It’s amazing how so much can be written on a math situation that never comes up after 3rd grade. These Facebook posts get tens of thousands of comments.

It actually comes up a lot more now than ever due to advanced calculators. People have to know how their calculator handles this type of syntax all the time, and not all calculators handle it the same way.

All the normies had a TI calculator in high school and there’s me with my HP. Had to do it hard mode learning the math and how to use the darn calculator too. RPN all the way!

Bachelors of Physics here as well.
I also want to add that we use fractions a lot, but when a denominator gets unwieldy, or when you’re double checking your calculation with dimensional analysis… you usually just write a denominator out as a multiplicand raised to (-1).
I guess if you wanted to get cheeky, you could say division is really a two step “exponentiation then multiplication” operation, so PEMDAS should say:
6 ÷ 2(1+2) = 6 ÷ 2(3) = 6 x [2(3)]^(-1) = 6 x [6]^(-1) = 1
Edit: Wow. I guess a lot of people on here know PEMDAS, but don’t know what cheeky means.

The shit I experienced
An 80s style hair metal math video
"Please excuse my dear aunt Sally"
I saw that video in the 7th grade.......two decades and multiple degrees ago.....that shit worked.

yesss PEMDAS! Parentheses exponents multiplication division addition subtraction! Haha I actually enjoyed algebra because of all the cool formulas! But geometry? Forget about it lol

Math is only as good as its agreed upon notation. In this case, the notation is ambiguous, and mathematicians would not use ambiguous notation like this. They would either write it as 6 / [2(1 + 2)], for a solution of 1, or (6 / 2)(1 + 2), for a solution of 9.
Strictly speaking, executing the order of operations on it the way it is written would add 1 + 2, first (parentheses), then multiplication/division *from left to right*, so 6 / 2 = 3, and then 3 x 3 = 9. *However*, algebra has you simplify the parenthetical expression, 2(1 + 2), first, as 2(1) + 2(2) = 6, which is how one who has “seen some shit” arrives at a solution of 1.

Because you can interpret 6 / 2(3) as 6 / 2 * 3, so if you follow "order of operations", you read it from left to right, so it becomes 3 * 3 = 9.
However, higher level, whenever you implicitly imply multiplication via parenthesis, you always do that first.

You can take those “-2 points” up ur ass teacher man I did show my work my dog just ate it and unless you gonna pump his stomach to find it I suggest you give me back those 2 points for I staple my nuts to the whiteboard😤

PEMDAS is supposed to be done left to right, but in the order of PEMDAS. So you address the P left to right, then the E left to right, and so on. I just think people forget the proper way to do PEMDAS.

Not exactly. The M/D and A/S are treated as the same operation. If you’ve done your parentheses and exponents and there’s a division to the left of a multiplication, you do the division first.
PS: Sorry if I am agreeing with you and misunderstood what you were saying.

Nope you're absolutely agreeing with me and you are absolutely right and that's how PEMDAS is done. You address the P first left to right. Them the E left to right. Then the M/D left to right. Finally the A/S left to right. I just figured it was understood that's why I didn't type out the whole thing in my original comment.

It's 9.
Following Order of Operations, you start with everything inside the parenthesis, so you add 1 and 2 and get 3. Next, PEMDAS states that you do multiplication and division, but in order from left to right, and since 6/2 comes BEFORE 2(3), \[or 2\*3\] you would divide 6 by 2 first and THEN multiply 3 by 3. I'll do it in bullet-point for you guys
\- 6/2(1+2)
\- 6/2(3)
\- 6/2\*3
\- 3\*3
\- 9
You COULD do distributive property first, but I'm fairly certain this violates the Order of Operations.
edit: It's actually 1.
thanks to a few of you who pointed out that **even though the 2 sits on the outside of the bracket, it still applies to them, and therefore means that it would come first in the equation.** Here's how it's solved:
* 6/2(1+2)
* 6/2(3)
* 6/(6)
* 6/6
* =1

Honestly I’ve never looked at a / as anything but a division sign unless some says that have 3/4 of an apple, the fraction format makes no difference to me (save for formulas like the quadratic equation)

The ambiguity is whether there are unspoken parentheses or not. Like, in a fraction, you act as if the fraction is surrounded by parentheses. With a division symbol, there is disagreement about whether that is still the case

Yeah, true, any inline notation is ambiguous without proper parenthesis
Imo the slash symbol is the lesser of 2 evils because it at least makes people think about putting the parenthesis in, because 6 / 2(1+2) looks a lot more like it should give the answer of 1, so if I wanted the answer 9 I would know to write (6 / 2)(1+2)

A general guideline that I use is that whenever you must write a fraction in one line, put parentheses around the denominator if it has multiple components.
i.e. 6/(2(1+2)) = 1, 6/2 * (1+2) = 9

Agreed. When in doubt, just put parentheses wherever they apply.
Also, if you're writing both expressions in parentheses, you can just write (6/2)(1+2) to save a character without creating any ambiguity.

Seriously, this isn’t even really an order of operation question so much as it’s how you interpret the division symbol as well as whether 2(1+2) is a single entity or not. So 6 is either divided by 2 or divided by 2(1+2). Giving either (6/2)(1+2) or 6/(2(1+2))

Math problems like this used to pop up on 4chan all the goddamn time back in the day. The point of it is to provoke people into arguing over it, which drives engagement.

This is a great example of why you write stuff in fractions on paper and with a bunch of extra brackets, even if it seems redundant on a calculator or computer

The real confusion isn’t even order of operation it’s that the division symbol is being interpreted differently.
(6/2)(1+2) vs 6/(2(1+2))
I personally would interpret it as 6/(2(1+2)) where you set it up as a fraction and take 2(1+2) as a single entity (divisor) and the 6 is the dividend.
The problem is definitely stupid and only goes to show how poorly taught most people.

This is actually a really good example. There's technically only one solution, as the dress couldn't be both at once. With the dress, the answer could be different depending on the question: what do you _see_, which would make either answer correct, or what color *is* the dress, which would make one answer correct. The problem with math is, every problem has a solution like the second question, but everyone interprets it like it's the first. Simple math like this literally cannot have 2 unequal solutions, period

So much this.
By the same logic 6x/6x=x^2
Small coincidence: I teach math and this week I am rebuilding the oop unit. I was already planning on putting this question in, but now have a meme and recent flame war thread on the topic to include. A bit of serendipity.

If we take 6/(2*(1+2)), that's `6 2 1 2 + * /` in RPN.
Does RPN make sense when using a calculator? Yeah, its much faster imo.
But writing shit in rpn is just is just annoying and harder to read than infix. There's a reason everyone uses it

I don't get the ambiguity here. I always learned it as
P E MD AS. Making the grouped letters left to right, not one before the other. If you remember it that way then this becomes super easy

It's kind of a weird one. In higher level maths, you got a lot more orders of priority with things like mathematical implications and inference, last course I had we had 14 orders of priority, which ended with something similar as PEMDAS, **but**, the one thing you get taught really quickly is to eliminate any ambiguity. The first reason is that when you write divisions in any proof or paper you write it as numerator over denominator, not a division sign. The second reason if that if you do something like 1/2 * 3, you'll always write (1/2)*3, to remove any ambiguity.
Now, why is the reflex to do 6/6? Because in just about many complex calculations/theorems, you generally leave the division for last, so naturally, when you read something like that, you automatically interpret it as 6/(2(2+1)). Because nobody in their right mind would write it out like in the OP.

If you’re doing real math you’re gonna stop using the division sign real quick. It gives so much room for interpretation. It’s just not useful.
Is this (6/2)*(1+2)? Or 6/(2(1+2))? I have no idea.
Use fractions and parentheses people!

Exactly. No one in upper level STEM uses a division sign. Its ambiguous. Ambiguity in STEM is dangerous. Best case scenario you’ve just invalidated a paper worth of research due to a calculation error. Worst case scenario it can lead to people dying (whether that’s a dosage mistake in medicine, a bridge load miscalculation, producing a potentially dangerous runaway reaction etc.)
In fact as an upper year engineering student I read this and assumed that the implicit multiplication took precedence. This would be consistent with the division sign being treated as a fraction. That gets me 1. I do see the argument from the 9 group as well though, as it is a more strict adherence to B E DM AS.
[Here’s an rather long Harvard article (that I admit I haven’t read all the way through yet) that goes into the ambiguity](https://people.math.harvard.edu/~knill/pedagogy/ambiguity/index.html)

As someone who has gone through 4 levels of calculus for my engineering degree, I can't stand everyone going "buh-but PEMDAS, so this is correct". Technically yes, you're correct, but this is written with such horrible syntax that it hurts.
Typically having a number or entity directly attached to parentheses, you're supposed to treat it one entity. Literally no one writes things like this, an no one's answer is "right": whoever wrote this is just "wrong".
It's like reading a sentence written by a caveman and debating what they meant.

You don't know.
* Calculus
* Calculus 2: Multivariable calculus
* Calculus 2b\*: Multivariable calculus 2 (\*Only a handful of colleges break Multivariable into two classes)
* Calculus 3: Differential Equations
* Calculus 4: Fourier Transforms
* Calculus 5: Return to Pythagorus Lake
* Calculus 6: Albert's Revenge
* Calculus 7: A new hope
I always think that they jumped the shark after Calculus 3.

Idk some people think *Return to Pythagoras Lake* is the best in the series. It has that huge time jump between 4 and 5, but the philosophical implications are interesting enough to write a thesis about.

Yep. I'm also an engineer. This is just written to be confusing and order of operations is just a notation convention, which isn't always followed and can't be relied on if you do math for your job.

Yeah it's just straight up a bad way to write a formula.
My calculator understands orders of operations, and if I put in this calculation exactly as it's written the calculator returns "1" as the answer.
It gets ambiguous because the calculator treats implicit multiplication as a single term. If I write it again in the calculator but put a multiplication symbol between 2 and the parentheses then it returns 9.

Implicit multiplication isn't a hard law, it's just generally accepted practice in higher level maths and even there it can be fairly ambiguous. Depending on the context implicit multiplication can take higher priority on variables but not brackets which leaves us right where we started.

It's isn't about the order of operations. It's about how some people think of implied multiplication as having higher precedence than division. That's it

By reading all the comments, I feel everyone here is r/confidentlyincorrect (and correct)! The ***real*** answer is "I don't know ...math!?" All kidding aside, my question is who came up the rules of order of operations, PEMDAS, etc.? And how and why did they arrive at those standards and rules? Like, I wanna know the history of this to understand why we are still debating something that someone made up over 100 years ago!

PEMDAS is just a way to notate the math problem, you could use any order of operations, so long as both the writer and the solver of the problem are using the same notation method. Without an order of operations we would just have to make the problems more detailed.

[perhaps this post from r/engineers can be of use somehow](https://www.reddit.com/r/AskEngineers/comments/5icxyd/whats_the_actual_correct_answer_for_6212/)
Edit: gave detailed explanation of what I thought the answer was, got the sense I was wrong, googled it, found this instead.

I love how people that actually understand math can see problems like this are meant to make people argue lol. Math is all applicable theory. Order of operations is valid in simple math and up to a good point but to be honest it’s been deemed fundamentally flawed (hence the existence of such arguments). Also as for calculator arguments, bro we make calculators they are as flawed as us. Both answers are right depending on how you look at it. It’s about being open minded and understanding how both are right.

Well, I'm in math licence, I have not a clear opinion on this type of problem
In high math level we only use the fraction notation, and this avoid this type of problem, actually I want to answer 9 but my brain automatically put it in fraction and want to answer 1... So it might be 9 but it's confusing

PEMDAS => parenthesis => exponents => multiplication or division whatever first from left to right => addition or substraction whatever first from left to rignt. Given that order of operations rules: 6÷2(1+1) = 6 ÷ 2(3) = 6 ÷ 2×3 = 3×3 = 9.

6/2(2+1) = 9
6/((2)(2+1)) = 1
The answer to this is 9, first you solve the bracket, after that
You basically have 6/2*3 Wich equals 9
If you however go with 6/(2*3) you'd get one, in this case you'd multiply before the division but you need a bracket for that. Division and multiplication are equal in order of operations that's when you go from left to right.
In some countries PEMDAS is thought to students making it seem like multiplication is first in order of operation. Where I come from teachers will tell you it's brackets before point before line. (Bad translation) but it basically means, first the brackets, then the dots; multiplication/division, then the ones with lines; addition subtraction.

dear god only an hour and 720 comments... what have you done

It’s amazing how so much can be written on a math situation that never comes up after 3rd grade. These Facebook posts get tens of thousands of comments.

lol ikr

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It actually comes up a lot more now than ever due to advanced calculators. People have to know how their calculator handles this type of syntax all the time, and not all calculators handle it the same way.

RPN baby. RPN!

All the normies had a TI calculator in high school and there’s me with my HP. Had to do it hard mode learning the math and how to use the darn calculator too. RPN all the way!

Team Casio report in

Well i guess we're not exactly a gang but we exist at least.

No no, we are a gang now

I loved my HP 48G. You could do so much on that baby

I hated RPN until I got my HP 48SX. Now I have a hard time using "normal" calculators.

well. you'll be surprised how much it comes after 3rd grade. Especially in STEM

I have a Master’s in math and it never came up. You always write formulas in an unambiguous way using parenthesis or brackets.

Bachelors in Physics here. Can confirm. We write formula and equations out how they would be done. Not to trip up teenagers in an exam

Bachelors of Physics here as well. I also want to add that we use fractions a lot, but when a denominator gets unwieldy, or when you’re double checking your calculation with dimensional analysis… you usually just write a denominator out as a multiplicand raised to (-1). I guess if you wanted to get cheeky, you could say division is really a two step “exponentiation then multiplication” operation, so PEMDAS should say: 6 ÷ 2(1+2) = 6 ÷ 2(3) = 6 x [2(3)]^(-1) = 6 x [6]^(-1) = 1 Edit: Wow. I guess a lot of people on here know PEMDAS, but don’t know what cheeky means.

Accounting student here Wtf am I looking at I am so lost

If you are lost there as an accounting student you missed a big part of you degree lol.

n^(-1) = 1/n 6^(-1) = 1/6 6(6^(-1)) = 6/6 = 1/1 = 1

So, are you a 1 or a 9?

I distribute and get 7

Lol exactly, that’s the only correct answer for these dumb formulae. No one in a real world situation would express a mathematical problem like OP

So for an idiot like me, is the correct answer the crying lady 1 or the hulk hogan dude 9?

If you are young it's 9. If you are more experienced and have "seen some shit" it's 1.

The shit I experienced An 80s style hair metal math video "Please excuse my dear aunt Sally" I saw that video in the 7th grade.......two decades and multiple degrees ago.....that shit worked.

Man I haven't seen "Please excuse my dear aunt Sally" in at least 15 years.

yesss PEMDAS! Parentheses exponents multiplication division addition subtraction! Haha I actually enjoyed algebra because of all the cool formulas! But geometry? Forget about it lol

Couldn't have said it better myself. As a physicist, this made me chuckle!

I'm 31 and I got 1. But I don't understand how is math not absolute.

Math is only as good as its agreed upon notation. In this case, the notation is ambiguous, and mathematicians would not use ambiguous notation like this. They would either write it as 6 / [2(1 + 2)], for a solution of 1, or (6 / 2)(1 + 2), for a solution of 9. Strictly speaking, executing the order of operations on it the way it is written would add 1 + 2, first (parentheses), then multiplication/division *from left to right*, so 6 / 2 = 3, and then 3 x 3 = 9. *However*, algebra has you simplify the parenthetical expression, 2(1 + 2), first, as 2(1) + 2(2) = 6, which is how one who has “seen some shit” arrives at a solution of 1.

You don't have to be a mathematician. A programmer would not leave it ambiguous either.

Hah!

Ok... I meant a good programmer.

If I leave the parentheses out I can fit the whole thing in a single line! That's what's important, right?

Laughs in python

I said programmer.

Because you can interpret 6 / 2(3) as 6 / 2 * 3, so if you follow "order of operations", you read it from left to right, so it becomes 3 * 3 = 9. However, higher level, whenever you implicitly imply multiplication via parenthesis, you always do that first.

Exactly this. Interestingly, if I type into my scientific calculator 6÷2(1+2), I get 1. However if I type 6÷2x(1+2), I get 9.

because you turned it into 6÷2 × 1(1+2) which is 3 × 3

The horses name was Friday

proof?

I did it on a separate sheet of paper and left it at home🤷♂️

Did not show work -2 points

You can take those “-2 points” up ur ass teacher man I did show my work my dog just ate it and unless you gonna pump his stomach to find it I suggest you give me back those 2 points for I staple my nuts to the whiteboard😤

bet😈

Oh no

T-Teacher man…😳

do it jimmy, do it for me 🥵

How do I unread something

How to unmake life

Sass & Backtalk (-5 points)

If I got docked 5 points every time I was sassy or back talked I’d still be in high school.

Lets downvote everyone who is doing the wrong math and acting like Pythagoras

We don’t take kindly to showin smarts or educating round here

Easy now Skeeter they ain't harming nobody.

Asked my dad with two masters in math… its 1 its gotta be 1

PEMDAS: Parathases Exponents Multiplication/Division (LEFT TO RIGHT) Addition/Subtraction (left to right)

Lol this but at the same time on teacher taught left to right and one taught only in the order of pemdas

PEMDAS is supposed to be done left to right, but in the order of PEMDAS. So you address the P left to right, then the E left to right, and so on. I just think people forget the proper way to do PEMDAS.

Not exactly. The M/D and A/S are treated as the same operation. If you’ve done your parentheses and exponents and there’s a division to the left of a multiplication, you do the division first. PS: Sorry if I am agreeing with you and misunderstood what you were saying.

Nope you're absolutely agreeing with me and you are absolutely right and that's how PEMDAS is done. You address the P first left to right. Them the E left to right. Then the M/D left to right. Finally the A/S left to right. I just figured it was understood that's why I didn't type out the whole thing in my original comment.

Its very clearly not understood, that's the whole reason for this meme and the disagreements in the comments.

Lol, it's literally the reason this comment chain exists.

The disagreement apparently stems from the argument of whether implicit multiplication takes priority over explicit multiplication and division.

Yeah twas wack

Weird, I learned it as BEDMAS Brackets Exponents Division Multiplication Addiction Subtraction

In the USA its PEMDAS, most other countries use BEDMAS or BODMAS. I don’t recall addiction being on either list though.

Ha, I'll leave the typo. Was taught this in Canadian schools.

Bees Excuse Dear My Aunt Sally

BEDMAS: Brackets Exponents Division/Multiplication (LEFT TO RIGHT) Addition/Subtraction (left to right)

BIDMAS Brackets Indices Division/Multiplication Addition/Subtraction

BODMAS in the UK (Order)

I'm a UK boi but learned BIDMAS

Yes this is the way I learned

i always the multiplication-division and addition-subtraction didnt matter, just multi and divi had to be done before add and subtract.

Lol

It's 9. Following Order of Operations, you start with everything inside the parenthesis, so you add 1 and 2 and get 3. Next, PEMDAS states that you do multiplication and division, but in order from left to right, and since 6/2 comes BEFORE 2(3), \[or 2\*3\] you would divide 6 by 2 first and THEN multiply 3 by 3. I'll do it in bullet-point for you guys \- 6/2(1+2) \- 6/2(3) \- 6/2\*3 \- 3\*3 \- 9 You COULD do distributive property first, but I'm fairly certain this violates the Order of Operations. edit: It's actually 1. thanks to a few of you who pointed out that **even though the 2 sits on the outside of the bracket, it still applies to them, and therefore means that it would come first in the equation.** Here's how it's solved: * 6/2(1+2) * 6/2(3) * 6/(6) * 6/6 * =1

Oh my god. Haha my dad rethought it and gave me a lecture about it.

your original comment made me question my intelligence

This is why the division sign isn't used after arthemitic, fractions are so much more easier to understand.

Honestly I’ve never looked at a / as anything but a division sign unless some says that have 3/4 of an apple, the fraction format makes no difference to me (save for formulas like the quadratic equation)

The ambiguity is whether there are unspoken parentheses or not. Like, in a fraction, you act as if the fraction is surrounded by parentheses. With a division symbol, there is disagreement about whether that is still the case

It clears up ambiguity for those not experts in order of operations. For example here it could clarify if the intention is (6÷2)x(1+2) or 6÷(2x(1+2))

Something something grammar correction

Oh whoops didn't not even see that.

This is made to confuse people, any sane person who wanted to express a working like this wouldn't write it in this manner

The ÷ symbol is a curse upon mathematics

It would have been the same with a slash symbol. If you write it as a fraction, it becomes very clear what the answer is

Yeah, true, any inline notation is ambiguous without proper parenthesis Imo the slash symbol is the lesser of 2 evils because it at least makes people think about putting the parenthesis in, because 6 / 2(1+2) looks a lot more like it should give the answer of 1, so if I wanted the answer 9 I would know to write (6 / 2)(1+2)

>Yeah, true, any inline notation is ambiguous without proper parenthesis Laughs in prefix and postfix

A general guideline that I use is that whenever you must write a fraction in one line, put parentheses around the denominator if it has multiple components. i.e. 6/(2(1+2)) = 1, 6/2 * (1+2) = 9

Yeah, but (6/2) * (1+2) would be more clear.

Agreed. When in doubt, just put parentheses wherever they apply. Also, if you're writing both expressions in parentheses, you can just write (6/2)(1+2) to save a character without creating any ambiguity.

Or, you could just put 9 to idiot-proof it.

I usually tell my students to put parentheses around thier numerator denominators. May look clutter a bit, but it gets rid of this misinterpretation.

Seriously, this isn’t even really an order of operation question so much as it’s how you interpret the division symbol as well as whether 2(1+2) is a single entity or not. So 6 is either divided by 2 or divided by 2(1+2). Giving either (6/2)(1+2) or 6/(2(1+2))

It should seriously just be either fractionated or do a multiple with an inverse. So 6 x 1 ------------ 2(1+2) or just 6 ------- 2(1+2)

This is made to see who shares the shit on social media so developers/ad firms can see how far a particular network of people reaches.

Math problems like this used to pop up on 4chan all the goddamn time back in the day. The point of it is to provoke people into arguing over it, which drives engagement.

The one trick pony show the whole internet has been made into thanks to social media marketing.

And yet I said ÷ was ambiguous and got UHMN ACKTUALLY'd, guess no redditor would miss a chance to be both pedantic and wrong. ¯\\\_(ツ)\_/¯

This is a great example of why you write stuff in fractions on paper and with a bunch of extra brackets, even if it seems redundant on a calculator or computer

The real confusion isn’t even order of operation it’s that the division symbol is being interpreted differently. (6/2)(1+2) vs 6/(2(1+2)) I personally would interpret it as 6/(2(1+2)) where you set it up as a fraction and take 2(1+2) as a single entity (divisor) and the 6 is the dividend. The problem is definitely stupid and only goes to show how poorly taught most people.

In all my years it's always been this.

I see a gold and white dress

It says Laurel.

Nope, it's obviously going clockwise.

It’s Yanny.

This is actually a really good example. There's technically only one solution, as the dress couldn't be both at once. With the dress, the answer could be different depending on the question: what do you _see_, which would make either answer correct, or what color *is* the dress, which would make one answer correct. The problem with math is, every problem has a solution like the second question, but everyone interprets it like it's the first. Simple math like this literally cannot have 2 unequal solutions, period

You almost make me cry with memories of a simpler world.

The answer is clearly syntax error >:(

He forgot the semicolon

Segmentation fault (core dumped)

Truly a C moment.

Reminds me of a joke I saw on reddit some time ago Why is "python" a better language? Bcoz it's above C level Or something

And a star

It's clearly undefined behaviour. If you don't specify parenthesis, each ~~compiler~~ person might generate different result.

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“There are no stupid answers” -Every teacher ever

They say "there are no stupid questions" never heard a version about answers

On Line 69 but there’s only 5 lines

This. If I'm given this equation, my response is rewrite it in a proper and unambiguous format.

As an upper year engineering student, this is a horrible way to write out math problems and is only intended to confuse people

So much this. By the same logic 6x/6x=x^2 Small coincidence: I teach math and this week I am rebuilding the oop unit. I was already planning on putting this question in, but now have a meme and recent flame war thread on the topic to include. A bit of serendipity.

When reddit writes your lesson plan

X=1

I guess I walked into that one. Nice!

Or x=-1

Idk how they got 1 and 9 I got George Washington

It's not George Washington it's climate change

Nah, it's the financial crisis of 2008.

Close, I got the Great Depression

Personally I got the cave that Christ was sealed in but I'm probably wrong

It’s El Niño, you morons.

No, it’s the Alamo.

Dude it’s obviously Zimbabwe how do you mess that up?

Nonsense it’s obviously the reason the chicken crossed the road

You know what youre so close, but its south africa

When I did it I got the guy who killed hitler but in bad at math so it’s probably not right

I mean I got 1889 was I close or

No you all are wrong the answer is the War crimes in Yugoslavia.

George Washington was the first president. First is also written as 1st. George Washington = 1

Or use more parentheses to eliminate ambiguity. (6/2)•(1+2) = 9 6/(2•(1+2)) = 1

Yes

Or use reverse polish notation. No need for parentheses.

If we take 6/(2*(1+2)), that's `6 2 1 2 + * /` in RPN. Does RPN make sense when using a calculator? Yeah, its much faster imo. But writing shit in rpn is just is just annoying and harder to read than infix. There's a reason everyone uses it

6/2(1+2) is sane thing I think just without the mult. Sign

I don't get the ambiguity here. I always learned it as P E MD AS. Making the grouped letters left to right, not one before the other. If you remember it that way then this becomes super easy

It's kind of a weird one. In higher level maths, you got a lot more orders of priority with things like mathematical implications and inference, last course I had we had 14 orders of priority, which ended with something similar as PEMDAS, **but**, the one thing you get taught really quickly is to eliminate any ambiguity. The first reason is that when you write divisions in any proof or paper you write it as numerator over denominator, not a division sign. The second reason if that if you do something like 1/2 * 3, you'll always write (1/2)*3, to remove any ambiguity. Now, why is the reflex to do 6/6? Because in just about many complex calculations/theorems, you generally leave the division for last, so naturally, when you read something like that, you automatically interpret it as 6/(2(2+1)). Because nobody in their right mind would write it out like in the OP.

It's deez nuts end of story

you might want to get that checked out

it’s neither, the answer to everything is 42!

So like, 1.4050061e+51?

Thank you

No problem, babe. Anything for my lovely bean.

r/suddenlyDating

Reddit shits on Facebook a lot. But damn if it doesn’t get more and more like Facebook everyday.

We will all be our parents on Facebook, just on Reddit and our kids will be back on Facebook or some other app

I got 27

Future Nobel prize winner here

a true visionary

The only correct answer

If you’re doing real math you’re gonna stop using the division sign real quick. It gives so much room for interpretation. It’s just not useful. Is this (6/2)*(1+2)? Or 6/(2(1+2))? I have no idea. Use fractions and parentheses people!

Exactly. No one in upper level STEM uses a division sign. Its ambiguous. Ambiguity in STEM is dangerous. Best case scenario you’ve just invalidated a paper worth of research due to a calculation error. Worst case scenario it can lead to people dying (whether that’s a dosage mistake in medicine, a bridge load miscalculation, producing a potentially dangerous runaway reaction etc.) In fact as an upper year engineering student I read this and assumed that the implicit multiplication took precedence. This would be consistent with the division sign being treated as a fraction. That gets me 1. I do see the argument from the 9 group as well though, as it is a more strict adherence to B E DM AS. [Here’s an rather long Harvard article (that I admit I haven’t read all the way through yet) that goes into the ambiguity](https://people.math.harvard.edu/~knill/pedagogy/ambiguity/index.html)

Apple calculator: “Best I can do is 2.”

As someone who has gone through 4 levels of calculus for my engineering degree, I can't stand everyone going "buh-but PEMDAS, so this is correct". Technically yes, you're correct, but this is written with such horrible syntax that it hurts. Typically having a number or entity directly attached to parentheses, you're supposed to treat it one entity. Literally no one writes things like this, an no one's answer is "right": whoever wrote this is just "wrong". It's like reading a sentence written by a caveman and debating what they meant.

TIL there are more than 3 levels of calculus.

You don't know. * Calculus * Calculus 2: Multivariable calculus * Calculus 2b\*: Multivariable calculus 2 (\*Only a handful of colleges break Multivariable into two classes) * Calculus 3: Differential Equations * Calculus 4: Fourier Transforms * Calculus 5: Return to Pythagorus Lake * Calculus 6: Albert's Revenge * Calculus 7: A new hope I always think that they jumped the shark after Calculus 3.

They jumped the ω

Idk some people think *Return to Pythagoras Lake* is the best in the series. It has that huge time jump between 4 and 5, but the philosophical implications are interesting enough to write a thesis about.

Calc 1-3 plus diff. eq.

Yep. I'm also an engineer. This is just written to be confusing and order of operations is just a notation convention, which isn't always followed and can't be relied on if you do math for your job.

Yeah it's just straight up a bad way to write a formula. My calculator understands orders of operations, and if I put in this calculation exactly as it's written the calculator returns "1" as the answer. It gets ambiguous because the calculator treats implicit multiplication as a single term. If I write it again in the calculator but put a multiplication symbol between 2 and the parentheses then it returns 9.

Implicit multiplication isn't a hard law, it's just generally accepted practice in higher level maths and even there it can be fairly ambiguous. Depending on the context implicit multiplication can take higher priority on variables but not brackets which leaves us right where we started.

Professor here. If you use the division sign in your expressions beyond middle school, just be a stripper or something.

or at least use () god damn it

Yup

It's isn't about the order of operations. It's about how some people think of implied multiplication as having higher precedence than division. That's it

By reading all the comments, I feel everyone here is r/confidentlyincorrect (and correct)! The ***real*** answer is "I don't know ...math!?" All kidding aside, my question is who came up the rules of order of operations, PEMDAS, etc.? And how and why did they arrive at those standards and rules? Like, I wanna know the history of this to understand why we are still debating something that someone made up over 100 years ago!

PEMDAS is just a way to notate the math problem, you could use any order of operations, so long as both the writer and the solver of the problem are using the same notation method. Without an order of operations we would just have to make the problems more detailed.

[perhaps this post from r/engineers can be of use somehow](https://www.reddit.com/r/AskEngineers/comments/5icxyd/whats_the_actual_correct_answer_for_6212/) Edit: gave detailed explanation of what I thought the answer was, got the sense I was wrong, googled it, found this instead.

Nice karma farm. It’s a great idea.

(* Reminds self to repost in 6 months *)

I love how people that actually understand math can see problems like this are meant to make people argue lol. Math is all applicable theory. Order of operations is valid in simple math and up to a good point but to be honest it’s been deemed fundamentally flawed (hence the existence of such arguments). Also as for calculator arguments, bro we make calculators they are as flawed as us. Both answers are right depending on how you look at it. It’s about being open minded and understanding how both are right.

1. (1+2) = 3 2. 6÷2 =3 3. Since there is nothing between 6÷2 and (1+2), mulitply it 4. 3×3 = 9 Its nine

Well, I'm in math licence, I have not a clear opinion on this type of problem In high math level we only use the fraction notation, and this avoid this type of problem, actually I want to answer 9 but my brain automatically put it in fraction and want to answer 1... So it might be 9 but it's confusing

Aunt sally would be very disappointed.

PEMDAS => parenthesis => exponents => multiplication or division whatever first from left to right => addition or substraction whatever first from left to rignt. Given that order of operations rules: 6÷2(1+1) = 6 ÷ 2(3) = 6 ÷ 2×3 = 3×3 = 9.

6/2(2+1) = 9 6/((2)(2+1)) = 1 The answer to this is 9, first you solve the bracket, after that You basically have 6/2*3 Wich equals 9 If you however go with 6/(2*3) you'd get one, in this case you'd multiply before the division but you need a bracket for that. Division and multiplication are equal in order of operations that's when you go from left to right. In some countries PEMDAS is thought to students making it seem like multiplication is first in order of operation. Where I come from teachers will tell you it's brackets before point before line. (Bad translation) but it basically means, first the brackets, then the dots; multiplication/division, then the ones with lines; addition subtraction.

The right answer is that it's bad notation.

How about Polish notation? × ÷ 6 2 + 2 1 Much better and perfectly unambiguous!

Yeah that's pretty clearly 9

"so does multiplication always come first, or is it multiplication/division?" "yes"

Multiplication or division. Which ever comes first. In this case reading left to right, division comes first. Edit: spelling

Division is multiplication in a way cuz when u divide by x ur multiplying by 1/x

are the "*" and "/" equals to "×" and "÷"? because we learned that "." is "×" and ":" is "÷"

In programming x is * and ÷ is /. It's also better to use it in a text, because you don't confuse it with punctuation.

wait how do you get one

Damn I got 5

Pejmdas Juxtaposition is the assumption that the 2 is multiplied by the parentheses first before the division lmfao