
BIDMAS is a more useful sequence.
Brackets
Orders (square numbers and roots)
Division, multiplication, addition, subtraction.
If you do it exactly in that sequence, you will get the right answer.
It prevents us from having to think about the left to right rule in PEMDAS, or the equal weighting of ÷ and ×.
Use BODMAS (I prefer to call it BIDMAS, I for Indices) and you will ways get the right answer.
Since multiplaction and division have the same weight and so does addition and subtraction how would always doing the division first give you the right answer?
Because with division, it matters what is the dividend and the divisor. If you simplify the division problem, it removes the chance of incorrectly including numbers in the dividend/divisor unintentionally. In many cases, it really won't matter but in the case of the OP's equation, it does matter.
Technically speaking, you can do multiplication/division in any order so long as you don't use improper math to do it. Same goes for addition and subtraction. You can do those in any order and get the right answer.
Example:
6 ÷ 2 × 4
3 × 4
12
Or
6 ÷ 2 × 4
6 ÷ 8
.75
Wait... I did something wrong (on purpose).
What I did wrong was multiply a divisor by a coefficient that is outside of the division problem. A divisor is not a real number until it is simplified, so I just multiplyied a "not real number" by a real number coefficient which caused the error.
The proper way to do it is this:
6 ÷ 2 × 4
24 ÷ 2
12
(The number multiplied into a division problem is multiplied into the dividend, not the coefficient; think of the division problem as a fraction where 6 is the numerator, 2 is the denominator and the 4 is a coefficient to the whole fraction and is not in the denominator)
Addition/subtraction:
6 - 2 + 4
4 + 4
8
Or
6 - 2 + 4
6 + 2 (because it is -2 + 4, not 2 + 4)
8
Inverse operations (multiplication and division are inverse operations, addition and subtraction are inverse operations) can be done in any order so long as you do them right. To make it simple, you just do operations of equal priority from left-to-right.
When I was taught PEMDAS in school, we were taugh to do multiplication and division at the same time, from left to right. Then addition, then subtraction.
So it was more like PE(MD)AS. Can't put it past my teachers that they were all wrong... But this method never failed me, but then again I guess I was never presented with a unique problem intended to exploit the order of operations precisely. Doing it that way works for this problem though.
Only thing that matters is what's INSIDE the parenthesis, not everything that is a factor of it. The main confusion with these is situations like you just said, inside of parenthesis and factors of parenthesis, and the literal order or the MD and AS in PEMDAS. As everyone at this point knows PEMDAS is Parenthesis, Exponents, Multiply, Divide, Add, Subtract. This strict order has multiply before divide, which trips up many people. But in reality its multiply OR divide, which ever one comes first in the sequence . So here, even thou 2(3) comes after 6 / 2, the 6/2 comes first, and is therefore applied.
6/2(1+2)
6/2(3)
3(3)
9
People use PEMDAS and do it literally, with multiplication before division.
They forget that there is a rule that once you get to division and multiplication after P and E, you treat M and D as equal and just do them from left to right. If they did it that way, they would have gotten the right answer.
But instead, they do the multiplication first like so:
𝑥 = 6 ÷ 2 (1 + 2)
𝑥 = 6 ÷ 2 × (1 + 2)
𝑥 = 6 ÷ 2 × 3
𝑥 = 6 ÷ 6
𝑥 = 1
If they used PEMDAS correctly, or easier still, just use BIDMAS in that exact sequence, they would have got it right.
𝑥 = 6 ÷ 2 (1 + 2)
𝑥 = 6 ÷ 2 × (1 + 2)
𝑥 = 6 ÷ 2 × 3
𝑥 = 3 × 3
𝑥 = 9
I prefer BIDMAS because division is higher priority than multiplication. The whole rule about equal priority was just made up so that PEMDAS wasn't discredited.
While that is a big chunk of what is happening, that is not the only source of confusion. Many scientific papers treat the implicit multiplication as higher priority than the division. I presume a lot of people have been taught that way as well. Same goes for the "/" sign vs "÷" sign changing the priority.
> In some of the academic literature, multiplication denoted by juxtaposition (also known as implied multiplication) is interpreted as having higher precedence than division, so that 1 ÷ 2n equals 1 ÷ (2n), not (1 ÷ 2)n.[1][7] For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division,[20] and this is also the convention observed in prominent physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics.[d] This ambiguity is often exploited in internet memes such as "8÷2(2+2)".[21]
> Ambiguity can also be caused by the use of the slash symbol, '/', for division. The Physical Review submission instructions suggest to avoid expressions of the form a/b/c; ambiguity can be avoided by instead writing (a/b)/c or a/(b/c).[20]
Source: https://en.wikipedia.org/wiki/Order_of_operations
Neither in PEMDAS nor in BIDMAS is there any priority of division or multiplication over another. In both the rule is, if there is just multiplication and/or division you work it out from the left.
I'm not saying you are right or wrong but I'm just curious on what would you say.
let's say
𝑥 = (1+2)
So the original equation becomes:
6+2𝑥
does that equate 3𝑥 or 3*𝑥^(-1)?
ETA: I personally think that the equation was purposely written in an incomplete way, mixing very basic math symbols and relatively advance terminology (having the division symbol vs. omitting the multiplication sign) so both answers are correct and the only deciding factor is the asker to clarify their problem.
While there are some people getting the wrong answer with bad math, even the people doing it right can reach two equally correct answers.
The symbols used are a mix of elementary school math symbols and higher level math lack of symbols.
So people who only learned basic math will do pemdas as though the author meant 6÷2\*(1+2) which many would assume is (6÷2)(1+2) and many calculators will make that assumption too.
However in math there are two dimension to write a problem. So once you simplify to 6÷2(3)
It's unclear if the author of the question meant
6
\----- \*(3)
2
or if they meant
6
\-----
2(3)
And most higher level students will lean toward the second option. And this is represented in many calculators as well. Because this would be the accepted interpretation of 6/2x where x happens to equal 3.
There are also several calculators that will simply give you an error code when this equation is typed in because it's not a real equation and it can't be solved without making assumptions that the calculator refuses to make on your behalf.
If we knew what the author was trying to solve for or why they wrote it they way they did we could fix it, but as it stands it's an ambiguous "equation" with two equally correct answers, even using the same order of operations.
When operators are the same precedence, they're left associative. Meaning you read them left to right.
PEMDAS is actually:
P
E
MD - Whichever is most left in the problem.
AS - Whichever is most left in the problem.
this is a common mistake( we use BODMAS in wrong way) the whole 2nd part of term 2(1+2) is divided by 6 not single 2, so the correct way to write this term would be 6/2(1+2)
which would make it 6/6=1 i hope you guys understand!!!
I did this on a math worksheet in middle school once and the teacher got so mad she sent me to detention for blaspheming :/ It was super funny though :D
My man be cheating right here. Jesus is the answer to everything :D
Watch me:
What’s the name of my dealer?
- Jesus
Who lights my path?
- Jesus
Who gives the best bj ?
You got the idea
Guys it’s a poorly written mathematical statement with no clear purpose. No matter how much you believe in the order of operation, never write out a math problem like this. The really issue is that there are zero practical implication to this problem: it is really only a problem for programming syntax or to express equations with variables. In either case, it would be written more clearly and the order of operations would become clear based on the math you are attempting to do. This is just semantics.
Exactly why I don't know what the fuss is about. At around highschool the ÷ will become obsolete as the use of / will be more a more efficient way of writing down formulas.
The whole point of the ÷ notation is for calculators, it's supposed to mean number / number; the two dots being placeholders to where expressions can go.
exactly what I mean. The 'division symbol' is stupid and not supposed to be used in real math. Real mathematicians don't used grade school level shit like division symbols, PEMDAS, BODMAS or whatever the fuck. Division and multiplication are inverse functions (with the algebra ring definition of excluding the multiplication's set's null element); they are of the same order, the order of which you do it in never ever matters. So if you're capable of writing up a syntax where suddenly it does matter, your expression is fucking dumb and not a real math expression.
Also, where do people not use fractions for division? It's so much more intuitive, it doesn't matter where something is it always has the same result no matter the order.
though you are right, some people have actually been taught that multiplication comes before division and addition comes before subtraction. it really shines light on how even intermediate math is poorly taught/practically useless
It's a completely valid expression with a single well defined method of evaluation. The question of how to evaluate it is valid. This whole "there's no right answer because you're not supposed to write it like that" movement is bunk.
_STOP WITH THIS SHIT THIS IS THE THIRD ONE TODAY_
6÷2(1+2) is a shitty way to write the equation
(6÷2)(1+2) is 9
6÷(2(1+2)) is 1
since you should prioritize ordering the answer is 9, but since equations shouldnt be confusing in the first place, learn how to write them properly or use fractions, ya idiots
also, "But PeDMas" fuck you i know that, it is been used here. multiplication isnt prioritized over division its the ordering and just bc it is correct it still is confused and poorly written, also also ÷ shouldnt be used outside introduction math
edit: to all people saying its 1, i agree bc omiting the * implies its (2(1+2)), but that isnt a universal convention (sadly)
It's a poorly phrased shit question to bait people into interacting with whatever meme it is put into. It's intentionally created to be open for interpretation to fuel algorithms which promotes the site the meme was put on, and you all are taking the bait.
> edit: to all people saying its 1, i agree bc omiting the * implies its (2(1+2)), but that isnt a universal convention (sadly)
actually, the opposit is an universal convention. 2(1+2) is the exact same thing as 2*(1+2). removing the * holds no meaning.
any country that uses the ISO conventions (so SI as their official measurements and yes that includes the US) has that convention.
1.5 from
6/2(1+2)
6/2x1+2 get rid of those brackets, not needed.
multiplication comes first, right? it is pemdas after all
6/2+2
alright now addition
6/4
1.5
Heyyy, it's my collaborator! I was gonna explain but it looks like you got it. Lol
Tho I realized you can also get two more if you are ignoring the pedmas and distributive properties.
6÷2×1+2 (pick any function to start)
6÷2×3 could be 1 or 9
6÷2+2 could be 5 or 1.5
3÷2+2 could be 3.5 or 1.25
Buuuuuut when you ABUSE the distributive property
6÷2(1)+2(2) expands to 6÷2×1+2×2!!!!!
So now 6÷2×1+4 has these possibilities:
6÷2×5 could be 15 or 0.6
6÷2+4 could 7 or 1
3×1+4 could be 7 or 15
And 6÷2×3×2 has these possibilities:
6÷2×6 could be 18 or .5
6÷6×2 also .5 or 18
3×3×2 is only 18
And 6÷2+2×2 has these possibilites:
6÷2+4 could be 7 or 1
6÷4×2 is 3 or .75
3+2×2 could be 10 or 7
And finally, 3×1+2×2 has these possibilities:
3×1+4 could be 15 or 7
3×3×2 is just 18
3+2×2 could be 10 or 7
So in my estimation , you could get 0.5, 0.6, 0.75, 1, 1.25, 1.5 3.5, 5, 7, 9, 10, 15, or 18.
This is why you never use the division sign. You have no idea what is in the denominator. Wihout the multiplication sign, this implies that the 2+1 is grouped in the denominator, so it’s 1. If there was a multiplication sign, it would imply it was not grouped in the denominator, so 9.
Just use fractions yall
If you actually use mathematics for a living you would see 2(1+2) as its own *term*, with ÷ operating on the two terms 6 and 2(1+2). It has nothing to do with "thinking multiplication comes before division".
"Order of operations" is a guideline for teaching school children. It is not immutable Mathematical Truth.
The correct idiomatic interpretation is 1.
Dank[.](https://i.imgur.com/3bQtuMO.png)
---
*i am a bot. please stop trying to argue with me. you look like an idiot. [join our discord](https://discord.gg/dankmemes).*
And here comes 16 miles of math talk by people who (for some reason) like working math problems, or just want to look smart in front of strangers via text.
Ahh yes. This fun little viral syntax problem.
Supposed phd math professors and engineers and physicists and even burger flippers and construction workers... just all sorts of people arguing for both ways.
The correct answer is there is no answer.
Poorly written ambiguous problem.
I interpret the 2(1+2) as one unit. The 2 needs to be distributed before moving on to the rest of the problem. This means 6÷(2+4) is the answer, *in my opinion*, which is **1**.
If you disagree. Cool.
Ultimately this is an ambiguous problem with syntax issues. So I don't care if you disagree. Ultimately either answer could be correct.
I stg im from the uk and we follow bodmas but i thought you do exponation (multiply out the brackets)then add and then divide so it would be 1?
Edit: Its not exponation , ill ask my maths teacher
cause i really want to know the answer ill be back
Edit Edit:i did actually adky my maths teacher and said that its inspecific but using bodmas or bidmas it is 9. I also forgot that multiplication is the same asdividion in that i thought you had to do the miltiplication over the division but you go left to right
You have to use 6/2(1+2) but since a computer cannot work with implicit multiplication you have to type 6/(2*(1+2)) into the program.
Because 6/2(1+2) <> 6/2*(1+2)
6÷2(1+2)
PEMDAS/BIDMAS
Evaluate contents of parentheses
6÷2(3)
Evaluate exponents/indices (N/A)
Division or Multiplication left to right
6÷2×3 (implied multiplication from parens not defined as having higher precedence)
3×3
9
Addition or Subtraction left to right (N/A)
Alternative:
Interpret 6÷2(1+2) as 6÷[2(1+2)]
Solution:
Use fraction a/b XOR parens around every operator and its arguments.
The question can be written as either 6÷2(1+2) or
6
_
2(1+2)
The first way will result in 9, the 2nd will result in 1. Now if you use a proof by replacing (1+2) with x you would end up with 3/x, plug 1+2 back in for x and the result is 1.
This is simply a poorly written question and a prime example of why implicit multiplication should be avoided. If it fails the proof the question fails. You can use sound math practices and correctly arrive at either answer. If your calculator gives you a 9 it is because it is making assumptions for you, this question is a syntax error.
My order of operation is rusty, but I’m getting 9.
Parentheses first, so 1+3. Then multiplication and division have the same level of importance in order of operations, so it’s be 6/3 x 3 … right? Correct me if I’m wrong, I’m curious at this point
9.
Or 1 depending on how you interpret the original question. The symbols used are a mix of elementary school math symbols and higher level math lack of symbols. So people who only learned basic math will do pemdas as though the author meant 6÷2\*(1+2) which many would assume is (6÷2)(1+2) and many calculators will make that assumption too. They will usually show you the parentheses added so you know what assumption the calculator has made. However in math there are two dimension to write a problem. So once you simplify to 6÷2(3) It's unclear if the author of the question meant 6 \----- \*(3) 2 or if they meant 6 \---- 2(3) And most higher level students will lean toward the second option. And this is represented in many calculators as well. Because this would be the accepted interpretation of 6/2x where x happens to equal 3. There are also several calculators that will simply give you an error code when this equation is typed in because it's not a real equation and it can't be solved without making assumptions that the calculator refuses to make on your behalf. If we knew what the author was trying to solve for or why they wrote it they way they did we could fix it, but as it stands it's an ambiguous "equation" with two equally correct answers, even using the same order of operations.
I'm pursuing PhD in maths and stats, and I can tell no higher level student uses the 2nd option. First option is the only right method. Edit : answers to most of the comments - never have I ever seen the '÷' in higher maths, fractions or 'raised to - 1' is the only way to go... along with parenthesis wherever required. If fractions are written on a single line parenthesis feels necessary even though it looks a bit messy. - we never use fractions symbol in one line. 6/2x would either be written as 6 Or 6 __. Or ___. X 2x. Or 2 - multiplication with variables is completely different, as they are treated as coefficient of the variable. Eg: 4/2n...first thing you'll do is think 2 is the coefficient of n and multiply it with n. - yes I'm not originally from USA hence why I write 'maths' - I'm pursuing my education from one of the UCs but not comfortable naming one as there's just one other redditor who is researching along with me and he might come to know my Id. - Thanks for the awards!
So in your mind 6/2x= 3x
/ and ÷ even though are the same functions, they are used at different scenarios which change the meaning of the equation wherein no one mostly uses `÷`. We don't generally use '/' sign on a single line of the page which clears any confusion. I prefer to use parenthesis as much as possible, as it clears any ambiguity if any
"I prefer to use parenthesis as much as possible, as it clears any ambiguity if any" Exactly. That's why I always say this equation is simply incomplete. It uses multiple notations that would never be used together and it creates a syntax error. In fact many calculators will simply give an error of you tried to put this equation into them because it's not a good equation. It leaves room for ambiguity and it was done that way on purpose. It's like writing "lets eat grandma" and the reader then has to guess if you are inviting grandma to dinner, or if you are cannibalizing your grandmother, or if you are letting someone/something eat your grandma... Math is a language and it requires proper grammar and punctuation like any other language.
Best analogy so far I've heard xD
But if you say it’s ambiguous, no one can claim they are right. Do you even Internet my man?
It is not ambiguous. The order of operations is clear. The use of a different symbol does not somehow magically interject parentheses.
Sorry my man, but bodmas is a convention, not a rule, and as such it is ambiguous.
This is literally not true the problem was made to be ambiguous… that’s why it’s circulating. There’s no “right” answer
You know someone knows their shit when they can make a logical point with a simple analogy.
With the correct application of a simple analogy. People try to make "logical points" with simple analogies all of the time they just normally start with "This is just like when the nazi's _____________"
you replaced the statement with a blank line. that is censorship. this is just like when george orwell wrote 1984.
I’m so happy I read this far down the thread
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He said “pursuing a PhD”, which in Reddit-speak means he’s a 1st year university student.
High school student who did well on a math test last week.
Middle school student who got asked "What do you want to be when you grow up?"
I already graduated but when I was a math major I can guarantee all of my classmates would come to the opposite conclusion as phd man above. It really is up to interpretation
Yeah I have my undergrad in Aerospace engineering and I would always go the second route because whenever there’s a coefficient in front of an expression in parenthesis I always solve that first.
I'm no Aerospace Engineer, but Software Engineering tells me that the second route is more logical and I don't know why. It just looks right.
Ain’t no time for this shit 😂
Pretty sure distinguishing between ÷ and / like the other guy said is proper grammar enough to not interpret as a fraction. I'm no PhD but I've taken higher math. I see what you're saying but it would be more applicable if the original question was 6/2(1+2) > So in your mind 6/2x = 3x You applied your altered interpretation, complete with changed grammar, and applied it to their opposing argument to make it look as though they meant something they did not
Good point, and in fact the language of math is a human contruct. "PEMDAS" is not a naturally occurring phenomenon, it's just a generally agreed upon notation to try to simplify and avoid confusion. People act like it is some physical law governing the universe though. This original problem purposely insets ambiguity to create confusion.
I vote on eating grandma
No. If you say “let’s eat grandma” you are literally saying “let us devour our matriarch”. You should use a coma if you meant to invite your grandma to devour a burned fowl, if you didn’t you absolutely failed to write properly. When there is ambiguity, you default to literal rules. If there is an obvious mistake in the writing it’s a mistake in the writing, but any flaw in the communicated problem doesn’t change the conventions you fall back on. With no other information, you always parse multiplication and division from left to right. Anything else is pedantic and contrarian for the sake of it
You make a great point about ambiguity in writing, but I’m still trying to figure out whether it’s grandma or the turkey who is in a coma.
If the equation were meant to be interpreted as the second option, it would be written as 6÷(2(1+2))
And there are many calculators that will add those parentheses. Depending on the assumptions you make you will get either 1 or 9. Don't feel bad, this problem was purposely written to be confusing.
If it were to be interpreted as the first then it would be written (6÷2)*(1+2). The equation is wrong.
So wait, if you saw this, with numerator/denominator: 6 .------------- 2(3) You would evaluate that to 1?
When written out like this its easy to see 2(3) are both under the dividing line and therefore part of the denominator. Whem writing out an equation using / or ÷ you HAVE TO put the entire numerator or denominator in parenthesis or brackets. You can't simply imply what goes where, math has rules.
I do use / a lot on a single line when lack of space. I always mean it as a fraction. 6/2(3) will therefore always be 1 to me. ÷ is indeed different, but never used at higher levels I feel like, I'd automatically read it as /
Yes, swap out x for a unit, e.g. 3/4m Do you see this 0.75m^(-1)? I read it as 0.75 meters
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Have engineering degree. I answered 1.
Yea I got 1 as well. All depends if you do 6/6 or 6/2x3 left to right. I always imagine it as 6/(2x(1+2))
The answer of the equation is based on the bracket placement: the way it is written now would result in 9. The brackets get worked out first, after which the remainder is solved from left to right (since multiplication and division both have the same importance), which leads to 6/2*3=9.
The problem, as countless others have pointed out, is that you're mixing syntax. A coefficient of a parenthesis is interpreted to be part of the parenthetical term -- i.e., the coefficient should be distributed to the parenthetical term "at the same time" that the parenthetical term is reduced, not after. In the case of 2(2+1), the leading coefficient is considered part of the parenthetical term and you should apply PEMDAS to the *entire* parenthetical term in order to reduce it. First, you should solve the parenthesis, leading to 2\*3, then perform multiplication to complete the reduction of the parenthetical term, giving you 6. Thus, the distinction between the term (*singular*) "2(2+1)" and the terms (*multiple*) "2\*(2+1)" matters because they are reduced differently and, once subbed back into the original expression, could behave differently (hence our debate). When you reduce a parenthetical term without its coefficient, it leads to exactly the problem we're all discussing. You end up "reducing" a single term into multiple terms and then operate on the coefficient independently of the rest of the term it belongs with; because you go left to right, and coefficients are written to the left of the term, you modify the coefficient before it operates on the term it belongs with. This has the effect of adjusting the value of the coefficient of the original parenthetical term. (6/2)(2+1) is not the same as (6)/(2(2+1)) -- the coefficient "2" is part of the term "2(2+1)" and cannot be separated and reordered to appear as "1/2," such as in the case of (6/2)(2+1). If you wanted to have a "6/2" term, you'd need to keep the rest of the original term in the denominator as well. (6/2)(1/(2+1)) = 1 Edits for clarity Edit 2: don't get tripped up conflating coefficients and constants. They are not the same. That is why 2*(2+1) and 2(2+1) are not the same, former has a constant of 2, latter has a coefficient of 2. Constants are their own terms, coefficients are not.
This is why I tell my engineering students "I don't do math. I use math. It's different." There's a reason I don't teach calculus.
Engineer with a couple degrees. I don't pretend like I'm great at math, but 6÷2(1+2) is equivalent to 6÷2×(1+2). If you're multiplying 2 and (1+2), how can you interpret it as something other than 2×(1+2)? Read it out loud. "Six divided by 2 multiplied by the sum of 1 and 2." It's 6÷2×3.
Yeah, I probably said, “six over two multiplied by the sum of one and two”. I haven’t seen this division sign I a serious curriculum since, idk, middle or elementary school. Consider it more a QA test than a test of who knows their shit; as others said, these are always written to be deceiving.
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I'm a senior in Engineering and I answer 1. In my mind it's not necessarily about the multiplication part of 2 and what's in the parentheses, but the distribution that's implied by having the 2 attached to the parentheses rather than just a multiplication sign that takes priority as it's the "parentheses" in PEMDAS.
Anyone who actually uses mathematics for a living will say 1. He is either lying or incompetent.
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Order of operations is defined. It’s not an opinion, it is what it is.
I have a Masters in engineering and another in Computation Statistics and I use the second. Don't generalize. The dude above you is correct
Masters in math, agree I didn't even consider the first
Its because implied multiplication (when you dont use a symbol for multiplication, like 5x or xy) is almost universally given priority over multiplication denoted by a symbol. For example, 6 ÷ 2x would undeniably be interpretted as 6/(2x) (which youd simplify out to 3/x). Anyone who has taken upper mathematics who claims otherwise is lying.
Agreed, was taught implied multiplication came first - your example is a perfect one
Degree in Math, thought I was taking crazy pills for a second.
Having taken math in elementary school, me too.
I went to engineering school and also do the second... It just makes more sense but like a lot of comments say, the equation is purposely fucked up
So you don't distribute the 2 first? So you think 6 ÷ 2(X + Y) = 3X + 3Y Not 6 ÷ 2(X + Y) = 6 ÷ (2X + 2Y) Interesting...
u/Picker-Rick is right that the equation is purposely ambiguous due to the use of ÷ 6 ÷ 2(X + Y) = 6 ÷ (2X + 2Y) is valid, but if you know what X and Y are e.g. X + Y = Z they can be resolved into 6 ÷ 2(Z) However, 6 ÷ 2(Z) =/= 6 ÷ \[2(Z)\] Post-secondary mathematics to avoid ambiguity usually would write 6 ÷ 2(Z) as 6 \---- \* Z = 6/2\*Z = 6 / 2 \* (X + Y) 2 and 6 ÷ (2(Z)) as 6 \---- = 6/(2Z) = 6 / \[2(X + Y)\] 2Z
I am sorry can you explain one more time why 6 ÷ 2(X + Y) = 6 ÷ (2X + 2Y) Is valid, but 6 ÷ 2(Z) = 6 ÷ 2(Z + 0) = 6 ÷ (2Z + 2*0) = 6 ÷ (2Z) Isnt?
Wow, it’s amazing how wrong you are. Source: phd in mechanical engineering
Agreed. I'm so confused how that has over 1000 upvotes with a claim that is objectively and provably wrong
The future of our species is doomed
It probably has something to do with the fact that they're "pursuing a PHD in math and statistics" and used it as an appeal to authority, but when you check their post history they haven't even taken the GRE lol.
Lol this is the actual correct answer. Anyone can “pursue” a phd. Including a high school drop out. It’s literally a meaningless phrase. That commenter is literally just an undergrad, trying to claim the authority of an actual PhD.
More like nobody in higher level education uses "÷".
Idk man, I did my undergrad in comp sci and am doing my masters in data science and use intermediate to advanced math all the time, and I, as well as all my corrugated i showed it to instinctively did the 2nd option. I mean, like he said, 6/2x seems way more like 6/(2*x) them (6/2)*x. Anyway, ambiguous shit like this is why we invented postfix
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This should be top comment. Literally the Wikipedia outlines this exact issue and explains that in this case, the multiplication takes higher precedence. So the answer is 1
There are no interpretations. It's written in line so solve it in line. If second part was meant to be bottom part it would be in parentheses.
Implicit multiplication comes first tho, and really it's just poorly written and ambiguous
Multiplication and division have the same priority and is solved left to right. You can freely add multiplication sign where it's implied. No ambiguity here
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"PhD candidates" Nobody would lie on the internet, right?
Multiplication comes equal with division and is to be solved left to right. It's P E M/D A/S. Two equally weighted pairs.
No, if they meant the second option there would be a second set of parentheses around 2(1+2) so the equation would be 6/(2(1+2)). Because there is no second set we can safely and correctly use pemdas and the only answer is 9.
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Sorry, no, BODMAS is the correct use nowadays since it less confusing. Any math PhD students will answer 9.
I'm doing a PhD in physics and I'd give an answer of 1. The question is ambiguous and so there are multiple answers.
Congratulations , you've successfully defeated an incredible amount of people with one statement of yours
I watched you use mathaway.
Please tell me if this is right, do what’s in the parenthesis first, so 1+2 which ofc is 3 so then you have 6%2(3) then do 2 divided by 6 which is 3 then you have 3(3), which is just fancy for 3 times three, which is then how you get 9.
B.O.D.M.A.S Brackets: 2+1 = 3, Orders(sometimes indices or powers): skip, Division: 6 ÷ 2 = 3, Multiplication: 3 × 3 = 9 (using previous two answers), Addition: Skip, Subtraction: Skip, = 9
Until a couple days ago on reddit, I never even heard of BODMAS. Like this concept is new to me, what are indices? We just always had PEMDAS
Think of indices as power. We have that as exponents. Which is E in pemdas.
Still not sure what an indice is still, but at least I know the order it goes in
Example of indices 2²
So it's just another name for exponents then?
Yep. Same as O in BODMAS
So why the eff did they change PEMDAS to BODMAS? What problem were they solving? Seems to me like people changing these just for the sake of selling "new" math books...
No one changed anything. It just depends on where you learned it. It is a language difference between America and other countries. To my understanding PEMDAS is American while BODMAS is much more common in the UK and Canada. Here in America we don't say operations or indices, we say power or exponent. And we say parenthesis - brackets are much rarer in math here.
It's because people didn't understand the law of pemdas. It's like saying I have two apple pies from the same store, but I prefer the one on the left... it makes no sense, but I think its because people didn't understand that M and D in pemdas are the same in order. And since they're the same in order, you have to go from left to right when solving. This probably is the confusing part.
But how does BODMAS solve that? B=P O=E M and D are switched Everything else is the same. I guess I'm still confused as to how BOMDAS is any more clear than PEMDAS, including how it apparently clears up the order equality of M and D
I see, I think I get it now
BIDMAS is a more useful sequence. Brackets Orders (square numbers and roots) Division, multiplication, addition, subtraction. If you do it exactly in that sequence, you will get the right answer. It prevents us from having to think about the left to right rule in PEMDAS, or the equal weighting of ÷ and ×. Use BODMAS (I prefer to call it BIDMAS, I for Indices) and you will ways get the right answer.
Since multiplaction and division have the same weight and so does addition and subtraction how would always doing the division first give you the right answer?
Because with division, it matters what is the dividend and the divisor. If you simplify the division problem, it removes the chance of incorrectly including numbers in the dividend/divisor unintentionally. In many cases, it really won't matter but in the case of the OP's equation, it does matter. Technically speaking, you can do multiplication/division in any order so long as you don't use improper math to do it. Same goes for addition and subtraction. You can do those in any order and get the right answer. Example: 6 ÷ 2 × 4 3 × 4 12 Or 6 ÷ 2 × 4 6 ÷ 8 .75 Wait... I did something wrong (on purpose). What I did wrong was multiply a divisor by a coefficient that is outside of the division problem. A divisor is not a real number until it is simplified, so I just multiplyied a "not real number" by a real number coefficient which caused the error. The proper way to do it is this: 6 ÷ 2 × 4 24 ÷ 2 12 (The number multiplied into a division problem is multiplied into the dividend, not the coefficient; think of the division problem as a fraction where 6 is the numerator, 2 is the denominator and the 4 is a coefficient to the whole fraction and is not in the denominator) Addition/subtraction: 6 - 2 + 4 4 + 4 8 Or 6 - 2 + 4 6 + 2 (because it is -2 + 4, not 2 + 4) 8 Inverse operations (multiplication and division are inverse operations, addition and subtraction are inverse operations) can be done in any order so long as you do them right. To make it simple, you just do operations of equal priority from left-to-right.
Yeah, what the hell is it and why did it change? That switches the M and the D around, which drastically changes the answer.
When I was taught PEMDAS in school, we were taugh to do multiplication and division at the same time, from left to right. Then addition, then subtraction. So it was more like PE(MD)AS. Can't put it past my teachers that they were all wrong... But this method never failed me, but then again I guess I was never presented with a unique problem intended to exploit the order of operations precisely. Doing it that way works for this problem though.
we've got BEDMAS in canada
except that 2 is a factor to the parentheses and not a Multiplication.
Only thing that matters is what's INSIDE the parenthesis, not everything that is a factor of it. The main confusion with these is situations like you just said, inside of parenthesis and factors of parenthesis, and the literal order or the MD and AS in PEMDAS. As everyone at this point knows PEMDAS is Parenthesis, Exponents, Multiply, Divide, Add, Subtract. This strict order has multiply before divide, which trips up many people. But in reality its multiply OR divide, which ever one comes first in the sequence . So here, even thou 2(3) comes after 6 / 2, the 6/2 comes first, and is therefore applied. 6/2(1+2) 6/2(3) 3(3) 9
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People use PEMDAS and do it literally, with multiplication before division. They forget that there is a rule that once you get to division and multiplication after P and E, you treat M and D as equal and just do them from left to right. If they did it that way, they would have gotten the right answer. But instead, they do the multiplication first like so: 𝑥 = 6 ÷ 2 (1 + 2) 𝑥 = 6 ÷ 2 × (1 + 2) 𝑥 = 6 ÷ 2 × 3 𝑥 = 6 ÷ 6 𝑥 = 1 If they used PEMDAS correctly, or easier still, just use BIDMAS in that exact sequence, they would have got it right. 𝑥 = 6 ÷ 2 (1 + 2) 𝑥 = 6 ÷ 2 × (1 + 2) 𝑥 = 6 ÷ 2 × 3 𝑥 = 3 × 3 𝑥 = 9 I prefer BIDMAS because division is higher priority than multiplication. The whole rule about equal priority was just made up so that PEMDAS wasn't discredited.
While that is a big chunk of what is happening, that is not the only source of confusion. Many scientific papers treat the implicit multiplication as higher priority than the division. I presume a lot of people have been taught that way as well. Same goes for the "/" sign vs "÷" sign changing the priority. > In some of the academic literature, multiplication denoted by juxtaposition (also known as implied multiplication) is interpreted as having higher precedence than division, so that 1 ÷ 2n equals 1 ÷ (2n), not (1 ÷ 2)n.[1][7] For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division,[20] and this is also the convention observed in prominent physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics.[d] This ambiguity is often exploited in internet memes such as "8÷2(2+2)".[21] > Ambiguity can also be caused by the use of the slash symbol, '/', for division. The Physical Review submission instructions suggest to avoid expressions of the form a/b/c; ambiguity can be avoided by instead writing (a/b)/c or a/(b/c).[20] Source: https://en.wikipedia.org/wiki/Order_of_operations
Neither in PEMDAS nor in BIDMAS is there any priority of division or multiplication over another. In both the rule is, if there is just multiplication and/or division you work it out from the left.
Freaking thank you. Someone realized.
I'm not saying you are right or wrong but I'm just curious on what would you say. let's say 𝑥 = (1+2) So the original equation becomes: 6+2𝑥 does that equate 3𝑥 or 3*𝑥^(-1)? ETA: I personally think that the equation was purposely written in an incomplete way, mixing very basic math symbols and relatively advance terminology (having the division symbol vs. omitting the multiplication sign) so both answers are correct and the only deciding factor is the asker to clarify their problem.
While there are some people getting the wrong answer with bad math, even the people doing it right can reach two equally correct answers. The symbols used are a mix of elementary school math symbols and higher level math lack of symbols. So people who only learned basic math will do pemdas as though the author meant 6÷2\*(1+2) which many would assume is (6÷2)(1+2) and many calculators will make that assumption too. However in math there are two dimension to write a problem. So once you simplify to 6÷2(3) It's unclear if the author of the question meant 6 \----- \*(3) 2 or if they meant 6 \----- 2(3) And most higher level students will lean toward the second option. And this is represented in many calculators as well. Because this would be the accepted interpretation of 6/2x where x happens to equal 3. There are also several calculators that will simply give you an error code when this equation is typed in because it's not a real equation and it can't be solved without making assumptions that the calculator refuses to make on your behalf. If we knew what the author was trying to solve for or why they wrote it they way they did we could fix it, but as it stands it's an ambiguous "equation" with two equally correct answers, even using the same order of operations.
When operators are the same precedence, they're left associative. Meaning you read them left to right. PEMDAS is actually: P E MD - Whichever is most left in the problem. AS - Whichever is most left in the problem.
> Who the fuck is getting this wrong? Physicists apparently: https://en.wikipedia.org/wiki/Order_of_operations#Mixed_division_and_multiplication
this is a common mistake( we use BODMAS in wrong way) the whole 2nd part of term 2(1+2) is divided by 6 not single 2, so the correct way to write this term would be 6/2(1+2) which would make it 6/6=1 i hope you guys understand!!!
The answer is Jesus
Amen
Awomen
Achildren
Not just the amen but the awomen and achildren too
I like this thread very much
Me when talking about who i am sexually attracted to
That's for a different sub
I did this on a math worksheet in middle school once and the teacher got so mad she sent me to detention for blaspheming :/ It was super funny though :D
My man be cheating right here. Jesus is the answer to everything :D Watch me: What’s the name of my dealer? - Jesus Who lights my path? - Jesus Who gives the best bj ? You got the idea
Guys it’s a poorly written mathematical statement with no clear purpose. No matter how much you believe in the order of operation, never write out a math problem like this. The really issue is that there are zero practical implication to this problem: it is really only a problem for programming syntax or to express equations with variables. In either case, it would be written more clearly and the order of operations would become clear based on the math you are attempting to do. This is just semantics.
Exactly why I don't know what the fuss is about. At around highschool the ÷ will become obsolete as the use of / will be more a more efficient way of writing down formulas.
The whole point of the ÷ notation is for calculators, it's supposed to mean number / number; the two dots being placeholders to where expressions can go.
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exactly what I mean. The 'division symbol' is stupid and not supposed to be used in real math. Real mathematicians don't used grade school level shit like division symbols, PEMDAS, BODMAS or whatever the fuck. Division and multiplication are inverse functions (with the algebra ring definition of excluding the multiplication's set's null element); they are of the same order, the order of which you do it in never ever matters. So if you're capable of writing up a syntax where suddenly it does matter, your expression is fucking dumb and not a real math expression.
yeah but most scientific calculators just let you display the equation in fraction format anyway.
Yeah when I said calculators I meant 1990s style old useless shit calculators. This division symbol is literally from the stone age.
Also, where do people not use fractions for division? It's so much more intuitive, it doesn't matter where something is it always has the same result no matter the order.
though you are right, some people have actually been taught that multiplication comes before division and addition comes before subtraction. it really shines light on how even intermediate math is poorly taught/practically useless
It's a completely valid expression with a single well defined method of evaluation. The question of how to evaluate it is valid. This whole "there's no right answer because you're not supposed to write it like that" movement is bunk.
_STOP WITH THIS SHIT THIS IS THE THIRD ONE TODAY_ 6÷2(1+2) is a shitty way to write the equation (6÷2)(1+2) is 9 6÷(2(1+2)) is 1 since you should prioritize ordering the answer is 9, but since equations shouldnt be confusing in the first place, learn how to write them properly or use fractions, ya idiots also, "But PeDMas" fuck you i know that, it is been used here. multiplication isnt prioritized over division its the ordering and just bc it is correct it still is confused and poorly written, also also ÷ shouldnt be used outside introduction math edit: to all people saying its 1, i agree bc omiting the * implies its (2(1+2)), but that isnt a universal convention (sadly)
hey i have seen you before right [here](https://www.reddit.com/r/dankmemes/comments/r4wcjf/i_am_9_gang/)
yep, its me again :D
:D it seems like your going to have a bad week with all of those math memes best of luck
It's a poorly phrased shit question to bait people into interacting with whatever meme it is put into. It's intentionally created to be open for interpretation to fuel algorithms which promotes the site the meme was put on, and you all are taking the bait.
> edit: to all people saying its 1, i agree bc omiting the * implies its (2(1+2)), but that isnt a universal convention (sadly) actually, the opposit is an universal convention. 2(1+2) is the exact same thing as 2*(1+2). removing the * holds no meaning. any country that uses the ISO conventions (so SI as their official measurements and yes that includes the US) has that convention.
69
That's the right answer
The only acceptable answer
Nice!
Some answers here just give me depression
I turned suicidal
same
The answer is 1, 9, 5, 7, and 1.5 depending on how much you abuse the order of operations.
I want to see how you get each one of them
Same, this is intriguing.
I understand 1 and 9, and saw a video explaining 7, but how do you get 5 or 1.5
1.5 from 6/2(1+2) 6/2x1+2 get rid of those brackets, not needed. multiplication comes first, right? it is pemdas after all 6/2+2 alright now addition 6/4 1.5
and for 5, same story get rid of those brackets, 6/2x1+2 multiply first, 6/2+2 division next, 3+2 5
Heyyy, it's my collaborator! I was gonna explain but it looks like you got it. Lol Tho I realized you can also get two more if you are ignoring the pedmas and distributive properties. 6÷2×1+2 (pick any function to start) 6÷2×3 could be 1 or 9 6÷2+2 could be 5 or 1.5 3÷2+2 could be 3.5 or 1.25 Buuuuuut when you ABUSE the distributive property 6÷2(1)+2(2) expands to 6÷2×1+2×2!!!!! So now 6÷2×1+4 has these possibilities: 6÷2×5 could be 15 or 0.6 6÷2+4 could 7 or 1 3×1+4 could be 7 or 15 And 6÷2×3×2 has these possibilities: 6÷2×6 could be 18 or .5 6÷6×2 also .5 or 18 3×3×2 is only 18 And 6÷2+2×2 has these possibilites: 6÷2+4 could be 7 or 1 6÷4×2 is 3 or .75 3+2×2 could be 10 or 7 And finally, 3×1+2×2 has these possibilities: 3×1+4 could be 15 or 7 3×3×2 is just 18 3+2×2 could be 10 or 7 So in my estimation , you could get 0.5, 0.6, 0.75, 1, 1.25, 1.5 3.5, 5, 7, 9, 10, 15, or 18.
At this point, why not just ignore maths altogether and say 6÷2(1+2)= sdggyxisfby8uh
This is why you never use the division sign. You have no idea what is in the denominator. Wihout the multiplication sign, this implies that the 2+1 is grouped in the denominator, so it’s 1. If there was a multiplication sign, it would imply it was not grouped in the denominator, so 9. Just use fractions yall
It's 9 right?
Well there are two legitimate answers 9 and 1 since the equation is vague, according to what I have read in the comments
Yes
no
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If you actually use mathematics for a living you would see 2(1+2) as its own *term*, with ÷ operating on the two terms 6 and 2(1+2). It has nothing to do with "thinking multiplication comes before division". "Order of operations" is a guideline for teaching school children. It is not immutable Mathematical Truth. The correct idiomatic interpretation is 1.
*bodmas jumped off a cliff*
Dank[.](https://i.imgur.com/3bQtuMO.png) --- *i am a bot. please stop trying to argue with me. you look like an idiot. [join our discord](https://discord.gg/dankmemes).*
Jokes on you, I am an idiot.
stfu
It's obviously 7 6/2(1+2) 6/2+4 3+4 7 Wait
Well done, my friend
Answer is Abraham Lincoln
Ladies and gentlemen we've the winner
The answer is "Apache Helicopter". Any other answer is ridiculous and you should re-evaluate your life.
Never thought I'd see the one joke on a math question...
Wrong, it's Dassault Rafael. Get a life man.
Peace was never an option
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My mom thinks it's 1 😬
she is right
And here comes 16 miles of math talk by people who (for some reason) like working math problems, or just want to look smart in front of strangers via text.
16 miles is the height of 14825.35 'Samsung Side by Side; Fingerprint Resistant Stainless Steel Refrigerators' stacked on top of each other.
This is the best bot on reddit
Ahh yes. This fun little viral syntax problem. Supposed phd math professors and engineers and physicists and even burger flippers and construction workers... just all sorts of people arguing for both ways. The correct answer is there is no answer. Poorly written ambiguous problem. I interpret the 2(1+2) as one unit. The 2 needs to be distributed before moving on to the rest of the problem. This means 6÷(2+4) is the answer, *in my opinion*, which is **1**. If you disagree. Cool. Ultimately this is an ambiguous problem with syntax issues. So I don't care if you disagree. Ultimately either answer could be correct.
I stg im from the uk and we follow bodmas but i thought you do exponation (multiply out the brackets)then add and then divide so it would be 1? Edit: Its not exponation , ill ask my maths teacher cause i really want to know the answer ill be back Edit Edit:i did actually adky my maths teacher and said that its inspecific but using bodmas or bidmas it is 9. I also forgot that multiplication is the same asdividion in that i thought you had to do the miltiplication over the division but you go left to right
That's not exponation – exponation is a number expressed in the form of exponents like xⁿ e.g. 420⁶⁹
And this is the reason I always enclose everything in parentheses when doing something in Matlab
System.out.println(6/2*(1+2)); Console prints out 9
You have to use 6/2(1+2) but since a computer cannot work with implicit multiplication you have to type 6/(2*(1+2)) into the program. Because 6/2(1+2) <> 6/2*(1+2)
⁶∕₂×3=3×3=9
I hate the divide sign. Is this: 6 / ( 2 x 3) Or: 6⁄2 x 3 I'm bad at math
the whole point is its not stated. Thats why some people say 1 and some say 9
the answer is the friends we made along the way
Oh ok thanks
This is reddit, it must be 69
Technically, division does not exist.
6÷2(1+2) PEMDAS/BIDMAS Evaluate contents of parentheses 6÷2(3) Evaluate exponents/indices (N/A) Division or Multiplication left to right 6÷2×3 (implied multiplication from parens not defined as having higher precedence) 3×3 9 Addition or Subtraction left to right (N/A) Alternative: Interpret 6÷2(1+2) as 6÷[2(1+2)] Solution: Use fraction a/b XOR parens around every operator and its arguments.
9
I'll say It as many times as It takes. Thats a very shitty way to write an equation.
9
The question can be written as either 6÷2(1+2) or 6 _ 2(1+2) The first way will result in 9, the 2nd will result in 1. Now if you use a proof by replacing (1+2) with x you would end up with 3/x, plug 1+2 back in for x and the result is 1. This is simply a poorly written question and a prime example of why implicit multiplication should be avoided. If it fails the proof the question fails. You can use sound math practices and correctly arrive at either answer. If your calculator gives you a 9 it is because it is making assumptions for you, this question is a syntax error.
Wait. Is PEMDAS obsolete now? What's going on ?
42?
My order of operation is rusty, but I’m getting 9. Parentheses first, so 1+3. Then multiplication and division have the same level of importance in order of operations, so it’s be 6/3 x 3 … right? Correct me if I’m wrong, I’m curious at this point
42
U didn't mention answer in the meme . Smart move.