# So what is it smart guy?March 13, 2013 4:17 PM   Subscribe

The facebook question that has everyone stirred up... I got 9. I am a fifty-one year old white guy. Did new math f-ck me up?

math question has eveyone stumped
posted by shockingbluamp (236 comments total) 21 users marked this as a favorite

I'm pretty sure the plane can take off, but only if it's piloted by a literal viking.
posted by flaterik at 4:23 PM on March 13, 2013 [50 favorites]

We learned the order of operations as BODMAS in from Mr. Ridley at Cedary Junior High in 1986 or so, and therefore the answer is "1".
posted by KokuRyu at 4:23 PM on March 13, 2013 [14 favorites]

math question has eveyone stumped

Math question has 2 answers, either of which can be right depending on how fighty you want to get about order of operations.
posted by The Bellman at 4:23 PM on March 13, 2013 [7 favorites]

As a math professor, I'm sad that people are arguing about a meaningful question like this when they could be fighting over something important like whether 0.999999..... = 1.
posted by escabeche at 4:25 PM on March 13, 2013 [53 favorites]

Journalist has column inches to fill, browses Facebook for inspiration
posted by ook at 4:25 PM on March 13, 2013 [9 favorites]

I have been fighting this battle since 1993. The wise instructor I had in college for Math Ed told us to teach students you do multiplicative operations before you do additive operations, but for just multiplicative or just additive you go in order from left to right. But you would be shocked how many college Elementary Algebra students get this problem wrong from years of PEMDAS.

Bottom line: PEMDAS is evil.
posted by wittgenstein at 4:26 PM on March 13, 2013 [2 favorites]

At fifty one, he should be old enough not to care. Me, I am only interested in knowing what the Goddamn SAT folk think is right, and that only because at some point the offspring will have to take the Goddamn SAT and spit back whatever they want.

(For the record, offspring and I both got 1. But we're more than willing to change that answer.)
posted by IndigoJones at 4:26 PM on March 13, 2013 [3 favorites]

I read through the article thinking "why would anybody fight over this?" and then he said the correct answer according to the majority is 9.

That's BULLSHIT, man!
posted by bpm140 at 4:27 PM on March 13, 2013 [50 favorites]

```\$ perl -le 'print (6/2*(1+2))' 9```

And anyone who says otherwise is an APL programmer.
posted by straw at 4:29 PM on March 13, 2013 [16 favorites]

Obelus! Vinculum!!! I had no idea there were words for these, or that the line over the long division and square root numbers was a separate symbol.
posted by vytae at 4:30 PM on March 13, 2013 [7 favorites]

Isn't the issue with this problem that it is written in a way that nobody would actually do, so it ends up being like your English teacher asking you to diagram a sentence fragment with no verbs and people arguing what the predicate is?
posted by MCMikeNamara at 4:31 PM on March 13, 2013 [23 favorites]

Also, the answer is obviously 1.
posted by MCMikeNamara at 4:32 PM on March 13, 2013 [12 favorites]

Abelian operators, there's a traitor in your midst!
posted by The Power Nap at 4:32 PM on March 13, 2013 [2 favorites]

As a programmer, I would say the answer is always to add more parentheses for clarification.
posted by Foosnark at 4:33 PM on March 13, 2013 [66 favorites]

I don't have time for this, I'm still trying to think of a movie that doesn't have the letter S in it.
posted by cortex at 4:33 PM on March 13, 2013 [36 favorites]

The problem is not with maths.
it's with notation, in particular the limitation of typing an equation on one line.

In the year 2013 there should be no need to write equations on one line, they're awful to read.
Hand write the equation like any decent mathematician, and I'll give you the answer.

While we're at it, would someone please tell microsoft to fix the formulas in excel, so that they can layout like hand written equations (multiple lines, square root sign etc), they could be so much easier to read.
posted by Dr Ew at 4:33 PM on March 13, 2013 [12 favorites]

We learned the order of operations as BODMAS in from Mr. Ridley at Cedary Junior High in 1986 or so, and therefore the answer is "1".
I was taught BODMAS too, but the answer is 9.
posted by Jehan at 4:33 PM on March 13, 2013 [6 favorites]

Well, see I would have coded it like this because, you know, order of operations..

\$ perl -le 'print ( 6 / (2*(1+2) ) )'
1
posted by dobie at 4:33 PM on March 13, 2013 [6 favorites]

I assume the people who get worked up over this are the same people who submit unskippable science questions to OKCupid.
posted by ckape at 4:35 PM on March 13, 2013 [3 favorites]

This is a wonderful counterargument to the claim that there are no stupid questions.
posted by ckape at 4:37 PM on March 13, 2013 [36 favorites]

Cortex: Halloween.
posted by schyler523 at 4:39 PM on March 13, 2013

posted by carter at 4:39 PM on March 13, 2013 [7 favorites]

Well, see I would have coded it like this because, you know, order of operations..

\$ perl -le 'print ( 6 / (2*(1+2) ) )'
1
--dobie

If this was an SAT question, and you hand drew in the extra parentheses before marking the answer '1', I don't think they would take your reworking of the original question into consideration.
posted by eye of newt at 4:40 PM on March 13, 2013 [3 favorites]

I had to RTFA to understand why this was even a thing.

If it were written 6 ÷ 3 * (1+2) there might be a lot less controversy.
posted by Foosnark at 4:40 PM on March 13, 2013 [2 favorites]

If it were written 6 ÷ 3 * (1+2) there might be a lot less controversy.

Why's that, exactly? Is it because numbers which aren't integers don't exist?
posted by King Bee at 4:42 PM on March 13, 2013

The thing that gets to me is that everyone is spending so much time arguing about the order of operations when almost everybody agrees on that, and it's the associativity that makes the big difference here. I guess it's because everybody remembers learning BODMAS, or PEMDAS, but there wasn't a catchy term for "left to right".

(I couldn't remember if it was left-to-right or right-to-left and had to do this:
```GHCi, version 7.0.3: http://www.haskell.org/ghc/  :? for help
Prelude> :i (/)
class Num a => Fractional a where
(/) :: a -> a -> a
...
-- Defined in GHC.Real
infixl 7 /
Prelude> ```
Do I win any nerd points?)
posted by benito.strauss at 4:43 PM on March 13, 2013 [4 favorites]

The problem here is that ÷ is a meaningless symbol that no real mathematicians (or scientists, et al) actually use. If it were well defined the way that the rest of the operative symbols we use on a regular basis are, then it would be more obvious to all of you simpletons that the answer is 1.
posted by telegraph at 4:44 PM on March 13, 2013 [18 favorites]

Since we're using Arabic numbers, then you *always* go from right to left. Mashallah, the answer is wahid.
posted by NoMich at 4:50 PM on March 13, 2013 [26 favorites]

You'll find the answer in your heart if you can learn to love one another.
posted by perhapses at 4:53 PM on March 13, 2013 [7 favorites]

I got 9, too. Just start on the left and keep working. It made sense to me. When I saw people starting to insist it had to be 1, and then the 9'ers coming in insisting on their answer, I was shocked.
posted by etaoin at 4:53 PM on March 13, 2013 [1 favorite]

This is totally the math equivalent of the classic XKCD about nerd (mis) communication. I teach at one of the high temples of nerdery and pointless pedanticism and I can't think of a single person who would have a response other than "wtf, where are the parentheses?"

It reminds me of the intro to the C programming language, where Ritchie devotes a page to apologizing for the order of operations. (Seriously, the basics are as you'd expect but who ought to win in the cage match between multiplication and bitwise logic? We end up teaching our beginning programmers to use parentheses like they're going out of style, just in case.)
posted by range at 4:54 PM on March 13, 2013 [8 favorites]

My inability to "solve" this "problem" "correctly" clearly didn't prevent me from getting an 800 on GRE math, like pretty much everyone in every quantitative discipline ever.

Yesterday I did, however, have to sit through a 15-minute conversation about how math is confusing and ambiguous.

Nota bene: the aim of mathematical notation is to reduce ambiguity, not to introduce more of it and then police adherence to some arbitrary convention.

Also: the obelus ÷ is a historical curiosity and serves no real purpose, except to confuse grade-school students.

Also also: let's all learn Polish notation.
posted by Nomyte at 4:55 PM on March 13, 2013 [10 favorites]

I don't have time for this, I'm still trying to think of a movie that doesn't have the letter S in it.

Dude, I'll tell you tomorrow.
posted by madcaptenor at 4:56 PM on March 13, 2013 [1 favorite]

The thing that gets to me is that everyone is spending so much time arguing about the order of operations when almost everybody agrees on that, and it's the associativity that makes the big difference here. I guess it's because everybody remembers learning BODMAS, or PEMDAS, but there wasn't a catchy term for "left to right".

But the the point of associativity is that it's neither left-to-right or right-to-left. Or both, depending if you like 'both' or 'neither' better. The scourge of this PEMDAS nonsense (which I never learned) is that students don't realise that multiplication and division are the same thing (when written non-ambiguously). For some reason they understand that they can add and subtract in whatever order, but freeze when faced with a choice of whether to multiply or divide first.
posted by hoyland at 4:57 PM on March 13, 2013

I wonder how much of this is related to the "guess the teacher's password" education style.

I mean, if we hadn't all been trained in third grade to believe that the answer had to be either "one" if the teacher was thinking of the number one, or "nine" if the teacher was thinking of the number nine -- and that our job as students was to get really good at guessing which number the teacher was thinking of -- would there still be argument on that point? Or would we just be able to say "Huh. Ambiguity sucks. I'm glad real academic publishers hire editors for shit like this" and move on without insisting on a single answer?
posted by Now there are two. There are two _______. at 4:57 PM on March 13, 2013 [6 favorites]

What about the words that end in 'gry?'
posted by Obscure Reference at 4:57 PM on March 13, 2013 [1 favorite]

The problem here is the person who wrote that equation was being a dick on purpose.

I haven't seen it yet, but I am sure I will get shares from WBMJ Country Radio 98.4 and Dick's Drain Snaker's and Mom's Fried Chunk's Family Restaurant all asking what I think the answer is all up in my feed, shared by all the people I went to high school with, my mom, my dad, my aunt and some of my co-workers.

Anyway, it's 9. Or 1. Or I hate your equation and I hate your ass face.
posted by louche mustachio at 4:59 PM on March 13, 2013 [17 favorites]

There are two legitimate answers to this question. One is 9, and the other one is wrong.
posted by vidur at 4:59 PM on March 13, 2013 [8 favorites]

The answer is actually zero, because ÷ is the symbol for subtraction! (At least that's what the socialist dictatorship of Norway tried to trick my seven year old brain into believing)
posted by ymgve at 4:59 PM on March 13, 2013 [3 favorites]

Oh man, Norwegians are assholes. Why would you write a column of plusses and minuses with a version of the minus sign that's like ten times easier to mistake for a plus sign?

(Also on my shit list: whatever jerk invented the goddamn lowercase letters, for that b/d/p/q crap.)
posted by Now there are two. There are two _______. at 5:03 PM on March 13, 2013

Also: the obelus ÷ is a historical curiosity and serves no real purpose, except to confuse grade-school students.

Also you can make this little face with it:

(°÷°)

never mind that guy looks like a smug little jerk
posted by louche mustachio at 5:04 PM on March 13, 2013 [18 favorites]

For some reason they understand that they can add and subtract in whatever order, but freeze when faced with a choice of whether to multiply or divide first.

Do you think it's because in a situation like this you get different answers depending on which one you pick? Maybe?
posted by Diablevert at 5:04 PM on March 13, 2013 [1 favorite]

For some reason they understand that they can add and subtract in whatever order

Consider 5 - 4 + 3:

(5 - 4) + 3 = 4
5 - (4 + 3) = -2

You were saying?
posted by ymgve at 5:07 PM on March 13, 2013 [2 favorites]

Someone should send Slate some math papers and blow their minds. All these greek letters mean different things all over the place!
posted by ecmendenhall at 5:08 PM on March 13, 2013 [1 favorite]

For what it's worth, the post was linking to page two of the article. Fixed that. Makes a bit more sense starting from the start.

And anyway, the obelus is actually meant to be read in this context as a UFO; it's actually a sort of story problem wherein you're supposed to figure out the season, episode and scene of the X-Files being referred to by reinterpreting the symbols as characters from the series.

I won't give away the answer, but if it helps you to get started, Mulder and Scully are obviously the number 1 and number 2 characters on that show, and 2(1+2) is pretty clearly a one of them having a thought bubble about the two of them getting together.
posted by cortex at 5:09 PM on March 13, 2013 [15 favorites]

> they understand that they can add and subtract in whatever order,

6 − 2 − 1 ???

6 − (2 − 1) ≠ (6 − 2) − 1

> We end up teaching our beginning programmers to use parentheses like they're going out of style, just in case.

Well, I assume that when McCarthy saw where LISP was going he scooped up most of the parenthesis futures at a low price, and that MIT has vast underground reserves of them that it makes available to its staff and students.
posted by benito.strauss at 5:12 PM on March 13, 2013 [4 favorites]

6 − 2 − 1 is really 6 + (-2) + (-1). More generally, you don't actually need the subtraction sign if you have unary negation.

(And you don't need the division sign if you have unary reciprocaling. But I don't know a good notation for that.)
posted by madcaptenor at 5:15 PM on March 13, 2013 [10 favorites]

So grammar 'nazi' is soooooo last season now? and 'order of operations fascist' is what the cool kids (on fb) are now?
Who's this generation's DFW to write that overly annotated screed on prescriptivist v descriptivist maths?
posted by OHenryPacey at 5:15 PM on March 13, 2013 [4 favorites]

This is a bullshit question. But the answer is nine.
posted by lrobertjones at 5:17 PM on March 13, 2013

1/2s = 0.5s or 0.5hz? but then
2m/2s = 1 ms or 1 m/s?
posted by Pyry at 5:18 PM on March 13, 2013 [1 favorite]

I've never been clear about what the "New Math" even means. Was that the set theory and base 8 parts of the elementary school curriculum that they'd teach for a week before dropping it and moving on to the 7 + 5 = ? worksheets?
posted by thelonius at 5:19 PM on March 13, 2013 [3 favorites]

I'm surprised the image just flat out says ANSWER IT.

Cause I'd be all, "Fuck you Facebook! You're not the boss of me!"

Isn't it supposed to try and trick me, like "X% of people can't answer this simple question, can you?"
posted by RobotHero at 5:21 PM on March 13, 2013 [2 favorites]

Toward the end of the article: "(2:3 is commonly the same as 2/3 in ratios)."

Um. No.
posted by etc. at 5:21 PM on March 13, 2013 [2 favorites]

Yes, there is no problem with the maths but with the representation. More exactly, the author of the formula hasn't made explicit what is the formal grammar (a context-free / BNF one would suffice) he's following. Depending on the grammar, you can get 9 or 1 according to how the grammar reflects left or right associativity of / cases. Of course, the author can be a thorough son of a bitch and clarify, later on and after the bodycount of arguing people is high enough, that his grammar is ambiguous and hence the answer is both 9 and 1. Then again, I'm a computer scientist, so my worldview is hardly what you'd expect from a casual facebook poster.
posted by Iosephus at 5:22 PM on March 13, 2013 [4 favorites]

Looks like I'm even worse at math than I thought.
posted by pentagoet at 5:23 PM on March 13, 2013

I came up with 9, realized it was a trick, and then came up with 1, and then realized that was the true trap... 1 only works if it's 6/(2(1+2)). Look at it this way... what if it was (1+2)6/2?
posted by Slap*Happy at 5:25 PM on March 13, 2013

I don't know why we're arguing about this here. I'm sure that there's a Boston housewife who's discovered one simple trick that will give the answer.
posted by benito.strauss at 5:26 PM on March 13, 2013 [12 favorites]

9. The amount of debate over this alarms me. You do the parenthesis first and treat 6÷2(3) as 6÷2·3, going left to right.
posted by hellomina at 5:26 PM on March 13, 2013 [5 favorites]

I don't know why we're arguing about this here. I'm sure that there's a Boston housewife who's discovered one simple trick that will give the answer.

I'm not sure I can trust you if you don't include small icons for all fifty states in this assertion.
posted by cortex at 5:29 PM on March 13, 2013 [4 favorites]

(And you don't need the division sign if you have unary reciprocaling. But I don't know a good notation for that.)

You'll sometimes see notation where the superscript -1 in n-1 is treated like a unary operator -- I mean, in domains where "inverse" is well-defined but "exponentiation" might not be.
posted by Now there are two. There are two _______. at 5:31 PM on March 13, 2013

The problem here is that ÷ is a meaningless symbol that no real mathematicians (or scientists, et al) actually use. If it were well defined the way that the rest of the operative symbols we use on a regular basis are, then it would be more obvious to all of you simpletons that the answer is 1.
and
6 − 2 − 1 is really 6 + (-2) + (-1). More generally, you don't actually need the subtraction sign if you have unary negation.

(And you don't need the division sign if you have unary reciprocaling. But I don't know a good notation for that.)
I should admit here that I never actually finished high school maths, so these comments are the equivalent of witchcraft to me. I'm stacking up the faggots as we speak...this devilment will not be let to flourish.
posted by Jehan at 5:31 PM on March 13, 2013

I'm not sure I can trust you if you don't include small icons for all fifty states in this assertion.

Does this mean we're getting the img tag back?

Or that Unicode has now completely jumped the shark?
posted by Now there are two. There are two _______. at 5:32 PM on March 13, 2013

Wait, so what is the right answer? Because I'm now doubting all the maths.
posted by DoubleLune at 5:33 PM on March 13, 2013

I came up with 9.

On a related note, my cat‘s name is Mittens.
posted by Jughead at 5:33 PM on March 13, 2013 [3 favorites]

posted by hellomina at 5:34 PM on March 13, 2013

Phew.
posted by DoubleLune at 5:35 PM on March 13, 2013

I see four lights.
posted by mollweide at 5:36 PM on March 13, 2013 [21 favorites]

Consider 5 - 4 + 3:

(5 - 4) + 3 = 4
5 - (4 + 3) = -2

You were saying?

Students understand that (5-4) + 3 = 5 + (-4+3). Clear now?
posted by hoyland at 5:36 PM on March 13, 2013 [1 favorite]

posted by (Arsenio) Hall and (Warren) Oates at 5:36 PM on March 13, 2013 [1 favorite]

THERE! ARE! 9! LIGHTS!!
posted by barnacles at 5:41 PM on March 13, 2013 [9 favorites]

Superscript -1 is indeed the most common notation for an inversion operation, that is, one in which operating an element and its inverse results in the unit element. This, independently of the elements you operate with being numbers or anything else you want to putz around with.

And again, the answer is 9, but if we share some assumptions in common about the representation used. Same as the 5 - 4 + 3 above. It does seem that most basic maths courses choose left to right associativity, so the 9 has a "most likely what you meant by this expression" sense that is not to be underestimated after all.
posted by Iosephus at 5:41 PM on March 13, 2013

6/2(1+2)
6/(2+4)
6/2+6/4
3+1.5

Four and a half!

No, wait.
6/2(1+2)
6/(2+4)
6/2+6/4
6/8/4

.1875!
posted by mrgoat at 5:42 PM on March 13, 2013 [7 favorites]

The author of the linked article is only adding to the confusion because she rewrites the question with spaces between the numbers and signs.
6÷2(1+2) versus 6 ÷ 2(1+2)

So even if people correctly do the parenthesis first, the spacing tricks them into solving the right hand side of the problem, since they are seeing it like 6 ÷ 2(3), when it is really 6÷2(3).
posted by hellomina at 5:42 PM on March 13, 2013 [1 favorite]

this facebook shit followed me to metafilter? we're fucked now.
posted by quonsar II: smock fishpants and the temple of foon at 5:45 PM on March 13, 2013 [11 favorites]

> I'm sure that there's a Boston housewife who's discovered one simple trick that will give the answer.

I'm not sure I can trust you if you don't include small icons for all fifty states in this assertion.

Oh, there's supposed to be a quick geo-look-up on your IP address, and <Boston> is supposed to be replaced with a plausible city that's near you. Do you not allow XMLHttpRequest() in posts?

Enable it for me, and that's the only thing I'll ever do with it. I promise. Really. No-backsies and cross-my-heart-hope-to-die. Pleeeeeease.
posted by benito.strauss at 5:45 PM on March 13, 2013 [1 favorite]

So even if people correctly do the parenthesis first, the spacing tricks them into solving the right hand side of the problem, since they are seeing it like 6 ÷ 2(3), when it is really 6÷2(3).

I'd think that if anything that would help. It groups the operation performed first more closely together.
posted by ChurchHatesTucker at 5:46 PM on March 13, 2013

Says the man who thinks the answer is 1. Which it is not... But to each his own.
Edit: okay wait, unless you mean it makes the side with the parenthesis stick out more (and agree the answer is 9), in which case I see what you mean.
posted by hellomina at 5:48 PM on March 13, 2013

They should have written it as exp(ln(6) - ln(2) + ln(2 + 1)) if they meant it to be 9.
posted by Monday, stony Monday at 5:49 PM on March 13, 2013 [1 favorite]

Since we're using Arabic numbers, then you *always* go from right to left. Mashallah, the answer is wahid.

My understanding was that the numbers in Naastaliq and the modern Arabic script are written from left to right, even if the words and sentences are written from right to left. The Arabs themselves were inspired by the numbers from the ancient Kharohi script, which was used in Afghanistan, Pakistan and north western India, although at what point the numbers moved from being Kharohi's right-to-left to Brahmi's left-to-right is an interesting question.
posted by the cydonian at 5:52 PM on March 13, 2013 [3 favorites]

I note that I have forgotten how maths works.
posted by turgid dahlia 2 at 5:53 PM on March 13, 2013

... Right, I'll be over here, by myself, since I got 1.

My brain did it as 6/(2(1+2)), since the 2(1+2) is a distinct expression.

I also had several old Russian math teachers along the way, which I have discovered well after the fact taught me a bunch of notation and process weirdness that was in no way American standard.

I'd never seen y=mx+b until I was in undergrad, when I was told that "you were told to write it that way, but really it is y=ax+b" ... which confused me since I was taught the a b notation from the start. Some other weirdnesses in my math linguistics:

My ≠ goes the opposite direction of everyone else's (from left down to right).
I was taught the a∤b notation very early (a does not divide b) but my slash goes the opposite direction, once again.
I use ≅ for "approximately equals", but ≈ for "rounded to equal", and I never use either for congruence, which is ≃.
All statements of the form -(a*b) are actually -1*(a*b).
I always put the variable I am solving for to the left, rather than right as I work.
posted by strixus at 5:53 PM on March 13, 2013

6 / 2(1+2)
6 / 2*(1+2)
(6/2) * (6/(1+2))
3 * 2

Six!
posted by Now there are two. There are two _______. at 5:54 PM on March 13, 2013 [2 favorites]

OMG I give up. I'm leaving.
posted by hellomina at 5:56 PM on March 13, 2013

And to outpedant myself shamefully, the "5 - 2" is "5 + (-2)"is one nasty little problem in expression meaning, caused by the use of the - sign for two very different things: (additive) inversion and the substraction operation. That in general x - y = x + (-y), where the left - is substraction and the right one inversion, is a lucky break coming from the properties of numbers and their operations. In practice, some have felt so annoyed by this confusing abuse of notation that they use a new sign for additive inverstion. See for instance the ML programming language, where you write -1 as ~1.
posted by Iosephus at 5:56 PM on March 13, 2013 [1 favorite]

It is interesting, but the unthinking, arithmetic-crunching part of ny brain screams 1 when I see the ÷ sign, but 9 when I see /. Make of that, what you will.
posted by the cydonian at 5:58 PM on March 13, 2013 [1 favorite]

(6/2) * (6/(1+2))
3 * 2

Six!

No way man, it's 27.

(6/2) * 6/(1+2)
3 * (6+3)
3 * 9
posted by mrgoat at 5:58 PM on March 13, 2013 [1 favorite]

If this has shown me anything, it is that I am frequently wrong.
posted by dobie at 6:07 PM on March 13, 2013

The answer is use fucking brackets, you moron.
posted by unSane at 6:08 PM on March 13, 2013 [6 favorites]

Thank you, Metafilter, for this topic redemption. Sure, it's gratuitous and probably not BotW, but I needed to be able to laugh about this topic like only The Blue could make me do.

The proliferation of these questions was one of the reasons I stopped using Facebook altogether. I wasn't so much put out by the ensuing controversy brought forth by questions that offered ambiguity, yet could easily be satisfactorily explained in the aggregate. Rather, I was utterly dismayed by the hordes of people who insisted, vehemently and angrily, that theirs was The One True Answer, and that all others should bow before their intellectual superiority. People who could neither adequately articulate why they were right, nor why their detractors were wrong. For fucking Basic Math.

I'm a software developer. I've plowed through many years of math in my education and professional life, and take it pretty seriously. But I don't have one iota of the hubris, on that topic or any other, that so very, very many of those folks display. Alas, it's too apt of an analogy for what's so horribly wrong in our New Internet Society.

I find that I hang out a lot more on Metafilter since then. Thanks for the laughs. You all make it a lot easier not to hate the world sometimes.
posted by Brak at 6:09 PM on March 13, 2013 [5 favorites]

wittgenstein: " Bottom line: PEMDAS is evil."

Please Excuse My Dear Aunt Sally is evil?
posted by IndigoRain at 6:09 PM on March 13, 2013

Since the obelus represents division, and division is the inverse of multiplication, I interpreted the equation as:

6 * 1/2 * 3 = 1.

Yeah, if I were programming it, I would make the order of operations explicit; 6/2*3 would be interpreted by the computer as (6/2) * 3, whereas 6/(2*3) would be interpreted as 1. Eh.

You'll sometimes see notation where the superscript -1 in n-1 is treated like a unary operator -- I mean, in domains where "inverse" is well-defined but "exponentiation" might not be.

Hear, hear. My guess is that most of us in math and science would answer 1. Listen to us, folks -- we deal with this kind of shit everyday.
posted by tickingclock at 6:09 PM on March 13, 2013 [2 favorites]

Yeah, I did this one mentally like most programming languages do, because that's how I learned order of operations -- first do everything inside parentheses, by the same rules that follow, then do all unary sign operators, (like, -6 means negative six), then exponentiation, then multiplication and division, and then addition, working left to right in each case.

However, it is kind of weird to write a problem that way... you would normally put an operator between the 2 and the (. Many languages would refuse to parse that.

So, if I was being super pedantic, my answer would be:

`TypeError: 'int' object is not callable`
posted by Malor at 6:11 PM on March 13, 2013 [3 favorites]

Oh, and if it wasn't obvious, my answer was 9.
posted by Malor at 6:14 PM on March 13, 2013

The facebook question that has everyone stirred up... I got 9.

I figured it was this one and thought, "No, nine is way low."
posted by ricochet biscuit at 6:15 PM on March 13, 2013 [1 favorite]

No way man, it's 27.

(6/2) * 6/(1+2)
3 * (6+3)
3 * 9

You were so close! Just gotta factor out the three.

3 * (6+3)
3 (1 * (6+1))
3 (1 * 7)
21
posted by Now there are two. There are two _______. at 6:17 PM on March 13, 2013 [2 favorites]

irb(main):001:0> 6/2(1+2)
SyntaxError: (irb):1: syntax error, unexpected '(', expecting \$end
6/2(1+2)

irb(main):002:0> 6/2*(1+2)
=> 9

Good point, Malor. My initial answer was 9 as well, with a caveat of "Use some damn parentheses. The next person maintaining this might suck at math."
posted by mrgoat at 6:19 PM on March 13, 2013

Also also: let's all learn Polish notation.
posted by Nomyte

wait, this is a real thing? holy cow! and so is Reverse Polish Notation! I thought my dad was just being a jerk when he used this term while teaching me to use my mom's HP 12c!
posted by vespabelle at 6:19 PM on March 13, 2013 [1 favorite]

Wait, hold on. I just remembered the Magical Number Nine skit from Square One. So we take the string 6÷2(1+2) and we add up all the digits, so that's 6+2+1+2 = 11, and then we add those together, and the answer is 2.

The answer is 2. Thanks, nine!
posted by cortex at 6:21 PM on March 13, 2013 [1 favorite]

And to outpedant myself shamefully, the "5 - 2" is "5 + (-2)"is one nasty little problem in expression meaning, caused by the use of the - sign for two very different things: (additive) inversion and the substraction operation. That in general x - y = x + (-y), where the left - is substraction and the right one inversion, is a lucky break coming from the properties of numbers and their operations. In practice, some have felt so annoyed by this confusing abuse of notation that they use a new sign for additive inverstion. See for instance the ML programming language, where you write -1 as ~1.

What is subtraction if not adding the inverse? From my math perspective, it's not a 'lucky break', it's what subtraction is. That you could perhaps implement them independently on a computer is incidental.
posted by hoyland at 6:24 PM on March 13, 2013 [2 favorites]

wait, this is a real thing?

posted by ChurchHatesTucker at 6:24 PM on March 13, 2013

I've seen this one going around lately:
40 - 32 ÷ 2 = 4!
posted by lucidium at 6:24 PM on March 13, 2013 [12 favorites]

wait, this is a real thing? holy cow! and so is Reverse Polish Notation!

Not only is it a real thing, RPN is probably the closest thing I had to a Religion as I was moving from Judaism towards Zen Buddhism.
posted by benito.strauss at 6:30 PM on March 13, 2013 [1 favorite]

Oops -- I see that above, I totally flipped my answers when writing them down. I promise I knew which answer was correct in my head -- I just have problems writing them down. Sigh.
posted by tickingclock at 6:30 PM on March 13, 2013

I got 14%.
posted by xedrik at 6:30 PM on March 13, 2013

It makes me sad to think that anyone would think this is an interesting question.
posted by miyabo at 6:31 PM on March 13, 2013

But maybe math teachers could use it as a jumping off point for discussing parse trees, postfix notation, and evaluating with a stack, so there's that.
posted by miyabo at 6:33 PM on March 13, 2013

The true answer is NINE and anyone who says anything different is a poopy face.
posted by deborah at 6:36 PM on March 13, 2013

When I type it into Google, I get 9, and, as this is how all math will be done in the future, this is therefore the right answer.
posted by Bunny Ultramod at 6:38 PM on March 13, 2013 [5 favorites]

I can't believe no one saw the guy in the gorilla suit walk right through the equation.
posted by markr at 6:38 PM on March 13, 2013 [32 favorites]

benito.strauss: "I don't know why we're arguing about this here. I'm sure that there's a Boston housewife who's discovered one simple trick that will give the answer."

And makes \$425K a year only working from home for 12 minutes a day?
posted by Samizdata at 6:40 PM on March 13, 2013

hellomina: "The author of the linked article is only adding to the confusion because she rewrites the question with spaces between the numbers and signs.
6÷2(1+2) versus 6 ÷ 2(1+2)

So even if people correctly do the parenthesis first, the spacing tricks them into solving the right hand side of the problem, since they are seeing it like 6 ÷ 2(3), when it is really 6÷2(3).
"

Whew!

So I don't have to kill myself for being a member of the 1 camp?
posted by Samizdata at 6:42 PM on March 13, 2013 [2 favorites]

deborah: "The true answer is NINE and anyone who says anything different is a poopy face."

And, no, once again you are wrong.

Yours is the face of poopiness.
posted by Samizdata at 6:45 PM on March 13, 2013

hoyland, you are right, I was fuzzily remembering the integers modulo n and (wrongly) thinking that additive inverse and subtraction were different there, but a quick googling shows me that no, even in such cases subtraction is additive inverse addition.

See, it IS an interesting question, it's making me dust off my old universal algebra courses! ;)
posted by Iosephus at 6:49 PM on March 13, 2013

Cortex:

The Day After Tomorrow, Law Abiding Citizen, The Dark Knight, The Double, Captain America, Daredevil, Brick, Bloodrayne, Highlander, Kung-Fu Panda, Green Mile, Finding Nemo, Ultraviolet, Gladiator

There are many more.
posted by JakeEXTREME at 6:53 PM on March 13, 2013

There is one answer, and the answer is one. Anybody who says otherwise is an idiot AND THAT IS THAT.

Also: Argo.
posted by Sys Rq at 6:56 PM on March 13, 2013

This isn't as bad as other Facebook math questions I've seen because this question is much more ambiguous. Some of the other ones will be something like "what does '5 + 9 x 0' equal?" and there will be legions of people arguing that anything multiplied by zero causes the whole equation to equal zero and they can not be swayed from their opinion and it just makes me unreasonably mad.

Also: Citizen Kane, Marley and Me, The Hunt for Red October, The Room, and The Human Centipede.
posted by A Bad Catholic at 6:59 PM on March 13, 2013 [1 favorite]

P.S. There are seven continents and four oceans.
posted by Sys Rq at 7:00 PM on March 13, 2013

That depends on whom you’re talking to, or what calculator or programming language you’re using.

Every answer I get on a calculator is 5318008.
posted by Smedleyman at 7:04 PM on March 13, 2013 [9 favorites]

That is NOT Numberwang.
posted by Crane Shot at 7:06 PM on March 13, 2013 [9 favorites]

ML just does that so you can override - and ~ separately it looks like. C++ solves that by having overloaded functions, but ML doesn't allow those.
posted by miyabo at 7:07 PM on March 13, 2013

Calling Europe a continent is ridiculous. Geologically, India has a far more legitimate claim, but they are modest enough to call themselves a sub-continent. Europe is a big peninsula with delusions of grandeur.
posted by foobaz at 7:14 PM on March 13, 2013 [2 favorites]

No, I think cortex is looking for one where the letter S does not appear even in the script. The answer is Baraka.
posted by ricochet biscuit at 7:17 PM on March 13, 2013 [4 favorites]

I was taught BODMAS too, but the answer is 9.

Dammit! So it is. How could I screw that up, and in such a public forum, too!
posted by KokuRyu at 7:23 PM on March 13, 2013

No, no go on Memento then?
posted by Samizdata at 7:24 PM on March 13, 2013

It's not a question about math, it's question about notation, which people can disagree on, and there is no right answer. It's dumb gotchas like this on math tests that make people hate math.
posted by empath at 7:25 PM on March 13, 2013 [10 favorites]

posted by carter at 7:25 PM on March 13, 2013

I'm confused as to why people are talking about order of operations twixt divide and multiply, when the issue is whether implicit multiplication has a higher order of precedence then explicit multiplication.

I'm pretty sure most who answer 1 (as do I) would answer 6 ÷ 2*(1+2) as 9. At least I would.

But I could be wrong -- would other 1ers still be 1ers if the multiplication symbol was explicit?
posted by lastobelus at 7:26 PM on March 13, 2013 [4 favorites]

once you get past the 5th grade, who uses ÷ for division, anyway?
posted by empath at 7:28 PM on March 13, 2013 [1 favorite]

Just out of curiosity, a question for the 9ers:

How do you solve 8 ÷ 2x where x = 2. If you solve it as 2, why do you treat this implicit multiplication differently?

Would you solve 8 ÷ 2(x) as 8? Are the parentheses standing in for an explicit multiplication?
posted by lastobelus at 7:31 PM on March 13, 2013 [9 favorites]

I'm pretty sure most who answer 1 (as do I) would answer 6 ÷ 2*(1+2) as 9. At least I would.

Oh, fuck, you're right. Fuck. Fuck.

You know, every now and then I get the feeling there might've been a reason I took grade 12 math (easy "trucker math" at that) twice.
posted by Sys Rq at 7:33 PM on March 13, 2013

(I definitely think it's the lack of a sign between the 2 and the bracket that fucked me up. It makes everything after the ÷ feel like one big chunk.)
posted by Sys Rq at 7:36 PM on March 13, 2013

As others have said, the premise is BS because of the ÷ symbol. Nobody uses that. It's deliberately creating ambiguity.
posted by Justinian at 7:38 PM on March 13, 2013 [1 favorite]

(I think it's the lack of a sign between the 2 and the bracket that fucked me up. It makes everything after the ÷ feel like one big chunk.)

You didn't fuck up. There is no right answer. It's ambiguously notated. This has nothing to do with being bad at math.
posted by empath at 7:39 PM on March 13, 2013 [4 favorites]

I've never felt more popular.
posted by Poor Neglected Obelus at 7:39 PM on March 13, 2013 [10 favorites]

But I could be wrong -- would other 1ers still be 1ers if the multiplication symbol was explicit?

It's equally ambiguous with and without the multiplication symbol. It might lead people to parse it as 6 ÷ (2*(1+2)) more readily, but it would still be ambiguous.

Actually, look at that. I copy and pasted (because I don't want to figure out how to type ÷) and then added parentheses in such a way as to get 1. That was not intentional.
posted by hoyland at 7:42 PM on March 13, 2013

You can take away my "multiplication indicated by juxtaposition is carried out before division" when you pry it from my cold dead hands.
posted by readyfreddy at 7:43 PM on March 13, 2013 [2 favorites]

Basically, this is using ÷ to get the problem you get when you write fractions with a / and aren't careful to make it clear what the denominator is. As someone who writes fractions with a /, the answer is not parentheses, but to make your / big.
posted by hoyland at 7:43 PM on March 13, 2013 [1 favorite]

Two dots run into each other. Lets call them (2.)

(1.) Says, "How many dots do you see?"
(1.) Replies, "Nine. How many do you see?"
(9.) Remarks, "I can see a million colors, man."
posted by vozworth at 7:44 PM on March 13, 2013

I'm pretty sure most who answer 1 (as do I) would answer 6 ÷ 2*(1+2) as 9. At least I would.

Not me. It is 1 and I am nailing my flag to the mast. I know that there's really an argument to be made for 9 as well, but it is now heresy so no more to be said.
posted by winna at 7:51 PM on March 13, 2013 [1 favorite]

Everybody knows it's not about BODMAS/PEMDAS...

posted by symbioid at 7:51 PM on March 13, 2013 [4 favorites]

(the Parenthetical Expression) : Is the story, unfolding.

-wrote every Oxford comma
posted by vozworth at 7:53 PM on March 13, 2013 [1 favorite]

You didn't fuck up. There is no right answer. It's ambiguously notated. This has nothing to do with being bad at math.

It isn't ambiguous, though.

I mean, yes, the author could mean 6 ÷ (2(1+2)), but that's not what they wrote, and if that's what they meant, they wrote it wrong. In PEDMAS or BOMDAS or whatever, despite the ordering of the letters, it's generally understood that the M and D (like the A and S) get equal priority, and should be operated left to right. Therefore, the only right way to read it is equivalent to (6÷2)(1+2), which equals nine.
posted by Sys Rq at 7:54 PM on March 13, 2013 [2 favorites]

Actual question from a first grade math test one of my children took last year: There are three ones and three tens. How many ones and tens are there together?
posted by humanfont at 7:58 PM on March 13, 2013

it's generally understood

Nice hand wave there, but it clearly isn't generally understood like that. All that means is you understand it like that. I was a math undergrad and I would evaluate that expression to 1 if a gun was put to my head, but it's a stupid stupid argument to have because brackets motherfuckers.
posted by unSane at 7:58 PM on March 13, 2013 [8 favorites]

Or to put it another way, either answer is correct because the expression is capable of (at least) two equally valid interpretations.
posted by unSane at 8:00 PM on March 13, 2013

(and left-to-right evaluation is just as arbitrary as multiplication-first evaluation)
posted by unSane at 8:01 PM on March 13, 2013 [1 favorite]

Old math v. new math makes no difference. The internal operators happen first. The answer is one.
posted by maggieb at 8:04 PM on March 13, 2013 [4 favorites]

(and left-to-right evaluation is just as arbitrary as multiplication-first evaluation)

Of course it's arbitrary, but it's conventional. English is written left to right, and that's every bit as arbitrary, but if someone were to write it backwards, you'd be right to say they were doing it wrong.
posted by Sys Rq at 8:07 PM on March 13, 2013 [1 favorite]

Just for fun, I want to go into the comment thread on the original article and explain what a C++ typedef is and how many of them keep the planes flying.
posted by RobotVoodooPower at 8:07 PM on March 13, 2013

I'd say 1, in an older, get-off-my-lawn sort of way. For reasons already stated.

Or 7, to be contrary, as expand the brackets first, which gives you 2 + 4, then 6/2 = 3, + 4 = 7.
posted by carter at 8:11 PM on March 13, 2013

It isn't ambiguous, though.

I mean, yes, the author could mean 6 ÷ (2(1+2)), but that's not what they wrote, and if that's what they meant, they wrote it wrong. In PEDMAS or BOMDAS or whatever, despite the ordering of the letters, it's generally understood that the M and D (like the A and S) get equal priority, and should be operated left to right. Therefore, the only right way to read it is equivalent to (6÷2)(1+2), which equals nine.

Your working under the assumption that the author meant it to be understood at all.

It was intentionally written ambiguously, using notation poorly suited to the problem.
posted by empath at 8:15 PM on March 13, 2013 [2 favorites]

I guess all I'm saying is that, while it could certainly be made less ambiguous, it is not actually ambiguous at all according to how I was taught, which I presume (with all the potential for utter wrongness that word promises) is the conventional way of doing things.

And, according to that convention, I got that shit wrong when I said it was 1, so, yes, I do indeed suck at math as it was taught to me. Yay!
posted by Sys Rq at 8:17 PM on March 13, 2013

Of course it's arbitrary, but it's conventional.

Honestly, not to mathematicians. Maybe to programmers (but I would always use brackets in a situation like this).
posted by unSane at 8:17 PM on March 13, 2013

It's a standard convention. Does anyone arguing for 1 have a cite that it's not? I can't find another convention on google, outside of some programming languages that do strict left-to-right. What else is in such common use among mathematicians that deviates from the PEMDAS/BODMAS standard?

If you want to specify another convention, include it in the question. If the question was "evaluate 6/2(1+2), giving implicit multiplication a higher precedence than division", then you get 1. Which is fine. But it wasn't the question.
posted by mrgoat at 8:18 PM on March 13, 2013 [1 favorite]

posted by Glibpaxman at 8:20 PM on March 13, 2013 [2 favorites]

Bottom line: PEMDAS is evil.

All the feet who celebrate that particular holiday are furious that you have insulted their traditions.
posted by louche mustachio at 8:20 PM on March 13, 2013

It's a standard convention

It's not standard convention to use the ÷ in problems like that.

I guess all I'm saying is that, while it could certainly be made less ambiguous, it is not actually ambiguous at all according to how I was taught

The way math is taught in elementary school is not the only way that math can be done.
posted by empath at 8:21 PM on March 13, 2013

The way math is taught in elementary school is not the only way that math can be done.

Well, then, by all means, give an example of another convention of mathematical notation in which this example of basic arithmetic can be interpreted to equal 1.
posted by Sys Rq at 8:33 PM on March 13, 2013

I'll give you that ÷ is not the standard sigil in use to signify division, it certainly isn't (which is why I've been using / instead), but that wasn't really my argument.

The way math is taught in elementary school is not the only way that math can be done.

Yes, true. But this is a question of the expectation of the order of operations. I'm being serious here, I was taught PEMDAS, and I can't find another way that is commonly accepted without being specified explicitly. I can find warnings that Excel doesn't follow "the standard", but not a commonly accepted alternative. Do you have one on hand? I mean, one with a big following or something?
posted by mrgoat at 8:36 PM on March 13, 2013

I guess all I'm saying is that, while it could certainly be made less ambiguous, it is not actually ambiguous at all according to how I was taught, which I presume (with all the potential for utter wrongness that word promises) is the conventional way of doing things.

If you submit an actual academic paper, and a reviewer is confused by your typesetting, arguing with them that oh my notation is totally clear it is you who are in the wrong is generally not going to work in your favor. Also, you don't really find yourself typesetting all constant expressions all that often. If you wrote something like x / 2(y+z) in an email, I suspect most people in the sciences would interpret it as x / (2*(y+z)) and not (x/2)*(y+z). However, some people will use latex even in informal communications, in which case there wouldn't be any ambiguity.
posted by Pyry at 8:36 PM on March 13, 2013 [1 favorite]

The English history teacher hit the girl with the umbrella. Never enrage a prescriptivist.
posted by chortly at 8:38 PM on March 13, 2013 [2 favorites]

It's a standard convention. Does anyone arguing for 1 have a cite that it's not? I can't find another convention on google, outside of some programming languages that do strict left-to-right. What else is in such common use among mathematicians that deviates from the PEMDAS/BODMAS standard?

The point is that this PEMDAS business is irrelevant. It's not an order of operations issue. It's exploiting shitty typography to make everyone make a choice about how to bracket the expression. Mathematicians don't have this issue because they use associativity to not write parentheses and thus don't need a convention on left to right vs right to left evaluation (at least not for arithmetic (it's a commutative ring!)--let's not mention the big left/right debate).
posted by hoyland at 8:41 PM on March 13, 2013 [1 favorite]

Only on Metafilter would this devolve into an argument on whether the relevant point is between shitty typography or proper evaluation of a math expression.

I don't disagree that it's shitty typography that's tricking some people.
posted by mrgoat at 8:47 PM on March 13, 2013 [1 favorite]

So, what I mean when I'm going on about associativity is the following. Associativity is the property where (a+b)+c = a+(b+c) and similarly for multiplication. (Subtraction and division are adding and multiplying by the additive and multiplicative inverses, respectively.) As a result, if you evaluate 2+3+5 from left to right and I do it from right to left (or in some random order if there were more than two additions) it makes no difference. This has nothing to do with PEMDAS, which is just telling you to do multiplication before addition and so on. The problem here is that they've (intentionally!) written it so you can't tell what the divisor is--whether it's just the 2 or the 2(2+1). They haven't told you what to take the multiplicative inverse of, in other words. Mathematicians don't have a left-right or right-left convention because one isn't needed--if it's ambiguous, you stick some parentheses in. (There's a whole business about whether you apply functions or act from the right or the left, but it's not relevant here.)
posted by hoyland at 8:49 PM on March 13, 2013 [1 favorite]

I'm being serious here, I was taught PEMDAS

PEMDAS has ambiguous cases and this is one of them. See the wikipedia article on it:

Exceptions to the standard
In cases where there is the possibility that the notation might be misinterpreted, parentheses are usually used to clarify the intended meaning, however due to the syntax of most major programming languages, it is usually hard or impossible to be ambiguous.
Similarly, there can be ambiguity in the use of the slash ('/') symbol in expressions such as 1/2x. If one rewrites this expression as 1 ÷ 2 × x and then interprets the division symbol as indicating multiplication by the reciprocal, this becomes

Hence, with this interpretation we have that 1/2x is equal to (1/2)x, and not 1/(2x). However, there are examples, including in published literature, where implied multiplication is interpreted as having higher precedence than division, so that 1/2x equals 1/(2x), not (1/2)x. For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division with a slash,[5] 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.[6] Wolfram Alpha treats implied multiplication without parentheses the same as explicit multiplication and implied multiplication with parentheses. 2x/2x, 2*x/2*x, and 2(x)/2(x) all yield x2.[7] The TI 89 and TI 86 calculators also yield x2 in all three cases.
Textbooks, tutorials and teachers generally highly recommend taking care to avoid writing potentially ambiguous expressions, using a horizontal fraction line format in handwritten documents or if mathematical typesetting is available, or by inserting additional parentheses.[citation needed]
Division is actually multiplication by the reciprocal. When you see something like x(y+z) in a an equation, you generally think of all of that as a single unit, so taking the inverse of one part of it is really unusual.

I think the difference here is between people who never touched math out of high school and people who took higher-level math like calculus and linear algebra, and actually need to make math work as opposed to people who memorized rules so they could pass a test.
posted by empath at 8:50 PM on March 13, 2013 [8 favorites]

I think the difference here is between people who never touched math out of high school and people who took higher-level math like calculus and linear algebra, and actually need to make math work as opposed to people who memorized rules so they could pass a test.

OH YEAH WELL I DIDN'T EVEN PASS, SMARTY-PANTS! SHOWS WHAT YOU KNOW
posted by Sys Rq at 8:55 PM on March 13, 2013 [2 favorites]

lastobelus: "Just out of curiosity, a question for the 9ers:

How do you solve 8 ÷ 2x where x = 2. If you solve it as 2, why do you treat this implicit multiplication differently?

Would you solve 8 ÷ 2(x) as 8? Are the parentheses standing in for an explicit multiplication
"

8 / 2 * x
and
8 / 2 * (x)

are exactly the same thing, and, when x is 2, solve to 8.

People seem to get confused by the removal of the symbols.
posted by graventy at 8:55 PM on March 13, 2013

Sorry, that came off as way condescending. It's just the fault of terrible high school teachers that people think of math that way, honestly.
posted by empath at 8:56 PM on March 13, 2013

That amused me way more than I thought it would, especially since I got 1. I'm not sure if that makes me like obeluses more or less.
posted by Sticherbeast at 8:59 PM on March 13, 2013

Spotlight in Mac OS 10.6 says 6 / 2(1+2) = 1. I blame Apple's recent stock declines on this.
posted by DakotaPaul at 9:04 PM on March 13, 2013

8 / 2 * x
and
8 / 2 * (x)

are exactly the same thing, and, when x is 2, solve to 8

No, these suffer from the same ambiguity.
posted by hoyland at 9:06 PM on March 13, 2013

In that case the brackets as written don't remove the ambiguity.

The ambiguous cases are:

(8/2)*x = 4x

and

8/(2*x) = 4/x

Part of the problem is that we're using '/' as a divisor, when in any remotely serious context you would write the expression with a long horizontal stroke dividing numerator and denominator, either in longhand or Latex.
posted by unSane at 9:13 PM on March 13, 2013 [1 favorite]

(And for that reason I tend to read the '/' as shorthand for 'everything that follows this is the denominator, because I read it as a horizontal line)
posted by unSane at 9:14 PM on March 13, 2013 [1 favorite]

No, that helps, empath. Thanks. In the example of 1/2x, I would have figured that meant (1/2) * x, (natural language: "one half x") which your cite specifies, but then goes on to say that some published journals and physics textbooks give higher precedence to implied multiplication. That's actually what I hadn't seen. It still looks like a break with a more common convention though. I guess I just never ran across a situation where "1/2x" would mean anything other than (1/2)*x.

I still prefer to use (and frequently, overuse) parentheses. But it's always been because most people I deal with have no idea what to do with math. I guess I'll keep doing it so as not to confuse people who are good with math as well.

Part of the problem is that we're using '/' as a divisor, when in any remotely serious context you would write the expression with a long horizontal stroke dividing numerator and denominator, either in longhand or Latex.

Right. Because my compiler knows what to do with that.
posted by mrgoat at 9:15 PM on March 13, 2013

Whoah, you guys are still here??

I can try to explain why 1 seems to me the more natural answer, though of course it is silly to talk about the "right" answer in this context.

The only reason I can think of to write 6 / 2(1+2) would be a context where you were substituting n = 1+2 into the expression 6/2n, and in this case the answer is 1.

If you were planning to multiply some value n to be multiplied by 6/2, you would surely write 6n/2, and then when you found that n was expressible as the sum of two other things, you would write 6(1+2)/2.

In the example of 1/2x, I would have figured that meant (1/2) * x,

Yeah, so this is a good example -- it's totally possible that some convention that somebody wrote down someplace tells you to interpret the string 1/2x as (1/2)*x, but in real life, 1/2x means the reciprocal of 2x. I don't know what PEMDAS is but it's certainly not something I've ever seen people adhere to in real life -- I suppose it must be like the formal rules of "English grammar" one sometimes sees written down, which in many cases are compliant with actual English, but in other cases deviate from it.

(Source: I am a mathematician and write lots of (non-LaTeX) e-mail involving algebraic expressions.)
posted by escabeche at 9:23 PM on March 13, 2013 [6 favorites]

My doctor made me drink PEBKAC once before doing some tests. It was disgusting.

(°÷°)
(° . °)
[] °!° []
posted by louche mustachio at 9:28 PM on March 13, 2013 [1 favorite]

The correct answer, as usual, is, disambiguate the question.
posted by bricoleur at 9:30 PM on March 13, 2013 [3 favorites]

The only reason I can think of to write 6 / 2(1+2) would be a context where you were substituting n = 1+2 into the expression 6/2n, and in this case the answer is 1.

irb(main):010:0> n=1+2
=> 3
irb(main):012:0> 6/2*n
=> 9

Maybe programming has just given me a habit of putting in my operators explicitly? I can't depend on the luxury of LaTeX. Or, for that matter, anything outside of the basic ASCII set.
posted by mrgoat at 9:36 PM on March 13, 2013

See this stack exchange discussion on multiplication by juxtaposition and programming languages.
posted by empath at 9:41 PM on March 13, 2013

to wit: So, the question is whether a/bc means (a/b)c or a/(bc). And the answer is, DON'T WRITE a/bc, because it will only cause confusion. Some people/software/whatever will make one interpretation, some will make the other, neither one has been endorsed by the Dalai Lama or any other great leader. Put in enough parentheses to make your writing foolproof.
posted by empath at 9:42 PM on March 13, 2013 [2 favorites]

I immediately disregard the obelus because no one uses that symbol in real math*. Thus the equation becomes
```  6
_____
2(1+2)
```
which is unambiguous. Factor out the two, it becomes
``` 3
___
1+2
```
which is clearly equal to 1.

So the correct answer is when the answer actually matters, you'd better learn how to write an unambiguous equation, asshole.

*Real math defined as day-to-day operations used in any scientific field in which I have worked.
posted by caution live frogs at 9:42 PM on March 13, 2013 [12 favorites]

Lastobelus "I'm pretty sure most who answer 1 (as do I) would answer 6 ÷ 2*(1+2) as 9. At least I would."

Exactly. That's what Mac OS spotlight answers.

I'm with the 1%
posted by panaceanot at 9:49 PM on March 13, 2013

Somewhere, the guy who made this is laughing hysterically, I think.

BTW, this thread is a shining example of why I love Metafilter. Who knew you could learn so much from a stupid Facebook challenge?

Oh yeah, the answer‘s still nine. Heh.
posted by Jughead at 10:01 PM on March 13, 2013

My calculations show that I (still) fucking hate math.
posted by Space Kitty at 10:02 PM on March 13, 2013 [2 favorites]

Honestly, I would never have predicted that we'd have started arguing about how to use division in math problems on facebook. I can't tell if this is a more intelligent or a less intelligent thing to be mad about. This could be progress, or it could be the worst.

I feel like I'm turning into the Smashing Pumpkins on the Hullabaloo tour: I don't even know anymore, man.
posted by Kiablokirk at 10:15 PM on March 13, 2013

Also: ...The Room

No good, The Room starred Tommy Wiseau, and that's two 'S's right there.
posted by cortex at 10:33 PM on March 13, 2013

cortex: となりのトトロ?
posted by aubilenon at 10:40 PM on March 13, 2013

1, on the grounds that multiplication by juxtaposition and division by / or by vinculum (I learned a new word!) are high-school and up (including professional) notation , while × for multiplication and ÷ for division are grade-school symbols, and professional notation takes precedence over the kiddie symbols.

Only half-joking there. Serious inasmuch as I mean to point out that mixing the two is at least partially responsible for the confusion. It's kind of like writing "sodiumOH" which is bizarre and would leave chemists scratching their heads even if they understood what you meant, as you're mixing different notations. Although it's not a perfect analogy as you don't have the kiddie/professional distinction there: either "sodium hydroxide" or "NaOH" would be acceptable.

For those arguing 9 on grounds of "all multiplication and division to be done left to right, regardless of particular notation used," I pose the following question:

6 ÷ 1/2 = ?
posted by DevilsAdvocate at 11:04 PM on March 13, 2013 [4 favorites]

TimeCube was right: we were ALL educated stupid.
posted by Uther Bentrazor at 11:09 PM on March 13, 2013

This whole thing kinda strikes me as more or less a trck question intended to confound, as in:

Punctuate the following:

What is the subject of this sentence
posted by ShutterBun at 11:29 PM on March 13, 2013 [4 favorites]

ShutterBun: Is the right answer to put ?!?!?!!!!?!! at the end?
posted by aubilenon at 11:40 PM on March 13, 2013 [1 favorite]

Metafilter: calculating plates of beans since 1999
posted by J.W. at 12:28 AM on March 14, 2013

J.W.: "Metafilter: calculating plates of beans since 1999"

Metafilter: OVERcalculating plates of beans since 1999

FTFY.
posted by Samizdata at 1:08 AM on March 14, 2013

Another Facebook question making the rounds: How many squares do you see?
posted by Red Loop at 2:47 AM on March 14, 2013

I'm still confused why so many people think the issue is whether * has a higher order of precedence than ÷ and not that the issue is that there is an IMPLICIT multiplication, and whether implicit multiplication has a higher order of precedence than BOTH * and ÷, despite the fact that the article spends several paragraphs discussing exactly that.
posted by lastobelus at 3:20 AM on March 14, 2013 [4 favorites]

Curious as to why people are getting worked up about the ÷ symbol, when everyone knows what it means.
posted by yath at 4:27 AM on March 14, 2013

Because what's being divided by is ambiguous if you don't use a horizontal bar and/or parentheses. You can replace the ÷ with a / or any other symbol you like, and it's still ambiguous. Division is multiplication by an inverse, and the ÷ doesn't really properly mark off what's being inverted. A horizontal bar does, and parentheses do.
posted by empath at 4:38 AM on March 14, 2013 [4 favorites]

Its absurd that an obvious NOTATION problem can develop into such arguments. This is the sort of notational ambiguity that results in blown up shuttles but has absolutely nothing to do with actual Mathematical concepts.
posted by mary8nne at 5:01 AM on March 14, 2013 [1 favorite]

I am a 51 year old white guy!

And I did get 9!

OP is a warlock!!!!
posted by The Deej at 5:42 AM on March 14, 2013

I don't have to work out other people's equations, and haven't for decades. I do sometimes try to figure something out for my own purposes by expressing it as an equation, and then I know unambiguously what order of operations I intended.
posted by jfuller at 6:08 AM on March 14, 2013

Also, data point - I'm a scientist.

posted by Sophie1 at 6:39 AM on March 14, 2013 [2 favorites]

Still not clear on what the Goddamn SATs think is correct. Anyone?
posted by IndigoJones at 6:50 AM on March 14, 2013

like jfuller, I do sometimes try to figure something out for my own purposes by expressing it as an equation, and then get completely lost and forget all my calculations.
posted by ambrosen at 6:58 AM on March 14, 2013

Still not clear on what the Goddamn SATs think is correct.

The SATs would not ask an ambiguous question like this in the first place. And if they did and discovered it after the fact, they would throw out the question—as they have on a few occasions in the past.
posted by DevilsAdvocate at 7:14 AM on March 14, 2013 [1 favorite]

The SATs would not ask an ambiguous question like this in the first place. And if they did and discovered it after the fact, they would throw out the question—as they have on a few occasions in the past.

Sounds like the making of a solid FPP, if it has not been done so already.
posted by coolxcool=rad at 7:23 AM on March 14, 2013

As has been pointed out, all this shows is that people are unclear about the difference between order of operations and the left-right or right-left associativity of multiplication operators.

If you really want to start a math Facebook fight, you should reexamine your life. No seriously, to start fight, just ask people if the repeating decimal .9999999......... is equal to 1.

Actually if you want to do this, reexamine your life. There must be something better you can do with your time than ask people who aren't mathematicians for their opinions on that issue.
posted by thelonius at 7:50 AM on March 14, 2013

After taking years of advanced math, here's how I would do it:

6/2(1+2)=x

There are not enough letters in this equation, so let's change everything over to letters.

A/B(C+B)=x

Now we know that C can be rewritten in terms of B:

A/B(B^y+B)=x

And since C was less than B, y must be less than 1. Therefore, B^y is negligible compared to B and we can ignore it.

A/B(B) = x

Which can be reduced to:

A/(B^2) = x

As A and B go to infinity, B is the dominant factor in this expression. The answer must be on the order of B^-2

x= O(B^-2)

Now, if you want an approximation that you can use to solve real-world problems, try the Order of Operations Handbook (E.U. Clid, et al) where x is tabulated in terms of a variety of A and B values.
posted by backseatpilot at 7:57 AM on March 14, 2013 [1 favorite]

Alternatively, A/B(B) = A, so x=A, giving the answer 6.
posted by unSane at 9:07 AM on March 14, 2013

it's mixing two different forms of operation, which is as confusing as using MLA endnotes and footnotes simultaneously, with each note reference pointing to two conflicting notes. multiplication by juxtaposition, 2(1+2), puts one in an algebraic framework such that one views it as 2x (where x = 1 + 2) and evaluates that expression first.

so pretty much the people who never mastered beyond basic math will answer 9 and those who thrived in algebra will correctly evaluate it as 1.
posted by fallacy of the beard at 9:07 AM on March 14, 2013 [2 favorites]

Students understand that (5-4) + 3 = 5 + (-4+3). Clear now?

In my experience tutoring students in math, this statement is not generally true, and for older students than one would like.

Wolfram Alpha treats implied multiplication without parentheses the same as explicit multiplication and implied multiplication with parentheses. 2x/2x, 2*x/2*x, and 2(x)/2(x) all yield x2.

What? No.
posted by jeather at 9:15 AM on March 14, 2013

also, the grammar of multiplication by juxtaposition, by the very proximity of its notation, indicates a 'tighter' multiplication bond. with 2 * x, each operand is discrete...either one could run off with a different partner at any time, but with 2x, those dudes are married and face the world together, evaluating themselves first and foremost.
posted by fallacy of the beard at 9:16 AM on March 14, 2013

Still not clear on what the Goddamn SATs think is correct.

Well, if you want to believe Slate, it's 9.
You can alternatively apply PEMDAS as schools do today: Simplify everything inside the parentheses first, then exponents, then all multiplication and division from left to right in the order both operations appear, then all addition and subtraction from left to right in the order both operations appear. (A better acronym would be PEMA, actually, to make it clear that multiplication and division are done together, and addition and subtraction are done together.) By that convention, 6 ÷ 2(1+2) = 6 ÷ 2 × (1+2) = 6 ÷ 2 × 3 = 3 × 3 = 9. If you were taking the ACT, SAT, or GRE (which would probably use parentheses to eliminate confusion), this method would yield the correct answer.
posted by achrise at 9:16 AM on March 14, 2013

The threshold for calling something a math problem has sunk frighteningly low.
posted by oxidizer at 9:36 AM on March 14, 2013

Wolfram Alpha treats implied multiplication without parentheses the same as explicit multiplication and implied multiplication with parentheses. 2x/2x, 2*x/2*x, and 2(x)/2(x) all yield x2.

In fact, even Alpha is not consistent about it -- it depends on what the operands are! Consider how it treats a/bc + a/2c: the first term gets "bc" in the denominator, while the second only gets 2, not 2c. And it's not because it thinks bc is a unique variable name; it's simplification shows that it understands bc to be (b)(c). It treats implied multiplication as having higher precedence than the division when the operands are variables, but of equal precedence (and hence evaluated in order left to right) when there's a number.
posted by Westringia F. at 9:44 AM on March 14, 2013 [4 favorites]

Range --

Thanks for that comment. I recently got all hatey on Verilogs order of operations for this:

a + b<<c

I always thought it was a Verilog peculiarity that << didn't have the same precedence as *, since << is basically a multiple by some number of 2s.

Your comment made me look up the C order to see it is the same. That's crazy.
posted by jclarkin at 9:45 AM on March 14, 2013

If you were taking the ACT, SAT, or GRE (which would probably use parentheses to eliminate confusion), this method would yield the correct answer.

"If you were taking the ACT, SAT, or GRE, they would ask another question which did not have the same notational ambiguity, and that question would have a definite answer."
posted by Sticherbeast at 10:11 AM on March 14, 2013

32. Solve this equation: 6 ÷ 2(1+2) =

a. 9

b. 1

c. ask for further clarification of the problem

d. START A REVOLUTION!!!!
posted by coolxcool=rad at 10:16 AM on March 14, 2013 [1 favorite]

i think the problem presented here is less a test of mathematics than an indicator of rote versus conceptual thinking. agents of the latter can detect an associativity in the equation that is too subtle for grade-school mnemonics.

appeals to programming conventions and computational engines are a bit silly; perl can calculate 9 * 5 but cannot tell you why you are multiplying 9 by 5. nor do i evaluate the content of a photograph by performing a systematic analysis of its pixel content.
posted by fallacy of the beard at 10:21 AM on March 14, 2013

This "problem" disappears just as soon as you write division the way God intended: as a friggin' fraction - and when I say fraction, I don't mean a piddly forward slash, but a horizontal line with a term on top and one below. Done.
posted by oxidizer at 11:35 AM on March 14, 2013 [1 favorite]

nor do i evaluate the content of a photograph by performing a systematic analysis of its pixel content.

You do if you want to deal with it using math.
posted by Malor at 11:38 AM on March 14, 2013

I think it is kind of interesting that the people who do tend to write out at least some math in plain text from time to time also seem to be the people who carry out the operations in the order that results in 1. While plain-text mathematical expressions quickly get either hairy or ambiguous, there is definitely a sorta-kinda community convention on how to write certain statements.
posted by Nomyte at 12:36 PM on March 14, 2013

I don't have time for this, I'm still trying to think of a movie that doesn't have the letter S in it.

Pootie Tang. You're welcome.

assuming this was a serious debacle
posted by davejay at 12:50 PM on March 14, 2013

6/2(1+2) = -2+8

The "/" symbol indicates subtraction, in my math symbol system.

The "(", ")" symbols indicate addition, in my math symbol system.

The "+" symbol denotes the decimal point, in my math symbol system.

The "-" symbol indicated negativity, in my math symbol system.

The order of precedence is -, (), +, /, in my math symbol system.

My answer is as valid as anyone else's, since the particular math symbol system wasn't specified.
posted by IAmBroom at 2:08 PM on March 14, 2013

I just found out that there is a programming language that actually uses ÷ for division. You guessed it, it's APL. And in APL, evaluation is from right to left. So, there seems to be a multiplication symbol missing, but from a programmer's perspective, the answer should obviously be 1.
posted by ikalliom at 2:27 PM on March 14, 2013

APL isn't a programming language, it's a clever way to detect alien intelligences in our midst.
posted by benito.strauss at 2:45 PM on March 14, 2013

I just found out that there is a programming language that actually uses ÷ for division. You guessed it, it's APL. And in APL, evaluation is from right to left. So, there seems to be a multiplication symbol missing, but from a programmer's perspective, the answer should obviously be 1.

You mean an APL programmer's perspective? Regular programmers are probably going to get 9 most of the time, at least if they parse the problem as computer languages do.
posted by Malor at 3:38 PM on March 14, 2013

40 - 32 ÷ 2 = 4

In MUMPS it does. MUMPS listens to parenthesis but otherwise, it goes strictly left to right. It does keep things simple even if it is different than almost every other programming language.

I think the mentions of programming languages is interesting because any (non-awful) language has to specify this kind of thing. There is only one valid answer in the context of any given computer language. Stuff way more subtle than this can easily trip you up if left to the winds.

Shouldn't algebraic expressions like this one have exactly one correct interpretation? Asking for more parenthesis to clarify is nice, but wouldn't mathematics be better if it didn't allow for needless ambiguities? I guess we don't have the same standards mechanisms?
posted by Foolhardy at 10:30 PM on March 14, 2013

Shouldn't algebraic expressions like this one have exactly one correct interpretation? Asking for more parenthesis to clarify is nice, but wouldn't mathematics be better if it didn't allow for needless ambiguities? I guess we don't have the same standards mechanisms?

If you were using standard mathematical notation for this problem, there wouldn't be any ambiguity.
posted by empath at 10:54 PM on March 14, 2013 [1 favorite]

For maximum parentheses we should try to translate "6 ÷ 2(1 + 2)" into lisp. We can't escape the fuss is over which is the most appropriate interpretation, but we can express them consistently and unambiguously:
1. `(/ 6 (* 2 (+ 1 2)))`
2. `(/ 6 (/ 2 (+ 1 2)))`
Alternatively,
1. `(/ 6 2 (+ 1 2))`
2. `(* 6 1/2 (+ 1 2))`
Personally, I think #1 wins on aesthetic and most-likely-what-the-author-meant grounds, but I feel skeptical about rationalizing it mathematically. I feel much less skeptical about the rationalizations for #2, but it's not enough to make up the difference.
posted by wobh at 1:12 AM on March 15, 2013

The answer is 1. 2x is not the same as 2 * x.

2x means (2 * x)

X is (1+2)

so 2x means (2 * (1+2))

It's not ambiguous if you remember algebra.
posted by gjc at 4:14 AM on March 15, 2013 [1 favorite]

It's not ambiguous if you remember algebra.

This is completely false. Your theory about 2x being (2*x) doesn't allow one to write 2*3*5.
posted by hoyland at 5:26 AM on March 15, 2013 [1 favorite]

And that one can write 2*3*5 without ambiguity is associativity which is kind of necessary. (Yes, there are non-associative things. I don't think we encounter any in elementary school.)
posted by hoyland at 5:27 AM on March 15, 2013 [1 favorite]

This is completely false. Your theory about 2x being (2*x) doesn't allow one to write 2*3*5.

It's not a "theory". I'll use a different variable in case that's what is confusing you.

2y = (2 * y)

Nothing about that rule precludes one from writing 2*3*5. The rule just says that when you use the 2y notation; that is, implied multiplication without an explicit operator, that takes precedence. 6 / 2y is not the same as 6 / 2 / y. 2y is one "blob" and should be solved for first. 6 / 2y = 6 / (2 * y)

(Moving to whiteboard)

We first follow the order of operations and simplify (1+2) to 3. Then we replace 3 with y. I think everyone can agree that's perfectly cromulent.

Now we assume the answer is 9 and solve backwards for y. We do not get y = 3.

In the second picture, we assume the answer is 1 and again solve backwards for y. This time we DO get y=3. The answer to the problem is 1.
posted by gjc at 8:26 AM on March 15, 2013 [1 favorite]

Nothing about that rule precludes one from writing 2*3*5. The rule just says that when you use the 2y notation; that is, implied multiplication without an explicit operator, that takes precedence.

I'm saying this rule does not exist. Mathematically, 'implied multiplication' is no different from 'multiplication'. Swap my 2*3*5 for xyz if it makes you happy. Multiplication is a binary operation. You have to decide if you're doing xy or yz first (or even xz first). So you're now going to require me to do it left-to-right or right-to-left. But the whole point is that this is not a choice one makes. In fact, it's a choice you must not be forced to make, otherwise all manner of things are going to go pear-shaped.

Guess what? My default parsing of the statement gets me 1, so you needn't condescend to me with your whiteboard. Doesn't make either of us right. The statement is ambiguous, full stop.
posted by hoyland at 9:49 AM on March 15, 2013

> like jfuller, I do sometimes try to figure something out for my own purposes by expressing
> it as an equation, and then get completely lost and forget all my calculations.

I should maybe clarify that I too am a member of the There's No Such Thing As Too Many Parens school and I use them by the truckload. I got this habit from my very first programming language (Applesoft BASIC) in which I tried typing in expressions the way I was used to writing them with a pencil, only to find Applesoft reducing them to something totally unanticipated. WTF dids this thing just do's? So, being a budding RTFM compulsive, I R'd the FM and discovered that Applesoft's order of operations was a defined and documented thing. There was a whole dense chapter on it in the manual that came in the same box as the 140k single-sided single-density Applesoft floppy.

I was just setting out to read and study and learn the OoO when I suddenly thought "Wait. Parentheses." And that's the way I've done it ever since. (I'm not quite that compulsive.)

Though I did pick up the ()s habit from BASIC, I do not think they count as brain damage.
posted by jfuller at 12:31 PM on March 15, 2013

Mathematically, 'implied multiplication' is no different from 'multiplication'.

Mathematically, it doesn't matter what precedence rules you use in that case, as long as you're consistent.
posted by empath at 3:16 PM on March 15, 2013 [1 favorite]