48÷2(9+3)=?????

[dockeryfan]

This has gone on for 42 pages and half the people have answered wrong. I weep for this board, for education, and for humanity.

I actually weep that people cannot see there is some ambiguity here. I weep that they think if they reduce 8x/4x they can't see how or why someone would come up with 2 and instead argue emphatically that it MUST be 2x^2. AND that it is clear as day that it should be so.

[terrifNick21]

That guy spent 8 minutes of his life to explain a wrong answer. What a shame.

---------- Post added April-14th-2011 at 11:04 AM ----------

How are you going to say there is no more parentheses, but in the same sentence you present the same problem with parentheses in it. Just because you add 9+3 doesn't mean you got rid of the parentheses. You get rid of it by multiplying 12 by 2 which will give you 24....divide and you will get 2!!!

24(12) is the same as if I would've put 24*12. There are no other equations that need to be solved in parentheses!!!!

[Pwyl]

Well, you better tell this guy that he's solving the problem incorrectly.

http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.54286.html

because OBVIOUSLY, as you say, if you take (y+x)/xy you should get (y+x)(1/x)(y). I mean it's clear as day to you, why isn't it clear as day to this guy? He must be an idiot. He clearly does not understand order of operations.

Look. I understand the answer is 288. I know this because of the divisor symbol.

But saying that every math guy out there would take 8x^2/2x = 1 and come up with x=cube root of 1/4 is idiotic.

They would not. And all you have to do is go to one of those tutor websites and put in a question and they'll all get it wrong I guarantee it.

Ask them a stupid question like how do I reduce 24x/8x and I would bet they all come up with 3. Not 3x^2

You seem to be mixing up things other people have said with what I said. Maybe you should go back and re-read what I wrote and respond to just that. I never said you would get cube root of 1/4 from the equation you posted. I absolutely conceded that you would most likely evaluate the 2x node as atomic.

What I AM saying is that if you present MOST people with the eauation 24x ÷ 8x, they're going to evaluate it the same as 24x/8x. And they'll do that because it means the same thing.

Further, your link has no ÷ symbols in it that I can see, so you don't know what operator symbol is being referenced there. The question could have been written in text as presented, or it could have been written with "/" inline, or even as a full fraction like

2

---

(2/x + 2/y)

And if you DO think the answer is 288, I really don't see what you're disagreeing with me about. If you punch the equation into a calculator with the / symbol, you get 288. Ditto that with Excel. So what's the beef?

[RansomthePasserby]

24(12) is the same as if I would've put 24*12. There are no other equations that need to be solved in parentheses!!!!

I don't get why people can't understand this.

[dockeryfan]

And if you DO think the answer is 288, I really don't see what you're disagreeing with me about. If you punch the equation into a calculator with the / symbol, you get 288. Ditto that with Excel. So what's the beef?

No beef, I guess, except when people are arguing so emphatically about this and crying for humanity and the such when there IS inherent ambiguity to this.

[Forehead]

I actually weep that people cannot see there is some ambiguity here. I weep that they think if they reduce 8x/4x they can't see how or why someone would come up with 2 and instead argue emphatically that it MUST be 2x^2. AND that it is clear as day that it should be so.

There really isn't any ambiguity here, and the answer is clear. Do the parenthese first. Once complete, parentheses no longer exist. Solve rest of problem using order of operations from left to right. I learned this in elementary school. Frankly, I don't even think the problem is that poorly written or difficult to understand.

[Redskin4ever]

It's not that shocking.

Just shows half the people on ES are dumb dumbs and the other half are geniuses.

I'd like to point out that more than likely most of the geniuses are liberals.

:evilg:

You mean the same liberals who run the education system that taught half the people on here to give the wrong answer?

[grego]

You mean the same liberals who run the education system that taught half the people on here to give the wrong answer?

good one

---------- Post added April-14th-2011 at 12:31 PM ----------

I actually weep that people cannot see there is some ambiguity here. I weep that they think if they reduce 8x/4x they can't see how or why someone would come up with 2 and instead argue emphatically that it MUST be 2x^2. AND that it is clear as day that it should be so.

i feel your frustration.

[Pwyl]

No beef, I guess, except when people are arguing so emphatically about this and crying for humanity and the such when there IS inherent ambiguity to this.

ok then. I think the only ambiguity for this problem is trying to infer intent of the equation. If you approach it as a straight-up arithmetic problem, and slavishly follow the order of operations like a computer would, the order of operations rules clear up the processing ambiguity.

[mjah]

You mean the same liberals who run the education system that taught half the people on here to give the wrong answer?

Typical, blame the teachers...

No amount of classroom education can fix a case of the raging stupids.

[Chiefinonhaze]

The 288's are still holding this down. It could sway in the other direction though.

[Thinking Skins]

http://www.youtube.com/watch?v=D8kVqjUO92c&feature=related

http://www.youtube.com/watch?v=D8kVqjUO92c&feature=related

He was cool til he went into the end about "you can argue with your math teacher" etc. I'm a math Ph.D. and I say the answer is 288, but (according to him) I'm assuming that juxtaposition doesn't hold. Him saying that "the math community ..." is BS because juxtaposition is not a rule observed by the math community. Here is a quote on the topic I found at Ask Dr, Math.

http://mathforum.org/library/drmath/view/57021.html

Date: 02/13/2000 at 13:59:53

From: Jerome Breitenbach

Subject: Order of Arithmetic Operations

Hi,

I'm a professor in the field of electrical engineering. Occasionally I remind my students of the precedence order regarding the four arithmetic operations: addition, subtraction, multiplication, and division. Apparently though, based upon viewing numerous Web sites and the messages of various on-line discussion groups, there seems to be some controversy regarding these simple rules! For example, compare

Mathnerds' Archive

http://www.mathnerds.com/archive/DetailedAnswer.asp?index=12768

with

Order of Operations, Electronics Mathematics (ELET141)

http://www.csi.edu/ip/ti/elec/math1-5e.htm

Alas, my search for an "authority" on this matter has been nearly fruitless. The closest thing I have found is the convention used by the _Mathematical Reviews_ of the American Mathematical Society (AMS), at

Mathematical Reviews Database - Guide for Reviewers

http://www.ams.org/authors/guide-reviewers.html

that "multiplication indicated by juxtaposition is carried out before division." Thus, in general, for any variables a, b and c, we would have a/bc = a/(bc) (assuming, of course, that b and c are nonzero). Indeed, this convention is consistent with what I have seen in many mathematical books at various levels; for example, on p. 84 of Allendoerfer and Oakley, _Principles of Mathematics_, 1969 (my pre-college math book), we find:

(a / x (c / d) = a c / b d

which is generally true only if the right side is interpreted as:

(a c) / (b d)

Notably, the above equality would *not* be generally true were we to interpret the right side as:

[(a c) / b] d

per the first Web page above (and many others), which states that one should "do multiplication and division as they come." However, perhaps this page is tacitly ignoring "implicit multiplication" (by juxtaposition) and only considering "explicit multiplication" (via some multiplication sign) - a distinction is made at:

Order of Operations - Dr. Math Archives

http://mathforum.org/dr.math/problems/wuandheil.05.19.99.html

Unfortunately, in every instance where I have seen someone assert the rule that one should first perform multiplication and division as they occur (from left to right), I have yet to see them give an example that *really* puts this rule to the test. Specifically, how would they evaluate:

6 / 2 x 3

According to their rule, we would obtain:

6 / 2 x 3 = (6 / 2) x 3 = 9

But, wouldn't it be less confusing to follow the AMS convention for *all* multiplications (implicit and explicit) thereby obtaining:

6 / 2 x 3 = 6 / (2 x 3) = 1

- just as we would obtain:

a/bc = 1

when a = 6, b = 2 and c = 3?

For when dealing with numerals rather than variables, juxtaposition is not an option for indicating multiplication (here, "23" would be read as "twenty-three" rather than "2 times 3").

This approach also makes practical sense, since it frequently happens that one has a series of multiplications divided by another series of multiplications (e.g., consider a binomial coefficient); for example,

one might desire to write the fraction:

5 x 4 x 3

---------

2 x 1

more compactly (and without parentheses) as:

5 x 4 x 3 / 2 x 1

especially if this is to be written in-line (i.e., *within* the surrounding text) rather than separately displayed as above.

Or, consider the convenience obtained when dealing with quantities expressed in scientific notation. For example, without resorting to

parentheses, we would interpret:

6 x 10^9 / 3 x 10^5

as

(6 x 10^9)/(3 x 10^5) = 2 x 10^4

rather than:

[(6 x 10^9)/3] x 10^5 = 2 x 10^14

Surely the former is typically the intended interpretation.

As I remember them being taught to me, the rules giving the precedence order for the four arithmetic operations are:

(1) all multiplication (in any order)

(2) all division, as they occur from left to right

(3) all addition and subtraction, as they occur from left to right

Moreover, even though an expression containing successive divisions such as

4/2/1

evaluates unambiguously by these rules, I would view such an expression as poor form. Based upon inquiries I have made of my math colleagues, I am not the only one who remembers multiplication as

being given *sole* top precedence.

Please comment.

Sincerely,

Jerome Breitenbach

P.S. Some people argue about arithmetic-operation precedence by referring to what this or that calculator or programming language does. However, I believe all such references are irrelevant; for what may be syntactically convenient for some computing device need not be convenient (or traditional) for human mathematical writing.

Date: 02/13/2000 at 23:05:28

From: Doctor Peterson

Subject: Re: Order of Arithmetic Operations

Hi, Jerome.

You made some good points. On the whole, I suppose I agree with you that it would be easier and perhaps more consistent to give multiplication precedence over division everywhere; but of course there is no authority to decree this, so the more prudent approach is probably just to recognize that there really isn't any universal rule. I ran across the same AMS reference that you found while trying to see if any societies had made official statements on the rules of operations in general; the fact that they took note of this one rule alone demonstrates only that this is the one rule on which there is not universal agreement at the present time, but it probably is growing in acceptance.

I've been continuing to research the history of Order of Operations, and one of the references in our FAQ now includes a mention of something I had also discovered, that the multiplication-division rule has never really been fully accepted:

Earliest Uses of Symbols of Operation - Jeff Miller

http://jeff560.tripod.com/operation.html

As a result, I'm not entirely surprised that you learned a different rule than I think I did. (I'm not sure I didn't first learn the equal-precedence rule in a programming class, however.)

When algebraic notation was first being developed, it was common for each writer to begin by explaining his own notation. If we could convince enough writers to follow your rule and state it at the beginning of whatever they wrote, maybe we could get it accepted. But even then, I'd rather continue to do as we do now; especially with the development of publishing software, mathematicians can easily avoid in-line expressions of the sort you refer to in published works, and in e-mail it's safest to use all the parentheses you need so that no one can misunderstand you, whether they remember the rules or not.

I think this is far preferable to making detailed rules that are likely to trick people. Sometimes one rule seems natural, and sometimes another, so people will forget any rule we choose to teach in this area. I've heard from too many students whose texts do "give an example that really puts this rule to the test," but do so by having them evaluate an expression like:

6/2(3)

that is too ambiguous for any reasonable mathematician ever to write. And no matter what the rule, we would still constantly see students write things like "1/2x" meaning half of x, so we'd still have to make

reasonable guesses rather than stick to the rules.

- Doctor Peterson, The Math Forum

[Toe Jam]

It's a conspiracy.

[HailGreen28]

The 288's are still holding this down. It could sway in the other direction though.

Evidently not. The poll is currently tied 98 to 98. :doh:

I hope people are picking "2" as a joke.

[zoony]

because I can, that's why.