I've learned something valuable from this thread. You all are a bunch of cunts with very little social skills.

This question was poorly written and can easily confuse. It isn't like someone cannot add 2+2. Calling people retards or fucking morons will get you no where, regardless of how correct you are.

The mods closed it at page 84... a poll showed that 1500 (the slim majority) thought the answer is 2.

What is going on in our schools? I think about the "Jaywalker" segment on Leno, but I dismiss those people as random idiots. But to actually get a majority out of a 3000+ sample size...words fail me.

I mean, yeah, those are bodybuilding forums, but I wouldn't expect anything that bad. Is this how all those ridiculous supplements are sold?

the answer is 288, though for some reason people are initially confused by how it is written and think the 2 is part of the brackets. coincidentally, i guarantee nobody would get it wrong if it was written like this:

LOL AT ALL THE PEOPLE SAYING 288. how the fuck do yo not know simeple order of operations. its clearly 2...

"Look, you're my best friend, so don't take this the wrong way. In twenty years, if you're still livin' here, comin' over to my house to watch the Patriots games, still workin' construction, I'll fuckin' kill you. That's not a threat, that's a fact.

For all of you arguing 2 instead of 288 because of PEMDAS, keep in mind that PEMDAS implies that you perform the operations WITHIN the parenthesis before anything else. When you have something like 2(12) on the other hand, it is the equivalent of 2*12 and does not take priority over divisions or other multiplications.

Money Never Sleeps? More like Money Never SUCKS amirite?!?!?!?

Rule 1: First perform any calculations **INSIDE** parentheses. Rule 2: Next perform all multiplications and divisions, working from left to right. Rule 3: Lastly, perform all additions and subtractions, working from left to right.

Solidarity, you bring up a good point, but I'm sticking to my guns here. While 48/2x is not 24x, 48/2(x) is a little more ambiguous since you could argue that it is the equivalent of 48/2*x.

Money Never Sleeps? More like Money Never SUCKS amirite?!?!?!?

black financier you might want to look at your own icon

You think the answer is 2 you are an idiot and your math is turrible. 288. learn basic 3rd grade math. well maybe 4th. http://www.wolframalpha.com/input/?i=48/2(9%2B3)&t=macw01

The answer to your question is 1) network 2) get involved 3) beef up your resume 4) repeat -happypantsmcgee

Investment Banking - Generalist - 2nd Year Associate

^ Haha, yeah seriously...

This really shouldn't need to be typed out and explained, but it seems some people here need to be schooled.

PEMDAS or BEDMAS where division and multiplication share the same order (whichever comes first) and similarly addition and subtraction share the same order (last) pending on whichever comes first in the equation.

48/2(9+3)

Step 1: (9+3) = 12 (bracket) Step 2: 48/2 = 24 Division comes before multiplication because it's shown earlier in the equation Step 3: 24(12) = 288

Seriously, why the hell are we discussing grade school math here?

Agree with the people saying this is written ambiguously. If you are going to put the divide symbol between the 48 and the 2 you should toput the multiplcation symbol between the 2 and the (

Anyway, those still in denial and not willing to accept the rules of order of ops, throw '=48/2(9+3)' in excel

Go ahead and plug it into excel. It'll show you this error:

Microsoft Office Excel found an error in the formula you entered. Do you want to accept the correction proposed below?

=48/2*(9+3)

Like I said, the question was very poorly written. It has nothing to do with order of operations here. You can interpret the question in both ways.

Excel does that because it is not programmed to interpret a number enclosed in parentheses as a factor. That said, the order of operations is not open to debate just because a software app can't interpret the syntax.

Investment Banking - Generalist - 2nd Year Associate

MBP - that's my point though. Yes the equation is poorly written, but it's an accepted fact that when you write something like y(z) it means y x z. And excel while not programmed to interpret enclosed numbers as a factor as whateverittakes said above, it recognizes that y(z) is generally interpreted as y x z and it makes the fix after giving you the error message.

The original equation 48/2(9+3) is 48/2*(9+3) NOT 48/(2(9+3)). The 2(9+3) is just a lazier version of 2*(9+3).

Ok, my entire point is that if there is no consistency in the way a question is formulated, regardless of how simple it is, there is room for interpretation. I can tell you that based on the way the question is written, if I interpret it to mean 48/2x, where x = 9+3, then I'm not wrong. If I interpret it to mean 48/2*x, then I'm still not wrong. I can even interpret y(z) to be some completely strange group action if I want, or that we are in a finite field of order 277, in which case the answer most certainly is not 288.

If you want common sense to apply to the solution, you need to write the question with a bit of common sense. Otherwise, you need to spell out all of your assumptions in the question.

Date: 02/13/2000 at 13:59:53 From: Jerome Breitenbach Subject: Order of Arithmetic Operations

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;

I've learned something valuable from this thread. You all are a bunch of cunts with very little social skills.

This question was poorly written and can easily confuse. It isn't like someone cannot add 2+2. Calling people retards or fucking morons will get you no where, regardless of how correct you are.

I'm confused as to how you find this poorly written, (9+3) does not equal /12/ or 12, but (12), as in a value to be multiplied. Making it 48 / 2 (12), then 24 (12), then 288.

Either way, I agree with ANT. Can't believe you guys are calling each other retards over a stupid math problem. Hah.

People like Coldplay and voted for the Nazis, you can't trust people Jeremy

I'm confused as to how you find this poorly written, (9+3) does not equal /12/ or 12, but (12), as in a value to be multiplied. Making it 48 / 2 (12), then 24 (12), then 288.

Either way, I agree with ANT. Can't believe you guys are calling each other retards over a stupid math problem. Hah.

Please read my earlier post. I explain the answer to your question.

I don't think there is any question that this is the greatest thread in WSO history.

Order of operations: Rule 1: First perform any calculations inside parentheses. Rule 2: Next perform all multiplications and divisions, working from left to right. Rule 3: Lastly, perform all additions and subtractions, working from left to right.

I don't think there is any question that this is the greatest thread in WSO history.

Order of operations: Rule 1: First perform any calculations inside parentheses. Rule 2: Next perform all multiplications and divisions, working from left to right. Rule 3: Lastly, perform all additions and subtractions, working from left to right.

Answer is 288, based on the way the OP wrote the equation. End of story.

Wrong. It is not the end of story. In elementary arithmetic (the one that contains the / sign) the operation x(y) is not defined. You can't just assume it means x*(y). If you assume that x(y) = x*(y), then the answer is 288. If you assume x(y) = (x*y), then the answer is 2. Since the operation to begin with is not properly define, the problem is not well formed. So, like I said, the answer depends on your assumptions. If you assume x(y) = x^y, the answer is something entirely different. You can even assume that there are no numbers greater than 53 (i.e. the field Z_53).

Once again, you assumed the question was asking 48/2*(9+3). But that is not what was written.

Anyway, those still in denial and not willing to accept the rules of order of ops, throw '=48/2(9+3)' in excel

sure, order of ops but as written implies 48/(2x) rather than 48/2*x

either way it's not a big deal

I originally sided with 288, but Solidarity brings up a very good argument for 2. So I change my answer to this: there is no answer. Some genius somewhere came up with this seemingly simple math problem that is fundamentally flawed in that it has ambiguous syntax. Probably laughing his ass off about how a bunch of dolts are arguing over something with no real answer

Money Never Sleeps? More like Money Never SUCKS amirite?!?!?!?

I did, and not to be a dick but I didn't see any room for different interpretations in it at all dude. While I get what you mean, it really is pretty straight forward and I think you're just confusing yourself by overanalyzing what x(y) could be.

I really don't mean this in the dick way I know it's going to come off (no pun intended).

Have you ever taken a serious course in mathematics? Not the bullshit you learn in high school or a basic calculus course in freshman year, but a rigorous course in algebra where you study groups, fields and other algebraic structures? If you had, you really wouldn't have made the statement about "overanalyzing what x(y) could be." Understanding what x(y) means is the entire source of the confusion in the question. And it's not defined in elementary arithmetic. It doesn't mean multiplication. PEMDAS/BEDMAS doesn't even apply until you define what x(y) means. Normally you can infer it from the question, but in this case you can't.

I did, and not to be a dick but I didn't see any room for different interpretations in it at all dude. While I get what you mean, it really is pretty straight forward and I think you're just confusing yourself by overanalyzing what x(y) could be.

I really don't mean this in the dick way I know it's going to come off (no pun intended).

Have you ever taken a serious course in mathematics? Not the bullshit you learn in high school or a basic calculus course in freshman year, but a rigorous course in algebra where you study groups, fields and other algebraic structures? If you had, you really wouldn't have made the statement about "overanalyzing what x(y) could be." Understanding what x(y) means is the entire source of the confusion in the question. And it's not defined in elementary arithmetic. It doesn't mean multiplication. PEMDAS/BEDMAS doesn't even apply until you define what x(y) means. Normally you can infer it from the question, but in this case you can't.

MBP, you are SPOT ON. If I had an SB to give you would get one. The definition of x(y) is absolutely the source of the ambiguity and the reason why this isn't as simple as it looks.

Money Never Sleeps? More like Money Never SUCKS amirite?!?!?!?

x(y) is a verrrrrrry well known abbreviation for x*(y). Look at any math book expanding a product, such as x!, and it is always represented as x(x-1)(x-2)...

The multiplication is obvious.

Also that calculator computes different values because of an error in the parser implementation.

Solving this equation the same way would give an answer of 2. This equation could easily be argued both ways. My first answer when I first saw it was 288, but after thinking about it, I'm sitting on the fence. I also have one calculator showing me 2 and one showing 288. Not sure which one to use for my finals lol

x(y) is a verrrrrrry well known abbreviation for x*(y). Look at any math book expanding a product, such as x!, and it is always represented as x(x-1)(x-2)...

The multiplication is obvious.

Also that calculator computes different values because of an error in the parser implementation.

I'm sorry, but where in that article does it say that x(y) is the same as x*(y)? I never denied that it is commonly understood that way. But it is also commonly understood in many other ways.

It's also pretty commonly understood that xy = yx, but in general it is completely wrong (look up non-abelian groups). And giving me one example of x! being expressed as x(x-1)...1 doesn't prove anything.

The multiplication, most certainly, is not obvious. And if you want to go with the conventional way of solving it, the answer is still 2.

x(y) is a verrrrrrry well known abbreviation for x*(y). Look at any math book expanding a product, such as x!, and it is always represented as x(x-1)(x-2)...

The multiplication is obvious.

Also that calculator computes different values because of an error in the parser implementation.

I'm sorry, but where in that article does it say that x(y) is the same as x*(y)? I never denied that it is commonly understood that way. But it is also commonly understood in many other ways.

It's also pretty commonly understood that xy = yx, but in general it is completely wrong (look up non-abelian groups). And giving me one example of x! being expressed as x(x-1)...1 doesn't prove anything.

The multiplication, most certainly, is not obvious. And if you want to go with the conventional way of solving it, the answer is still 2.

Since x(y) is understood by everyone to mean x*(y), that is the convention -> the conventional way of solving this leads to 288.

No need to bring up group theory for this, the operations being used here are commonly understood.

x(y) is a verrrrrrry well known abbreviation for x*(y). Look at any math book expanding a product, such as x!, and it is always represented as x(x-1)(x-2)...

The multiplication is obvious.

Also that calculator computes different values because of an error in the parser implementation.

I'm sorry, but where in that article does it say that x(y) is the same as x*(y)? I never denied that it is commonly understood that way. But it is also commonly understood in many other ways.

It's also pretty commonly understood that xy = yx, but in general it is completely wrong (look up non-abelian groups). And giving me one example of x! being expressed as x(x-1)...1 doesn't prove anything.

The multiplication, most certainly, is not obvious. And if you want to go with the conventional way of solving it, the answer is still 2.

Since x(y) is understood by everyone to mean x*(y), that is the convention -> the conventional way of solving this leads to 288.

By everyone? Really? Conventions aren't defined by ignorant people. They're defined by people who know what they are talking about. No mathematician would agree with you. They would all agree with me that this is an ill formed problem. And if they were forced to solve it, most of them would answer 2.

x(y) is a verrrrrrry well known abbreviation for x*(y). Look at any math book expanding a product, such as x!, and it is always represented as x(x-1)(x-2)...

The multiplication is obvious.

Also that calculator computes different values because of an error in the parser implementation.

I'm sorry, but where in that article does it say that x(y) is the same as x*(y)? I never denied that it is commonly understood that way. But it is also commonly understood in many other ways.

It's also pretty commonly understood that xy = yx, but in general it is completely wrong (look up non-abelian groups). And giving me one example of x! being expressed as x(x-1)...1 doesn't prove anything.

The multiplication, most certainly, is not obvious. And if you want to go with the conventional way of solving it, the answer is still 2.

Since x(y) is understood by everyone to mean x*(y), that is the convention -> the conventional way of solving this leads to 288.

By everyone? Really? Conventions aren't defined by ignorant people. They're defined by people who know what they are talking about. No mathematician would agree with you. They would all agree with me that this is an ill formed problem. And if they were forced to solve it, most of them would answer 2.

First off - just want to note I haven't been throwing shit at you.

Second - I can't believe your argument for a second. Parentheses are an accepted form of representing multiplication, just like * and x. parentheses are used constantly for that exact purpose in countless textbooks and journals. It's the way it's taught both in classes and in textbooks. Period.

You're claiming that mathematicians would treat x(y) as some weird new form of multiplication that works exactly as multiplication except it has the same priority as parentheses in the order of operations. This just isn't done in practice. Try to find a credible textbook that does that.

The accepted mathematical convention is that when two unknown numbers are juxtaposed, they are multiplied, and that multiplication takes precedence over division. Thus, in this case we multiply 2*12 before we divide, so we get 2.

x(y) is a verrrrrrry well known abbreviation for x*(y). Look at any math book expanding a product, such as x!, and it is always represented as x(x-1)(x-2)...

The multiplication is obvious.

Also that calculator computes different values because of an error in the parser implementation.

I'm sorry, but where in that article does it say that x(y) is the same as x*(y)? I never denied that it is commonly understood that way. But it is also commonly understood in many other ways.

It's also pretty commonly understood that xy = yx, but in general it is completely wrong (look up non-abelian groups). And giving me one example of x! being expressed as x(x-1)...1 doesn't prove anything.

The multiplication, most certainly, is not obvious. And if you want to go with the conventional way of solving it, the answer is still 2.

Since x(y) is understood by everyone to mean x*(y), that is the convention -> the conventional way of solving this leads to 288.

By everyone? Really? Conventions aren't defined by ignorant people. They're defined by people who know what they are talking about. No mathematician would agree with you. They would all agree with me that this is an ill formed problem. And if they were forced to solve it, most of them would answer 2.

First off - just want to note I haven't been throwing shit at you.

Second - I can't believe your argument for a second. Parentheses are an accepted form of representing multiplication, just like * and x. parentheses are used constantly for that exact purpose in countless textbooks and journals. It's the way it's taught both in classes and in textbooks. Period.

You're claiming that mathematicians would treat x(y) as some weird new form of multiplication that works exactly as multiplication except it has the same priority as parentheses in the order of operations. This just isn't done in practice. Try to find a credible textbook that does that.

The AMS actually says exactly that, that x(y) takes precedence over division.

x(y) is a verrrrrrry well known abbreviation for x*(y). Look at any math book expanding a product, such as x!, and it is always represented as x(x-1)(x-2)...

The multiplication is obvious.

Also that calculator computes different values because of an error in the parser implementation.

I'm sorry, but where in that article does it say that x(y) is the same as x*(y)? I never denied that it is commonly understood that way. But it is also commonly understood in many other ways.

It's also pretty commonly understood that xy = yx, but in general it is completely wrong (look up non-abelian groups). And giving me one example of x! being expressed as x(x-1)...1 doesn't prove anything.

The multiplication, most certainly, is not obvious. And if you want to go with the conventional way of solving it, the answer is still 2.

Since x(y) is understood by everyone to mean x*(y), that is the convention -> the conventional way of solving this leads to 288.

By everyone? Really? Conventions aren't defined by ignorant people. They're defined by people who know what they are talking about. No mathematician would agree with you. They would all agree with me that this is an ill formed problem. And if they were forced to solve it, most of them would answer 2.

First off - just want to note I haven't been throwing shit at you.

Second - I can't believe your argument for a second. Parentheses are an accepted form of representing multiplication, just like * and x. parentheses are used constantly for that exact purpose in countless textbooks and journals. It's the way it's taught both in classes and in textbooks. Period.

You're claiming that mathematicians would treat x(y) as some weird new form of multiplication that works exactly as multiplication except it has the same priority as parentheses in the order of operations. This just isn't done in practice. Try to find a credible textbook that does that.

The AMS actually says exactly that, that x(y) takes precedence over division.

x(y) is a verrrrrrry well known abbreviation for x*(y). Look at any math book expanding a product, such as x!, and it is always represented as x(x-1)(x-2)...

The multiplication is obvious.

Also that calculator computes different values because of an error in the parser implementation.

I'm sorry, but where in that article does it say that x(y) is the same as x*(y)? I never denied that it is commonly understood that way. But it is also commonly understood in many other ways.

It's also pretty commonly understood that xy = yx, but in general it is completely wrong (look up non-abelian groups). And giving me one example of x! being expressed as x(x-1)...1 doesn't prove anything.

The multiplication, most certainly, is not obvious. And if you want to go with the conventional way of solving it, the answer is still 2.

Why the f would you introduce group theory into plain algebra? Unless it is specified that you are given a dihedral group or something, ab does equal ba. 5+2 = 2+5 is not an invalid equation just because on a specific terrain right turn + left turn is not gonna lead you to the same point as left turn + right turn

x(y) is a verrrrrrry well known abbreviation for x*(y). Look at any math book expanding a product, such as x!, and it is always represented as x(x-1)(x-2)...

The multiplication is obvious.

Also that calculator computes different values because of an error in the parser implementation.

I'm sorry, but where in that article does it say that x(y) is the same as x*(y)? I never denied that it is commonly understood that way. But it is also commonly understood in many other ways.

It's also pretty commonly understood that xy = yx, but in general it is completely wrong (look up non-abelian groups). And giving me one example of x! being expressed as x(x-1)...1 doesn't prove anything.

The multiplication, most certainly, is not obvious. And if you want to go with the conventional way of solving it, the answer is still 2.

Since x(y) is understood by everyone to mean x*(y), that is the convention -> the conventional way of solving this leads to 288.

By everyone? Really? Conventions aren't defined by ignorant people. They're defined by people who know what they are talking about. No mathematician would agree with you. They would all agree with me that this is an ill formed problem. And if they were forced to solve it, most of them would answer 2.

First off - just want to note I haven't been throwing shit at you.

Second - I can't believe your argument for a second. Parentheses are an accepted form of representing multiplication, just like * and x. parentheses are used constantly for that exact purpose in countless textbooks and journals. It's the way it's taught both in classes and in textbooks. Period.

You're claiming that mathematicians would treat x(y) as some weird new form of multiplication that works exactly as multiplication except it has the same priority as parentheses in the order of operations. This just isn't done in practice. Try to find a credible textbook that does that.

lol, I've been completely bombarded with monkey shit on this thread. Oh well, thanks for not joining in.

Anyway, I've spotted the flaw in your logic. You think it is the brackets that tell you that you need to multiply. This is a very common misconception, and I don't really blame you or anyone else for falling prey to it. In actuality, it is the adjacency of two terms that tells you that you need to multiply them, whether or not there are any brackets. For example, xy means multiply x and y. Not (x)(y), which means multiply what's in the two pairs of brackets. It's when you want to place two terms adjacent to one another to express multiplication, but it may cause some confusion, then you use brackets to clarify. You don't use brackets to express the multiplication.

As an example, let the first term be a+b, and the second be c+d. If I want to show the product, I simply need to place the terms next to each other. Which results in a+bc+d. But this is not what we mean when accounting for pemdas, and so we need to specify with the parenthesis that we mean (a+b)(c+d).

So now that we've clarified what the parenthesis really mean (just that whatever operation pertains to the parenthesis, you perform that first) you can see that x(y) is symbol for an operation on the parenthesis. It means that you distribute x into what's inside. And since this is an operation on the parenthesis, you do it first. This is the proper convention, and this is the subtle difference between x(y) and x*(y). The latter separates x and (y), but the former brings them together into the same overall operation.

And before, all that talk about group theory and stuff, I wasn't using that as a proof that the answer is 2, all I was saying was that question is poorly formed, because while it's now obvious that the author meant 2(9+3) to mean 2*(9+3), he didn't account for the subtle distinction. Which is that when you use the division sign, you have to use the multiplication sign explicitly to be clear. You can't use the adjacency convention to express multiplication. When you don't use consistency in the formulation of the question, all interpretations are valid, even the outlandish ones I was using as an example.

Wrong. Excel doesn't say it's 288. Excel doesn't answer it until it guesses what you actually mean. It's only after you clarify what you mean to Excel that it answers 288. If the clarity had been provided in the OP from the very beginning, there wouldn't have been this outrageous debate over arithmetic.

If written in Excel exactly as typed above the answer is 288. My math guys here also said it is 288. (9+3) first then left to right to solve.

Who are your 'math' guys? Also, you can't type it exactly as it's shown in the OP in excel.

If you type it into Excel it autocorrects the equation to 48/2*(9+3). My "math" guys as in analysts. They did the equation then typed into excel to see what it said. Both arrived at 288.

If written in Excel exactly as typed above the answer is 288. My math guys here also said it is 288. (9+3) first then left to right to solve.

Who are your 'math' guys? Also, you can't type it exactly as it's shown in the OP in excel.

If you type it into Excel it autocorrects the equation to 48/2*(9+3). My "math" guys as in analysts. They did the equation then typed into excel to see what it said. Both arrived at 288.

Dude, that is exactly my point. There is a subtle difference between 2(9+3) and 2*(9+3) which I explained above, and it confused Excel as well, which is why it asked if you meant 2*(9+3) instead.

So to be clear, excel didn't answer the question. It answered another question which it assumed you meant to ask. These are two very different things. When I answered 2, I assumed the OP meant to ask another question. Had the question been written 48/2*(9+3), there would have been no debate, and excel would have just gone ahead and answered without the error message interruption.

And please don't refer to your analysts as math guys as if they're some sort of experts. They're probably engineering majors and haven't got a clue as to the subtleties that can arise in even the simplest mathematics.

looks like we have the back office team in this thread lined up nice and neat

All you're proving with this statement is that bankers are more ignorant about mathematics, not that there's anything wrong with that. Also, I'm not in the "back office"

Investment Banking - Generalist - 1st Year Analyst

What I agree with.

Distributive property of multiplication. Early Algebra.

The distributive property of multiplication CLEARLY states that the 2(9+3) is an entire term and CANNOT be broken up. 2(9+3) follows the distributive property which can be rewritten as (2*9+2*3). Let me repeat the 2 outside of the parenthesis follows the distributive property of multiplication and must be factored and simplified before performing any other operations on it.

So this can be rewritten as: 48 / (2*9 + 2*3)

Which leaves us with

48 / 24 = 2

Answer = 2.

Lastly for those using Google or any other online calculator. These do not understand many theorems or properties so you must explicitly explain what you mean. There is a difference between 48 / 2 *(9+3) and 48 / 2(9+3). The first notation reads 48 / 2 * 1(9+3) while the second reads 48 / (2*9+2*3). Be very careful with your signs.

If written in Excel exactly as typed above the answer is 288. My math guys here also said it is 288. (9+3) first then left to right to solve.

Who are your 'math' guys? Also, you can't type it exactly as it's shown in the OP in excel.

If you type it into Excel it autocorrects the equation to 48/2*(9+3). My "math" guys as in analysts. They did the equation then typed into excel to see what it said. Both arrived at 288.

Dude, that is exactly my point. There is a subtle difference between 2(9+3) and 2*(9+3) which I explained above, and it confused Excel as well, which is why it asked if you meant 2*(9+3) instead.

So to be clear, excel didn't answer the question. It answered another question which it assumed you meant to ask. These are two very different things. When I answered 2, I assumed the OP meant to ask another question. Had the question been written 48/2*(9+3), there would have been no debate, and excel would have just gone ahead and answered without the error message interruption.

And please don't refer to your analysts as math guys as if they're some sort of experts. They're probably engineering majors and haven't got a clue as to the subtleties that can arise in even the simplest mathematics.

I did read through your analysis and I agree with it. My initial reaction was 2, but after reading the debate thought I'd ask for other opinions in the office. Two people said 288 and one said 2 (the math major).

This is absurd. 48/2(9+3) can be rewritten as (48)/(2)(12) - I don't think anyone will argue that I can put ()s around numbers. Which can be re-written as (x)/(y)(z). Note (y)(z)=(y)*(z) So (x)/(y)*(z)=288. This is not ambiguous at all. I would also say that TECHNICALLY, 48/2x = 24x, though it would typically be interpreted differently.

And seriously, bringing group theory into this is ridiculous.

According to this Math Explanation , it's 288 as paranthesis are exactly the same as multiplication which is on the same level as division and should therefore be solved left to right

however according to this Math Explanation, it's 2 as paranthesis does outrank division and therefore should be solved first.

There does not seem to be a generally accepted way of resolving the conflict which explains why even the best scientific calculators are giving different solutions to the problem

Let's just agree that the question is too ambiguous and solid arguments can be found for both camps.

Investment Banking - Generalist - 2nd Year Analyst

Awon Eleyi Awon Eleyi Won Bad Gan:

According to this Math Explanation , it's 288 as paranthesis are exactly the same as multiplication which is on the same level as division and should therefore be solved left to right

however according to this Math Explanation, it's 2 as paranthesis does outrank division and therefore should be solved first.

There does not seem to be a generally accepted way of resolving the conflict which explains why even the best scientific calculators are giving different solutions to the problem

Let's just agree that the question is too ambiguous and solid arguments can be found for both camps.

Ding ding ding.

Ambiguity sucks and there's usually a reason the other guy thinks the way he does.

"Dude, not trying to be a dick here, but your shop looks like a frontrunner for the cover of Better Boilerrooms & Chophouses or Bucketshop Quarterly."

This is absurd. 48/2(9+3) can be rewritten as (48)/(2)(12) - I don't think anyone will argue that I can put ()s around numbers. Which can be re-written as (x)/(y)(z). Note (y)(z)=(y)*(z) So (x)/(y)*(z)=288. This is not ambiguous at all. I would also say that TECHNICALLY, 48/2x = 24x, though it would typically be interpreted differently.

And seriously, bringing group theory into this is ridiculous.

Totally and completely wrong. And I was not bringing in group theory to prove anything. It was just illustrative of how you *can* interpret the problem differently.

According to this Math Explanation , it's 288 as paranthesis are exactly the same as multiplication which is on the same level as division and should therefore be solved left to right

however according to this Math Explanation, it's 2 as paranthesis does outrank division and therefore should be solved first.

There does not seem to be a generally accepted way of resolving the conflict which explains why even the best scientific calculators are giving different solutions to the problem

Let's just agree that the question is too ambiguous and solid arguments can be found for both camps.

the calculator is only as smart as its operator if you put a problem in the calculator with -(1) and then you did another problem with (-1) you'd get two different answers.....

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Distributive property of multiplication. Early Algebra.

The distributive property of multiplication CLEARLY states that the 2(9+3) is an entire term and CANNOT be broken up. 2(9+3) follows the distributive property which can be rewritten as (2*9+2*3). Let me repeat the 2 outside of the parenthesis follows the distributive property of multiplication and must be factored and simplified before performing any other operations on it.

So this can be rewritten as: 48 / (2*9 + 2*3)

Which leaves us with

48 / 24 = 2

Answer = 2.

Lastly for those using Google or any other online calculator. These do not understand many theorems or properties so you must explicitly explain what you mean. There is a difference between 48 / 2 *(9+3) and 48 / 2(9+3). The first notation reads 48 / 2 * 1(9+3) while the second reads 48 / (2*9+2*3). Be very careful with your signs.

lol distributive property your dumb ass. how can you only distribute only part of the coefficient?

or do you seriously believe 48/2*(a+b) is not the same as 48/2(a+b) ???????

For the record I sent this to a list at my engineering school (top 5 in some disciplines, top 10 overall) to a list of engineers from biomed, chemE, aerospace, EE, compE, IE, mechE(phd), math/statistics, and even computer science and they were split between 2 and 288 also. At first I thought it was pretty straight forward its 288. But now I'm changing my mind that maybe it is written ambigiously.

OMFG no wonder no one knows how CDOs MBS ect ect are calculated. We cant even agree on a simple math problem that is obviously 288. It would be 2 if it was written like this 48/(2(9=3)). Since there isnt a 2nd set of brackets to quantify the the 2 times 12 step. Since it is written in a line item way you can rule out a fractional equation since its not written as a fraction.

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OMFG no wonder no one knows how CDOs MBS ect ect are calculated. We cant even agree on a simple math problem that is obviously 288. It would be 2 if it was written like this 48/(2(9=3)). Since there isnt a 2nd set of brackets to quantify the the 2 times 12 step. Since it is written in a line item way you can rule out a fractional equation since its not written as a fraction.

I understand credit derivatives and their pricing very well. And I assure you that both 288, and 2 are valid given the ambiguity in the way the question is written. It's poorly written. That's all there is to it. Can we please just all move on now?

OMFG no wonder no one knows how CDOs MBS ect ect are calculated. We cant even agree on a simple math problem that is obviously 288. It would be 2 if it was written like this 48/(2(9=3)). Since there isnt a 2nd set of brackets to quantify the the 2 times 12 step. Since it is written in a line item way you can rule out a fractional equation since its not written as a fraction.

I understand credit derivatives and their pricing very well. And I assure you that both 288, and 2 are valid given the ambiguity in the way the question is written. It's poorly written. That's all there is to it. Can we please just all move on now?

I was refering to people outside of banking, I should have specified that. My bad guys.

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This question is absolutely ambiguous. However, you can't say that both answers are correct. Both answers are actually incorrect and this question does not have an answer.

Answering EITHER 2 or 288 would imply turning 48/2(9+3) into either 48/2(x) where x = 9+3, 48/2*(9+3), or some other "equivalent expression." But you cannot do this. NONE of these other expressions are equivalent expressions, and there are no set-in-stone rules for how to apply the implied multiplication in the first question.

We can, however, based purely on mathematical tradition and such, debate about whether, if such a rule were created, the implied multiplication would be interpreted as 2(x) or 2*(9+3)

I personally think it makes more sense to give 2(9+3) prioirity over the 48/2. I'm not saying that it's the correct way, but I'm saying that for the future, this should be made the correct way of interpreting the problem.

48/2(9+3) = 288 with no ambiguity. The adjacency convention is for multiplication. It's not "inconsistent" to use adjacency to represent multiplication because this is never done for division...division is always specified by an actual symbol.

Also, I never said that (a+b)(c+d) = a+bc+d. I said that it is the convention to omit the multiplication symbol * where parenthesis makes it unnecessary. So (a+b)(c+d) = (a+b)*(c+d) as normal. Similarly, 10/(2+3)(1+1) = 10/(2+3)*(1+1) = 10/5*2 = 2*2 = 4.

And for those of you bringing up the distributive property of multiplication...that doesn't change the order of operations at all.

The point that people miss about PEMDAS is that it's really P E M/D A/S

multiplication and division happen at the same time (from left to right) as do addition and subtraction.

this means M and D are interchangeable so having MD is the same as DM

In your example the first is correct not because division always come before multiplication but because the division in the problem is first.

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You think the answer is 2 you are an idiot and your math is turrible. 288. learn basic 3rd grade math. well maybe 4th. http://www.wolframalpha.com/input/?i=48/2(9%2B3)&t=macw01

turrible knuckleheads don't know their order of operations. 48/2(9+3) > 48/2*12 > 24*12 > 288. Knuckleheads your math is so turrible it offends me. knuckleheads

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The point that people miss about PEMDAS is that it's really P E M/D A/S

multiplication and division happen at the same time (from left to right) as do addition and subtraction.

this means M and D are interchangeable so having MD is the same as DM

In your example the first is correct not because division always come before multiplication but because the division in the problem is first.

This is correct. If you are left with a multiplication part and division part, you go from left to right. One does NOT supersede the other. Same with addition and subtraction.

48/2(9+3) = 288 with no ambiguity. The adjacency convention is for multiplication. It's not "inconsistent" to use adjacency to represent multiplication because this is never done for division...division is always specified by an actual symbol.

Also, I never said that (a+b)(c+d) = a+bc+d. I said that it is the convention to omit the multiplication symbol * where parenthesis makes it unnecessary. So (a+b)(c+d) = (a+b)*(c+d) as normal. Similarly, 10/(2+3)(1+1) = 10/(2+3)*(1+1) = 10/5*2 = 2*2 = 4.

And for those of you bringing up the distributive property of multiplication...that doesn't change the order of operations at all.

First of all, division is just an artificial simplification as an illustrative tool to teach kids. There's no real definition of division in rigorous mathematics. There is only addition and multiplication. Subtraction is just addition of an additive inverse, and division is just multiplication of a multiplicative inverse (look up algebraic field for further clarification of how the number systems you are familiar with are constructed rigorously). That is why there are no short hand conventions for "division". So if the question had been written in conventional notation, there would be no confusion to begin with. This is the exact reason why mathematics is formed on a rigorous foundation. But of course, the material has to be bastardized when it is taught to kids, and then they have a hard time relearning it properly.

You missed my entire earlier point btw. I never said you were saying (a+b)(c+d) = a+bc+d. It was just an illustration.

My question is, how can you expect someone to find the answer when the basis of the problem is described in a non quanitive fashion such as, (a+b)(c+d) I mean honestly it would be much easier just to use number and give a damn answer.

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You think the answer is 2 you are an idiot and your math is turrible. 288. learn basic 3rd grade math. well maybe 4th. http://www.wolframalpha.com/input/?i=48/2(9%2B3)&t=macw01

turrible knuckleheads don't know their order of operations. 48/2(9+3) > 48/2*12 > 24*12 > 288. Knuckleheads your math is so turrible it offends me. knuckleheads

hahaha

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Ok, this has gotten out of hand. These are the two interpretations. Stop posting dumbass links to how pemdas works. Everyone knows that. That's not what's under dispute.

So thus far, we've used various casio and TI calculators to no avail. And then we consulted engineers, math prof's, computer science experts, blah blah blah... who also yielded similar ambiguity.

Yet no one, up until this point, sought the answer from the golden brushed-aluminum god that is the HP12C.

(Leveraged Sellout excerpt: "Excel Mobile, it speaks a pure, unambiguous language: Reverse Polish, a postfix notation that eliminates non-commutative issues.")

MBP but wouldn't you say for it to be read the first way you need another set of parenthesis? or would you say that doesn't matter?

That would really spell it out and take away the ambiguity. For sure. But not necessarily. See, my entire point from the start has been that no one would write the problem like this. In rigorous notation, it would be written in one of these two ways:

48(2^(-1))(9+3) = 288 or 48((2(9+3))^-1) = 2

There would be no division. Just multiplication and addition.

*Unnecessary overuse of brackets because can't type in mathematical notation here.

MBP but wouldn't you say for it to be read the first way you need another set of parenthesis? or would you say that doesn't matter?

That would really spell it out and take away the ambiguity. For sure. But not necessarily. See, my entire point from the start has been that no one would write the problem like this. In rigorous notation, it would be written in one of these two ways:

48(2^(-1))(9+3) = 288 or 48((2(9+3))^-1) = 2

There would be no division. Just multiplication and addition.

*Unnecessary overuse of brackets because can't type in mathematical notation here.

But since the parenthesis aren't there aren't you forced to do it in a way where the answer comes out to 288?

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Parathese/Brackets first (9+3=12), then (48/2=24, since you go from left to right), then (24*12=288).

I don't get the point of this post....

it's official... there's literally NOTHING more that can be said about this thread. this has to be the fiftieth time someone has said this exact thing. can we close this now please???

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sayandarula:

sixrings:

288 = 48/2(9+3)

Just order of operations

Parathese/Brackets first (9+3=12), then (48/2=24, since you go from left to right), then (24*12=288).

I don't get the point of this post....

it's official... there's literally NOTHING more that can be said about this thread. this has to be the fiftieth time someone has said this exact thing. can we close this now please???

Seconded... or probably the 10th person to agree. The reason why this hasn't ended even with me, you, and everyone writing out why it's 288... is because then the "2" camp will debate that parentheses =/= the same as multiplication and making their justifications for it or whatever else... and so on back and forth. No matter what else can be said, neither side will concede.

The middle ground can only be that this question can be better written so that there is no question for misinterpretation. Besides that, or a mod closing the thread, only way one group or the other would shut up is if someone like Stephen Hawking makes a public announcement to shut everyone up once and for all.

## Comments (245)

I've learned something valuable from this thread. You all are a bunch of cunts with very little social skills.

This question was poorly written and can easily confuse. It isn't like someone cannot add 2+2. Calling people retards or fucking morons will get you no where, regardless of how correct you are.

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(e^(i*pi))/(-0.5)

-MBP

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288 but my conversion process formulated from a vector application has it at 3.50

Amidoingitrite? U tell me. Umadbrah?

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in.

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2

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This isn't funny or interesting. Why is it here?

One of those lights, slightly brighter than the rest, will be my wingtip passing over.

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The way you wrote it, 288.

Is this a troll, or was this an interview question? I don't get this post to be honest.

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That's a pretty clever formulation, though, I like it.

One of those lights, slightly brighter than the rest, will be my wingtip passing over.

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To see if you so called "wall street geniuses" have the brain power to solve a simple mathematics equation.

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Who the fuck uses the fucking "/" symbol when writing terms?

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I saw this on Bodybuilding.com this morning...

http://forum.bodybuilding.com/showthread.php?t=133...

The mods closed it at page 84... a poll showed that 1500 (the slim majority) thought the answer is 2.

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Bodybuiding forum no wonder....actually didn't realize riods affected brain power...

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What is going on in our schools? I think about the "Jaywalker" segment on Leno, but I dismiss those people as random idiots. But to actually get a majority out of a 3000+ sample size...words fail me.

I mean, yeah, those are bodybuilding forums, but I wouldn't expect anything that bad. Is this how all those ridiculous supplements are sold?

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the answer is 288, though for some reason people are initially confused by how it is written and think the 2 is part of the brackets. coincidentally, i guarantee nobody would get it wrong if it was written like this:

48/2*(9+3)

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Silly hoes need to brush up on order of operations.

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no one writes divide sign like that, why not do

48/2*12 = 288

or you mean 48/ (2*12) = 2

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^Yeah, it's 2.

I win here, I win there...

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I hope both of you are joking...

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PEMDAS it's 2

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LOL AT ALL THE PEOPLE SAYING 288. how the fuck do yo not know simeple order of operations. its clearly 2...

"Look, you're my best friend, so don't take this the wrong way. In twenty years, if you're still livin' here, comin' over to my house to watch the Patriots games, still workin' construction, I'll fuckin' kill you. That's not a threat, that's a fact.

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Please excuse my dear aunt sally

http://en.wikipedia.org/wiki/Order_of_operations

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Order of operations is easy to forget I suppose

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I cant believe some of you think that is 288....

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ummm.... parentheses exponents multiplication division addition subtraction... with this how did you get 2?

also read my avatar icon.... It talks about your math skills

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288.

Obviously you do the (3+9) first because it's in the parenthesis, giving you:

48/2(12) which can be rewritten as 48/2*12

Since / and * are the same in order of operations, you go from left to right so 48/2*12 = 24*12 = 288.

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Please change your name. You are retarded.

Everyone who is a dumbass just got monkey shit thrown at them.

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hahahahahah its 288....

PEMDAS isnt set in stone; multiplication doesn't always come before division, it depends on the order found in the problem

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It is 2.

The way it is written is confusing, if it were written appropriately it would look like this:

48

--------- = 2

2(9+3)

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Some of you guys might actually be retarded you realize that 2 *12 is a quantity you cant divide the two then multiply by 12.

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For all of you arguing 2 instead of 288 because of PEMDAS, keep in mind that PEMDAS implies that you perform the operations WITHIN the parenthesis before anything else. When you have something like 2(12) on the other hand, it is the equivalent of 2*12 and does not take priority over divisions or other multiplications.

Money Never Sleeps? More like Money Never SUCKS amirite?!?!?!?

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When you have 2*12 that is a quantity you divide that entire thing into 48. Look 48/24 is the same thing as 48/12*2

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black financier you might want to look at your own icon

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I think the people who are writing 2 are just kidding around. I don't think anybody here really believes its 2.

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48/24 = 48/(12*2) but NOT (48/12)*2.

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seriously?

48/2(9+3) is an equivalent formulation to 48/2x...

HINT: the answer is not 24x

shit like this makes me wish I were a trader...

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lol - owned.

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Lmao you can't just change the way its written because you don't agree with it.

WSO is not your personal search function.

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From a children's math website: http://www.mathgoodies.com/lessons/vol7/order_oper...

Rule 1: First perform any calculations **INSIDE** parentheses.

Rule 2: Next perform all multiplications and divisions, working from left to right.

Rule 3: Lastly, perform all additions and subtractions, working from left to right.

Solidarity, you bring up a good point, but I'm sticking to my guns here. While 48/2x is not 24x, 48/2(x) is a little more ambiguous since you could argue that it is the equivalent of 48/2*x.

Money Never Sleeps? More like Money Never SUCKS amirite?!?!?!?

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You think the answer is 2 you are an idiot and your math is turrible. 288. learn basic 3rd grade math. well maybe 4th.

http://www.wolframalpha.com/input/?i=48/2(9%2B3)&t=macw01

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The answer is 288. The order of operation reads right to left for MD and AS - one does not have priority over the other.

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48/2(9+3) not 48/(2(9+3))

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I love the controversy this is igniting. Great post OP.

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^ Haha, yeah seriously...

This really shouldn't need to be typed out and explained, but it seems some people here need to be schooled.

PEMDAS or BEDMAS where division and multiplication share the same order (whichever comes first) and similarly addition and subtraction share the same order (last) pending on whichever comes first in the equation.

48/2(9+3)

Step 1: (9+3) = 12 (bracket)

Step 2: 48/2 = 24 Division comes before multiplication because it's shown earlier in the equation

Step 3: 24(12) = 288

Seriously, why the hell are we discussing grade school math here?

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Its 288. Order of ops. Honestly this is just poorly written.

Confusion breeds contempt. Evidenced by this thread.

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/end thread, it's 288

http://www.wolframalpha.com/input/?i=48%C3%B72%289...

Good trolling though!

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Order of operations. "Pemdas" my nukka.

And I'm not even back office, im acct - im not even IN the office........ throwback question to alg 2 & trig soph year of hs.

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You're not a trader for a reason.

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Please change your name to Chuckie Sullivan. It's more fitting.

I'm going to use this as an interview question. When an engineer gets it wrong, I'm going to laugh his ass out the door.

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Agree with the people saying this is written ambiguously. If you are going to put the divide symbol between the 48 and the 2 you should toput the multiplcation symbol between the 2 and the (

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Just so those of you who think its 2 don't feel dumb its being argued all over the internet right now.... comical.

WSO is not your personal search function.

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How sad...

Anyway, those still in denial and not willing to accept the rules of order of ops, throw '=48/2(9+3)' in excel

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sure, order of ops but as written implies 48/(2x) rather than 48/2*x

either way it's not a big deal

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Go ahead and plug it into excel. It'll show you this error:

Microsoft Office Excel found an error in the formula you entered. Do you want to accept the correction proposed below?

=48/2*(9+3)

Like I said, the question was very poorly written. It has nothing to do with order of operations here. You can interpret the question in both ways.

-MBP

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288.

easy to get confused, but think of it this way

48/2(9+3) => 48/2*12

if you don't believe it type it on a scientific calculator and see.

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Excel does that because it is not programmed to interpret a number enclosed in parentheses as a factor. That said, the order of operations is not open to debate just because a software app can't interpret the syntax.

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MBP - that's my point though. Yes the equation is poorly written, but it's an accepted fact that when you write something like y(z) it means y x z. And excel while not programmed to interpret enclosed numbers as a factor as whateverittakes said above, it recognizes that y(z) is generally interpreted as y x z and it makes the fix after giving you the error message.

The original equation 48/2(9+3) is 48/2*(9+3) NOT 48/(2(9+3)). The 2(9+3) is just a lazier version of 2*(9+3).

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48 / 2x =

a. 24/x

b. 24x

Discuss

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It's not written ambiguously. 48/2*12= (48/2)*12, and not 48/(2*12)

plug it into freaking excel without parentheses and see what you get

More is good, all is better

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Ok, my entire point is that if there is no consistency in the way a question is formulated, regardless of how simple it is, there is room for interpretation. I can tell you that based on the way the question is written, if I interpret it to mean 48/2x, where x = 9+3, then I'm not wrong. If I interpret it to mean 48/2*x, then I'm still not wrong. I can even interpret y(z) to be some completely strange group action if I want, or that we are in a finite field of order 277, in which case the answer most certainly is not 288.

If you want common sense to apply to the solution, you need to write the question with a bit of common sense. Otherwise, you need to spell out all of your assumptions in the question.

-MBP

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Those arguing 288 might find this interesting

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

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Thank you. My point entirely.

-MBP

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I think this thread just proved a lot of bankers are just as stupid as the rest of the population.

"The power of accurate observation is commonly called cynicism by those who have not got it." - George Bernard Shaw

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I would argue that they're dumber than everyone else. Based on this intellectual performance.

-MBP

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I'm confused as to how you find this poorly written, (9+3) does not equal /12/ or 12, but (12), as in a value to be multiplied. Making it 48 / 2 (12), then 24 (12), then 288.

Either way, I agree with ANT. Can't believe you guys are calling each other retards over a stupid math problem. Hah.

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288

"I'm tapped out Marv. American Express has got a hit man lookin' for me." - Bud Fox

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I have proof the answer is 288...

type it into an equation in excel... amirite?

Went from a poetry major to finance... funny how life works isn't it?

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Please read my earlier post. I explain the answer to your question.

-MBP

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I don't think there is any question that this is the greatest thread in WSO history.

Order of operations:

Rule 1: First perform any calculations inside parentheses.

Rule 2: Next perform all multiplications and divisions, working from left to right.

Rule 3: Lastly, perform all additions and subtractions, working from left to right.

Therefore,

1. (9+3) = 12

2. 48/2 = 24, 24(12) = 288

3. None left

Answer is 288, based on the way the OP wrote the equation. End of story.

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Wrong. It is not the end of story. In elementary arithmetic (the one that contains the / sign) the operation x(y) is not defined. You can't just assume it means x*(y). If you assume that x(y) = x*(y), then the answer is 288. If you assume x(y) = (x*y), then the answer is 2. Since the operation to begin with is not properly define, the problem is not well formed. So, like I said, the answer depends on your assumptions. If you assume x(y) = x^y, the answer is something entirely different. You can even assume that there are no numbers greater than 53 (i.e. the field Z_53).

Once again, you assumed the question was asking 48/2*(9+3). But that is not what was written.

-MBP

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EDIT: yeah, I get what you mean now but I don't think we're trying to distribute the 12 here... My 1/48th Chinese ancestry says so lol.

People like Coldplay and voted for the Nazis, you can't trust people Jeremy## Want to Vote on this Content?! No WSO Credits ?

lmfao. holy shit. can we all just agree that the question is written idiotically? no one would ever write it that way in the first place.

-MBP

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According to my calculator

But I tried it on my flatmates calculator and got different results lol

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I originally sided with 288, but Solidarity brings up a very good argument for 2. So I change my answer to this: there is no answer. Some genius somewhere came up with this seemingly simple math problem that is fundamentally flawed in that it has ambiguous syntax. Probably laughing his ass off about how a bunch of dolts are arguing over something with no real answer

Money Never Sleeps? More like Money Never SUCKS amirite?!?!?!?

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I really don't mean this in the dick way I know it's going to come off (no pun intended).

Have you ever taken a serious course in mathematics? Not the bullshit you learn in high school or a basic calculus course in freshman year, but a rigorous course in algebra where you study groups, fields and other algebraic structures? If you had, you really wouldn't have made the statement about "overanalyzing what x(y) could be." Understanding what x(y) means is the entire source of the confusion in the question. And it's not defined in elementary arithmetic. It doesn't mean multiplication. PEMDAS/BEDMAS doesn't even apply until you define what x(y) means. Normally you can infer it from the question, but in this case you can't.

-MBP

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My point exactly. The question is completely ambiguous.

-MBP

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When CALCULATORS argue over the right answer, you know the question is flawed, LOL.

Money Never Sleeps? More like Money Never SUCKS amirite?!?!?!?

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@ MBP

Haha. Yeah, I get what you mean. I edited my answer before I read your above post.

People like Coldplay and voted for the Nazis, you can't trust people Jeremy## Want to Vote on this Content?! No WSO Credits ?

for those who throw a shit at someone for saying 2.... please have a sense of humor

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Haha, just saw it now. This really was the best thread in a long time.

-MBP

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Jesus MBP you got me trying to work this out on pen and paper now... lol.

People like Coldplay and voted for the Nazis, you can't trust people Jeremy## Want to Vote on this Content?! No WSO Credits ?

MBP, you are SPOT ON. If I had an SB to give you would get one. The definition of x(y) is absolutely the source of the ambiguity and the reason why this isn't as simple as it looks.

Money Never Sleeps? More like Money Never SUCKS amirite?!?!?!?

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lol, fucking WSO. I get 3 monkey shits for being right the entire time. wow

-MBP

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It's clearly 3...

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http://en.wikipedia.org/wiki/Bracket_(mathematics)

x(y) is a verrrrrrry well known abbreviation for x*(y). Look at any math book expanding a product, such as x!, and it is always represented as x(x-1)(x-2)...

The multiplication is obvious.

Also that calculator computes different values because of an error in the parser implementation.

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hysterical.

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O really?

http://www.studygs.net/pemdas/pemdas2.htm

Solving this equation the same way would give an answer of 2. This equation could easily be argued both ways. My first answer when I first saw it was 288, but after thinking about it, I'm sitting on the fence. I also have one calculator showing me 2 and one showing 288. Not sure which one to use for my finals lol

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I'm sorry, but where in that article does it say that x(y) is the same as x*(y)? I never denied that it is commonly understood that way. But it is also commonly understood in many other ways.

It's also pretty commonly understood that xy = yx, but in general it is completely wrong (look up non-abelian groups). And giving me one example of x! being expressed as x(x-1)...1 doesn't prove anything.

The multiplication, most certainly, is not obvious. And if you want to go with the conventional way of solving it, the answer is still 2.

-MBP

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Since x(y) is understood by everyone to mean x*(y), that is the convention -> the conventional way of solving this leads to 288.

No need to bring up group theory for this, the operations being used here are commonly understood.

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By everyone? Really? Conventions aren't defined by ignorant people. They're defined by people who know what they are talking about. No mathematician would agree with you. They would all agree with me that this is an ill formed problem. And if they were forced to solve it, most of them would answer 2.

-MBP

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awesome. two TI's, two answers.

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Wow this is embarrassing for the investment banking community.

It's clearly 288.

Chromey calculator and my Casio calculator both say 288, too.

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First off - just want to note I haven't been throwing shit at you.

Second - I can't believe your argument for a second. Parentheses are an accepted form of representing multiplication, just like * and x. parentheses are used constantly for that exact purpose in countless textbooks and journals. It's the way it's taught both in classes and in textbooks. Period.

You're claiming that mathematicians would treat x(y) as some weird new form of multiplication that works exactly as multiplication except it has the same priority as parentheses in the order of operations. This just isn't done in practice. Try to find a credible textbook that does that.

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The accepted mathematical convention is that when two unknown numbers are juxtaposed, they are multiplied, and that multiplication takes precedence over division. Thus, in this case we multiply 2*12 before we divide, so we get 2.

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The AMS actually says exactly that, that x(y) takes precedence over division.

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[citation needed]

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Why the f would you introduce group theory into plain algebra?

Unless it is specified that you are given a dihedral group or something, ab does equal ba.

5+2 = 2+5 is not an invalid equation just because

on a specific terrainright turn + left turn is not gonna lead you to the same point as left turn + right turnMore is good, all is better

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This is not even algebra this is effing arithmetic

Algebra is where you have x+2=5, solve for x

Arithmetic is where you have 1+(2+4)/6

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Lol, good point!

More is good, all is better

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If written in Excel exactly as typed above the answer is 288. My math guys here also said it is 288. (9+3) first then left to right to solve.

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lol, I've been completely bombarded with monkey shit on this thread. Oh well, thanks for not joining in.

Anyway, I've spotted the flaw in your logic. You think it is the brackets that tell you that you need to multiply. This is a very common misconception, and I don't really blame you or anyone else for falling prey to it. In actuality, it is the adjacency of two terms that tells you that you need to multiply them, whether or not there are any brackets. For example, xy means multiply x and y. Not (x)(y), which means multiply what's in the two pairs of brackets. It's when you want to place two terms adjacent to one another to express multiplication, but it may cause some confusion, then you use brackets to clarify. You don't use brackets to express the multiplication.

As an example, let the first term be a+b, and the second be c+d. If I want to show the product, I simply need to place the terms next to each other. Which results in a+bc+d. But this is not what we mean when accounting for pemdas, and so we need to specify with the parenthesis that we mean (a+b)(c+d).

So now that we've clarified what the parenthesis really mean (just that whatever operation pertains to the parenthesis, you perform that first) you can see that x(y) is symbol for an operation on the parenthesis. It means that you distribute x into what's inside. And since this is an operation on the parenthesis, you do it first. This is the proper convention, and this is the subtle difference between x(y) and x*(y). The latter separates x and (y), but the former brings them together into the same overall operation.

And before, all that talk about group theory and stuff, I wasn't using that as a proof that the answer is 2, all I was saying was that question is poorly formed, because while it's now obvious that the author meant 2(9+3) to mean 2*(9+3), he didn't account for the subtle distinction. Which is that when you use the division sign, you have to use the multiplication sign explicitly to be clear. You can't use the adjacency convention to express multiplication. When you don't use consistency in the formulation of the question, all interpretations are valid, even the outlandish ones I was using as an example.

-MBP

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Who are your 'math' guys? Also, you can't type it exactly as it's shown in the OP in excel.

-MBP

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excel says it's 288, therefore it's 288.

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Wrong. Excel doesn't say it's 288. Excel doesn't answer it until it guesses what you actually mean. It's only after you clarify what you mean to Excel that it answers 288. If the clarity had been provided in the OP from the very beginning, there wouldn't have been this outrageous debate over arithmetic.

-MBP

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If you type it into Excel it autocorrects the equation to 48/2*(9+3). My "math" guys as in analysts. They did the equation then typed into excel to see what it said. Both arrived at 288.

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I skipped all the discussion: the question is poorly written and requires clarification.

Is they stupid....Engrish much?

__________________

............./'-/)........... (\-`\

............/....//........... ...\\....\

.........../....//............ ....\\....\

...../'-/..../'-\.........../- `\....\-`\

.././.../..../..../.|_......_| .\....\....\...\.\..

(.(....(....(..../.)..)..(..(. \....)....)....).)

.\................\/.../....\. ..\/................/

..\................. /........\..................../

....\..............(.......... ..)................/

Get busy living

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Dude, that is exactly my point. There is a subtle difference between 2(9+3) and 2*(9+3) which I explained above, and it confused Excel as well, which is why it asked if you meant 2*(9+3) instead.

So to be clear, excel didn't answer the question. It answered another question which it assumed you meant to ask. These are two very different things. When I answered 2, I assumed the OP meant to ask another question. Had the question been written 48/2*(9+3), there would have been no debate, and excel would have just gone ahead and answered without the error message interruption.

And please don't refer to your analysts as math guys as if they're some sort of experts. They're probably engineering majors and haven't got a clue as to the subtleties that can arise in even the simplest mathematics.

-MBP

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288 = bankers

2 = back office

looks like we have the back office team in this thread lined up nice and neat

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All you're proving with this statement is that bankers are more ignorant about mathematics, not that there's anything wrong with that. Also, I'm not in the "back office"

-MBP

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youre in big 4, your entire industry is considered back office.

U MAD?

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I make more money than you, U Jelly?

-MBP

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Does anyone else think it's 7? I keep getting 7.

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YA 60K IN TORONTO MAD JELLY BRO, U TOTALLY PWNING MY MEGAFUND 300K.

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What I agree with.

Distributive property of multiplication. Early Algebra.

The distributive property of multiplication CLEARLY states that the 2(9+3) is an entire term and CANNOT be broken up. 2(9+3) follows the distributive property which can be rewritten as (2*9+2*3). Let me repeat the 2 outside of the parenthesis follows the distributive property of multiplication and must be factored and simplified before performing any other operations on it.

So this can be rewritten as:

48 / (2*9 + 2*3)

Which leaves us with

48 / 24 = 2

Answer = 2.

Lastly for those using Google or any other online calculator. These do not understand many theorems or properties so you must explicitly explain what you mean. There is a difference between 48 / 2 *(9+3) and 48 / 2(9+3). The first notation reads 48 / 2 * 1(9+3) while the second reads 48 / (2*9+2*3). Be very careful with your signs.

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I did read through your analysis and I agree with it. My initial reaction was 2, but after reading the debate thought I'd ask for other opinions in the office. Two people said 288 and one said 2 (the math major).

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This is absurd.

48/2(9+3) can be rewritten as (48)/(2)(12) - I don't think anyone will argue that I can put ()s around numbers.

Which can be re-written as (x)/(y)(z).

Note (y)(z)=(y)*(z)

So (x)/(y)*(z)=288.

This is not ambiguous at all.

I would also say that TECHNICALLY, 48/2x = 24x, though it would typically be interpreted differently.

And seriously, bringing group theory into this is ridiculous.

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is princeton a target?

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According to this Math Explanation , it's 288 as paranthesis are exactly the same as multiplication which is on the same level as division and should therefore be solved left to right

however according to this Math Explanation, it's 2 as paranthesis does outrank division and therefore should be solved first.

There does not seem to be a generally accepted way of resolving the conflict which explains why even the best scientific calculators are giving different solutions to the problem

Let's just agree that the question is too ambiguous and solid arguments can be found for both camps.

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Ding ding ding.

Ambiguity sucks and there's usually a reason the other guy thinks the way he does.

"Dude, not trying to be a dick here, but your shop looks like a frontrunner for the cover of Better Boilerrooms & Chophouses or Bucketshop Quarterly."

-Uncle Eddie

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Totally and completely wrong. And I was not bringing in group theory to prove anything. It was just illustrative of how you *can* interpret the problem differently.

Also, 48/2x is24/x. Not 24x.

-MBP

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The answer is obviously 48/2(9+3), you can't expect an answer unless there is an = sign to start the equation....

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48/2(9+3) = 48/2 * 12 = 24 * 12 = 288

48/(2(9+3)) = 48/(2*12) = 48/24 = 2

/end

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http://www.google.com/#sclient=psy&hl=en&site=&sou...(9%2B3)&rlz=1R2ADFA_enUS404&aq=f&aqi=&aql=&oq=&pbx=1&bav=on.2,or.r_gc.r_pw.&fp=c0a798e739e242fa

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Python, C++, C#, C, Wolfram Alpha, Google, MATLAB all say 288.

/end story.

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Did he died?

Check out my WSO Blog

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BEMDAS (Brackets, Exponents, Multiply, Divide, Add, Subtract)

=48/2*(9+3)

=48/2*(12)

=48/24

=2

There have been many great comebacks throughout history. Jesus was dead but then came back as an all-powerful God-Zombie.

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hahahaha

no, it's in New Jersey, so it can't possibly be a reputable school

Get busy living

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the calculator is only as smart as its operator if you put a problem in the calculator with -(1) and then you did another problem with (-1) you'd get two different answers.....

WSO is not your personal search function.

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48/2(9+3) = 48 / 2 * (9+3) = 48 / 2 * (12) = 24 * 12 = 288

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This is clearly a test to see who goes to a target like Michigan

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http://forum.bodybuilding.com/showthread.php?t=133...

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wat

and regarding the calculators, the TI 86 > 85 > casio since everyone likes doing the "my cock > GS > your cock" thing. someone needs to try on an 89

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lol distributive property your dumb ass. how can you only distribute only part of the coefficient?

or do you seriously believe 48/2*(a+b) is not the same as 48/2(a+b) ???????

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For the record I sent this to a list at my engineering school (top 5 in some disciplines, top 10 overall) to a list of engineers from biomed, chemE, aerospace, EE, compE, IE, mechE(phd), math/statistics, and even computer science and they were split between 2 and 288 also. At first I thought it was pretty straight forward its 288. But now I'm changing my mind that maybe it is written ambigiously.

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OMFG no wonder no one knows how CDOs MBS ect ect are calculated. We cant even agree on a simple math problem that is obviously 288. It would be 2 if it was written like this 48/(2(9=3)). Since there isnt a 2nd set of brackets to quantify the the 2 times 12 step. Since it is written in a line item way you can rule out a fractional equation since its not written as a fraction.

Follow the shit your fellow monkeys say @shitWSOsays

Life is hard, it's even harder when you're stupid - John Wayne

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I understand credit derivatives and their pricing very well. And I assure you that both 288, and 2 are valid given the ambiguity in the way the question is written. It's poorly written. That's all there is to it. Can we please just all move on now?

-MBP

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A bunch of [non-target wannabe] bankers arguing with a MFE student about arithmetic.... Only on WSO.

MBP, you deserved those SBs.

LOL, these guys are still at it.

I win here, I win there...

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I was refering to people outside of banking, I should have specified that. My bad guys.

Follow the shit your fellow monkeys say @shitWSOsays

Life is hard, it's even harder when you're stupid - John Wayne

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This question is absolutely ambiguous. However, you can't say that both answers are correct. Both answers are actually incorrect and this question does not have an answer.

Answering EITHER 2 or 288 would imply turning 48/2(9+3) into either 48/2(x) where x = 9+3, 48/2*(9+3), or some other "equivalent expression." But you cannot do this. NONE of these other expressions are equivalent expressions, and there are no set-in-stone rules for how to apply the implied multiplication in the first question.

We can, however, based purely on mathematical tradition and such, debate about whether, if such a rule were created, the implied multiplication would be interpreted as 2(x) or 2*(9+3)

I personally think it makes more sense to give 2(9+3) prioirity over the 48/2. I'm not saying that it's the correct way, but I'm saying that for the future, this should be made the correct way of interpreting the problem.

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Sorry guys you are all incorrect. The answer is 42.

ambition is a state of permanent dissatisfaction with the present.

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Good Idea to post the link here and refer them to our discussion?

Get busy living

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48/2(9+3) = 288 with no ambiguity. The adjacency convention is for multiplication. It's not "inconsistent" to use adjacency to represent multiplication because this is never done for division...division is always specified by an actual symbol.

Also, I never said that (a+b)(c+d) = a+bc+d. I said that it is the convention to omit the multiplication symbol * where parenthesis makes it unnecessary. So (a+b)(c+d) = (a+b)*(c+d) as normal. Similarly, 10/(2+3)(1+1) = 10/(2+3)*(1+1) = 10/5*2 = 2*2 = 4.

And for those of you bringing up the distributive property of multiplication...that doesn't change the order of operations at all.

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The point that people miss about PEMDAS is that it's really

P E M/D A/S

multiplication and division happen at the same time (from left to right) as do addition and subtraction.

this means M and D are interchangeable so having MD is the same as DM

In your example the first is correct not because division always come before multiplication but because the division in the problem is first.

Disclaimer for the Kids: Any forward-looking statements are solely for informational purposes and cannot be taken as investment advice. Consult your moms before deciding where to invest.

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Confusion breeds contempt...couldn't have put it any better.

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turrible knuckleheads don't know their order of operations. 48/2(9+3) > 48/2*12 > 24*12 > 288. Knuckleheads your math is so turrible it offends me. knuckleheads

Making money is art and working is art and good business is the best art - Andy Warhol

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This is correct. If you are left with a multiplication part and division part, you go from left to right. One does NOT supersede the other. Same with addition and subtraction.

48 / 2(9+3) =

48 / 2 * 12 =

24 * 12 =

288

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Boom goes the dynamite.

Follow the shit your fellow monkeys say @shitWSOsays

Life is hard, it's even harder when you're stupid - John Wayne

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http://www.mathsisfun.com/operation-order-pemdas.html

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First of all, division is just an artificial simplification as an illustrative tool to teach kids. There's no real definition of division in rigorous mathematics. There is only addition and multiplication. Subtraction is just addition of an additive inverse, and division is just multiplication of a multiplicative inverse (look up algebraic field for further clarification of how the number systems you are familiar with are constructed rigorously). That is why there are no short hand conventions for "division". So if the question had been written in conventional notation, there would be no confusion to begin with. This is the exact reason why mathematics is formed on a rigorous foundation. But of course, the material has to be bastardized when it is taught to kids, and then they have a hard time relearning it properly.

You missed my entire earlier point btw. I never said you were saying (a+b)(c+d) = a+bc+d. It was just an illustration.

-MBP

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My question is, how can you expect someone to find the answer when the basis of the problem is described in a non quanitive fashion such as, (a+b)(c+d) I mean honestly it would be much easier just to use number and give a damn answer.

Follow the shit your fellow monkeys say @shitWSOsays

Life is hard, it's even harder when you're stupid - John Wayne

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hahaha

WSO is not your personal search function.

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Ok, this has gotten out of hand. These are the two interpretations. Stop posting dumbass links to how pemdas works. Everyone knows that. That's not what's under dispute.

48 / 2(9+3) = 2

48/2 (9+3) = 288

-MBP

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MBP but wouldn't you say for it to be read the first way you need another set of parenthesis? or would you say that doesn't matter?

WSO is not your personal search function.

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So thus far, we've used various casio and TI calculators to no avail. And then we consulted engineers, math prof's, computer science experts, blah blah blah... who also yielded similar ambiguity.

Yet no one, up until this point, sought the answer from the golden brushed-aluminum god that is the HP12C.

(Leveraged Sellout excerpt: "Excel Mobile, it speaks a pure, unambiguous language: Reverse Polish, a postfix notation that eliminates non-commutative issues.")

48 [enter] 2 [ / ] [enter] 9 [enter] 3 [ + ] [ * ] = 288

"1/10th the functionality, 10x the badass."

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That would really spell it out and take away the ambiguity. For sure. But not necessarily. See, my entire point from the start has been that no one would write the problem like this. In rigorous notation, it would be written in one of these two ways:

48(2^(-1))(9+3) = 288 or 48((2(9+3))^-1) = 2

There would be no division. Just multiplication and addition.

*Unnecessary overuse of brackets because can't type in mathematical notation here.

-MBP

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But since the parenthesis aren't there aren't you forced to do it in a way where the answer comes out to 288?

WSO is not your personal search function.

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This one goes to 11...

If I had asked people what they wanted, they would have said faster horses - Henry Ford

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It's 288...lol omg i can't believe this goes to 4 pages...

Consultant to a Fortune 50 Company

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omg, 4 pages? end this now!! http://lmgtfy.com/?q=48%C3%B72(9%2B3) now you have to argue to google.

Valor is of no service, chance rules all, and the bravest often fall by the hands of cowards. - Tacitus

Dr. Nick Riviera: Hey, don't worry. You don't have to make up stories here. Save that for court!

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talk about a throw back haha

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288 = 48/2(9+3)

Just order of operations

Parathese/Brackets first (9+3=12), then (48/2=24, since you go from left to right), then (24*12=288).

I don't get the point of this post....

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Just have to add in, I can't believe I spend my time answering it/I can't believe this is four pages long.

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Yeah man, I can't even remember the last time I heard that phrase!

Get busy living

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it's official... there's literally NOTHING more that can be said about this thread. this has to be the fiftieth time someone has said this exact thing. can we close this now please???

Money Never Sleeps? More like Money Never SUCKS amirite?!?!?!?

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ibtl

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the answer is 2. idk the point of this???

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Just read this whole post and want my ten minutes back

Get busy living

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TWO. It's an Arabic numeral system. There is no right to left fool!

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...but thats not the way it was written.

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look at what I caused...

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Seconded... or probably the 10th person to agree. The reason why this hasn't ended even with me, you, and everyone writing out why it's 288... is because then the "2" camp will debate that parentheses =/= the same as multiplication and making their justifications for it or whatever else... and so on back and forth. No matter what else can be said, neither side will concede.

The middle ground can only be that this question can be better written so that there is no question for misinterpretation. Besides that, or a mod closing the thread, only way one group or the other would shut up is if someone like Stephen Hawking makes a public announcement to shut everyone up once and for all.

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This has proved far more divisive than any political/economic/moral/school discussion. Look at the havoc you have created lol.

Making money is art and working is art and good business is the best art - Andy Warhol

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