Solve this simple math problem: 48/2(9+3)

[ncl]

There is little room for opinions in mathematics.

In maths, sure. But mathematical notations are *full* of ambiguities (just read gnasher's examples). This is one of them. And it has nothing to do with "one's understanding of order of operations."

As I wrote, the American Mathematical Society tells you "multiplication indicated by juxtaposition is carried out before division". The American Institute of Physics tells you "don't write 1/3x unless you mean 1/(3x)". The best I could find not leaning in this way was that the notation is ambiguous and should not be used (from a statistics institute, don't remember the country though).
Of course, you could still argue that the people in the AMS or AIP are just a bunch of morons who don't know their basic maths.

Lastly, it is quite poor math discussion skills to suggest that the right answer is merely an opinion.

Not in this case. It's a misunderstanding based on the fact that this expression can be interpreted in two different ways because of two different widespread conventions.
That's the reason I searched more on this issue. When I first read it, my first thought was "Who could be stupid enough to get 2 ?". Then it hit me: in a lot of books or papers I've read (I would even say, the majority of them), this expression would be evaluated as 2, because they used the juxtaposition=grouping rule. The other books avoided inline divisions entirely or used enough parenthesis to avoid any confusion.
And in the end, nobody cares. Based on context, you automatically get the convention used by the person who wrote the expression, without even thinking about it. Except, in this case, there isn't any context. Hence ambiguity.

People should realise that this problem, this misunderstanding, has very little to do with actual maths and more with typography.

And I will finish with this (I've wasted too much time on this ). You can argue all you want about who is right and who is wrong, it is pointless: this debate has been going for (at least) 40 years !

Now, skimming through this thread and others, I'm starting to think that the 50/50 split is more likely due to half the people learning PEMDAS and the other half learning PEDMAS, which is quite saddening

 

[iJohnHenry]

Now, skimming through this thread and others, I'm starting to think that the 50/50 split is more likely due to half the people learning PEMDAS and the other half learning PEDMAS, which is quite saddening

The vagaries of scientific notation make you sad?

You need to get out more. Oh, and turn on your TV.

 

[Mac'nCheese]

Previous residence in your butt, I believe.

Pointing out that I'm not a liar makes me stuck up? Ok.

at least you are being nice.

however you also are (more politely) making the same mistake that since many posters provide a 'demonstration' that agree with your position, than you conclude that your position is correct and all the 'demonstrations' that agree with the opposite views are incorrect and their proponent just 'refuse to admit that they are wrong'.



however, if you actually look at the links, they either only have the simple bedmas cases (which nobody contests) or, when they do have examples that resemble the problem mention here (with implied multiplication following a division sign) they actually conclude very clearly, that the implied multiplication is performed before the division, hnece the correct answer would be 2 not 288.




so, now that i have 'demonstrated' that 288 is not correct, are you going to come here and admit that you are wrong? or at least that it is ambiguous?

I would have no problem admitting either if proved. I looked at some of the links you showed and didn't see anything that would do either. You can feel free to cut and paste and show me what I missed. From what I see, everyone's proof of the answer 2 or that this is ambiguous always uses some sort of "when a problem is discussed in this way..." or "sometimes you could do this, IF the problem was this...." I see no proof that this very simple math problem, when taken exactly as written, has one very clear answer, 288. This is a simple test of a child's knowledge of the order of operation, plain and simple.

 

[ncl]

The vagaries of scientific notation make you sad?

No. That is actually fun (and can even be interesting). It's the fact that people will remember a stupid acronym but not its meaning.

You need to get out more.

A lot of people tell me that, but I never understand why

Oh, and turn on your TV.

I would, if only there was something interesting to watch...

 

[TuffLuffJimmy]

I would have no problem admitting either if proved. I looked at some of the links you showed and didn't see anything that would do either. You can feel free to cut and paste and show me what I missed. From what I see, everyone's proof of the answer 2 or that this is ambiguous always uses some sort of "when a problem is discussed in this way..." or "sometimes you could do this, IF the problem was this...." I see no proof that this very simple math problem, when taken exactly as written, has one very clear answer, 288. This is a simple test of a child's knowledge of the order of operation, plain and simple.

Here here.

I will admit, however, multiplication by juxtaposition does take precedence over other operations in some cases, usually in formulaic situations and that's only because the juxtaposition is short hand and should be understood as a single value. In this case it obviously has no precedence.

 

[MarkCollette]

purplemath, example 5: http://www.purplemath.com/modules/orderops2.htm
bctf, page 4 (2 in the page numbering in the pdf) example 3

I've read this thread, and the only website anyone's given, for their bizarre broken order of operations has been the purple math site. Well, they're wrong. And given the bazillion of other site that disagree with that one site, I think it's clear they made the mistake.

But let me spell out why I consider them wrong

16 ÷ 2[8 – 3(4 – 2)] + 1

Given the use of brackets () and [], I would assume that whoever made this equation is not relying on arcane order of operations rules, but is in fact being explicit. So, when it comes down to:

16 ÷ 2[2] + 1

I'm going to assume that since they used brackets everywhere else, and did not use a bracket to contain 2[2] as [2[2]], that they full well know that the division happens before the multiplication.

Put another way, if this magical "like terms" operator somehow has more precedence than multiplication and division, then which precedence does it have? If I have:

2x^2

If 2x is a like term, and has higher precedence than multiplication and division, does it also have higher precedence than exponents? Does it mean:

(2x)^2 gives 4xx

No, obviously not. So now we're saying that it somehow lies in-between exponents and /* on the precedence scale, but that none of the literature explains it as a special step, except for one practice example on one website.

Phew, that's pretty cool that one website can define how math works.

 

[balamw]

I've read this thread, and the only website anyone's given, for their bizarre broken order of operations has been the purple math site. Well, they're wrong. And given the bazillion of other site that disagree with that one site, I think it's clear they made the mistake.

The AMS link from the wayback machine provided earlier in the thread is a "hard math" link that supports this view. (http://waybackmachine.org/jsp/Inter...tp://www.ams.org/authors/guide-reviewers.html)

My problem with it is that I see it as an artificial typesetting convention.

1/2n or 1/2pi are one thing, but it breaks for me when the parentheses are added. (Bold p is supposed to be pi)

1/2(n+1) however ...

B

 

[McGiord]

A video answer

http://www.youtube.com/watch?v=B5XfCE_x6S4&feature=youtube_gdata_player

 

[MarkCollette]

The AMS link from the wayback machine provided earlier in the thread is a "hard math" link that supports this view.

So you mean something that's not actually on the Internet anymore? The AMS site is still there, so did they remove that resource themselves? Possibly since it's wrong?

EDIT: Added next part.

Oh wow, you guys are using a resource that's not an actual math resource, but is something about how to write TEX formulas to save on printing costs.

Formulas. You can help us to reduce production and printing costs by avoiding excessive or unnecessary quotation of complicated formulas. We linearize simple formulas, using the rule that multiplication indicated by juxtaposition is carried out before division. For example, your TeX-coded display

$${1\over{2\pi i}}\int_\Gamma {f(t)\over (t-z)}dt$$

is likely to be converted to

$(1/2\pi i)\int_\Gamma f(t)(t-z)^{-1}dt$

in our production process.

 

[balamw]

Oh wow, you guys are using a resource that's not an actual math resource, but is something about how to write TEX formulas to save on printing costs.

As I said, an artificial typesetting convention.

As you point out it isn't in the current version of the same document. Why?

I'm a 288 guy, but I do read the (1/2 pi i) stuff as it is intended. I don't know if it's the typesetting or the parentheses around it.

B

 

[Mac'nCheese]

http://www.youtube.com/watch?v=B5XfCE_x6S4&feature=youtube_gdata_player

I think we've found our new hitler in the bunker video. thanks for the laugh!

 

[RITZFit]

288 because that's what my TI-89 told me...

 

[125037]

288 because that's what my TI-89 told me...

I love those! They factor for you and everything. Best calculator ever.

 

[ncl]

Possibly since it's wrong?

FFS, it's _not_ wrong ! They removed it simply because at some point, they stopped reformatting the formulas.

If you want a resource still online: http://www.aip.org/pubservs/style/4thed/AIP_Style_4thed.pdf
I couldn't find a more recent version and it still is on the AIP servers. Page 23: "never write 1/3x unless you mean 1/(3x)" And it has nothing to do with printing cost but much more to do with readability and avoiding ambiguity. For years, tons of books and papers have been written (and are still written) with the convention that a/bc == a/(bc). People have been drilled with that convention, others not. That's the reason behind this argument.

Also, what AhmedFaisal said. At school (also in Europe but not Germany, but it was nearly a decade ago), "/" stood for the horizontal fraction bar and everything after was considered as part of the denominator. At the uni, as far as I can remember they never used "/" and always used the horizontal fraction bar (except when even that was ambiguous).

Again you can argue all you want that the people interpreting in one way or the other are wrong, but the fact is both are right and that this question has been debated for more than 40 years and there still isn't an agreement on the matter. And for more references: http://www.ntg.nl/maps/26/16.pdf Fifth page (numbered 124).

I'm a 288 guy, but I do read the (1/2 pi i) stuff as it is intended. I don't know if it's the typesetting or the parentheses around it.

And how would read this: |⟨X1,X2⟩|/∥X1∥∥X2∥ (one of the example in the above document) ?

In the end, gnasher729 said it best (post 103 at page 5 [25 posts per page]):
"The premise is incorrect from the start - this is not a mathematical problem, it is a problem of noting a very simple formula using ASCII characters only, and deciding how that sequence of ASCII characters should be interpreted."

 

[roadbloc]

Same brand scientific calculator, two different answers.

You're holding it wrong.

 

[balamw]

And how would read this: |⟨X1,X2⟩|/∥X1∥∥X2∥ (one of the example in the above document) ?

If typeset in TeX I would read it as the 2 camp intends. However, not in straight ASCII in an e-mail.

Again for me there are two major issues with this:

1. ASCII, unformatted e-mail vs. typesetting using TeX
2. A "formula" that includes only numbers

All the references are about properly formatted, typeset math using TeX, which is a very different beast than straight ASCII.

If the formula was presented with variable names x1/x2(a1+a2) and gave values for the variables and the context was clearer you might be able to suss it out better as in the case of

which I see as rather different from: |⟨X1,X2⟩|/∥X1∥∥X2∥

For one thing, without context, if I am supposed to read juxtaposition as multiplication then should I read X2 as X*2? Or 22 as "2*2=4", where does it end?

B

 

[blow45]

I was taken aback to read that the physics guys suggest that this could be interpreted as 2. I 've never seen this before except when writing informally. I still think though that it's a gross error and misunderstanding on the part of those voting for 2.

 

[McGiord]

I was taken aback to read that the physics guys suggest that this could be interpreted as 2. I 've never seen this before except when writing informally. I still think though that it's a gross error and misunderstanding on the part of those voting for 2.

The assumption of using an asterisk in between the 2 and the parenthesis makes the result to be 288.
If no assumption is made the result is 2.
The different software that give the result of 288 are also assuming that there is an asterisk.

If we re-read the OP post it is clear that there is nothing missing in the expression.

 

[blow45]

you are confusing me....you mean the assumption between 2 and the parentheses right? If nothing is assumed there, and in formal math nothing IS assumed there, then the answer is 288. I didn't say there was anything missing, just that I am not accustomed to this kind of notation implying a * there.

 

[McGiord]

you are confusing me....you mean the assumption between 2 and the parentheses right? If nothing is assumed there, and in formal math nothing IS assumed there, then the answer is 288. I didn't say there was anything missing, just that I am not accustomed to this kind of notation implying a * there.

Yes I mean the 2...my mistake

 

[TuffLuffJimmy]

The assumption of using an asterisk in between the 2 and the parenthesis makes the result to be 288.
If no assumption is made the result is 2.
The different software that give the result of 288 are also assuming that there is an asterisk.

If we re-read the OP post it is clear that there is nothing missing in the expression.

This isn't true at all. There's no reason that an asterisk would change the order of operations.

 

[-aggie-]

This isn't true at all. There's no reason that an asterisk would change the order of operations.

I was thinking the same thing.

 

[chris200x9]

holy crap 15 pages I can't believe ADULTS are this bad at math...I'd flunk an eighth grader for getting 2...congratulations half of macrumors you went full retard.

 

[blow45]

I wouldn't think everyone who's voted is an adult, still it's a bit disconcerting that half got it wrong.

 

[McGiord]

This isn't true at all. There's no reason that an asterisk would change the order of operations.

The asterisk do change the result, in any computer program the asterisk will make this expression provide a different result.
Try defining a variable with this expression in BASIC, PASCAL, FORTRAN.

I showed several examples of commonly used spreadsheet programs: excel, OpenOffice, Numbers, Google Docs, etc.

holy crap 15 pages I can't believe ADULTS are this bad at math...I'd flunk an eighth grader for getting 2...congratulations half of macrumors you went full retard.

What do you mean by full retard?

I wouldn't think everyone who's voted is an adult, still it's a bit disconcerting that half got it wrong.

Age and maturity are two different things, that there is a correlation between them doesn't explain why some people see things differently.

Why do you say that half are wrong?
The poll is showing otherwise.