48÷2(9+3) = ????

[Freakazoid]

i still hold that there were too many dumb people in this thread. I guarantee you 90% of the people who said 2 weren't going to the theory level, and were completely incorrectly using the order of operations

[Crisp]

Originally Posted by yakev724

The correct notation of the problem is

48÷2×(9+3) =

The OP's notation is ambiguous, and though I would argue that it (strongly) represents the above (yielding 288), many interpret it as

48÷[2(9+3)] =

yielding 2.

Anyone who says the notation is unambiguous (i.e. claiming the answer is definite) is, imho, incorrect.

That is all.

Ambiguous?!

You perform the operation that is put in front of you.
If you don't understand it, that's another problem, but you CANNOT say 'he meant this, so the answer is this'. You solve what is written.

A person who writes 2 - (-2)=x did not mean to write 2+2=x
He wanted the first equation to be solved.
You can't cross out the question and make up your own. wtf?


48÷2(9+3)=X is the question and it is written in correct mathematical terms and signs.

48÷2(9+3)=X can ALSO be written as:

48/2 (9+3)=X
(48/2)(9+3)=X
48÷2 x (9+3)=X
48/2 x (9+3)=X


Which ever one of those you want to use, the answer will ALWAYS be 288.

There is nothing ambiguous about math. It's the only subject that is NOT open to interpretation.

With all due respect, both your opinion and my opinion do not count in math.
It has nothing to do with opinion.

2+2 IS 4 not '2+2 is in my opinion 4' but could be something else also.


I understand that some people do not have math backgrounds or majors, but I do not understand if someone tells you the statement above, and you still continue to argue that it could be a different answer or it's open to interpretation.

[ragingclue]

Originally Posted by Freakazoid

i still hold that there were too many dumb people in this thread. I guarantee you 90% of the people who said 2 weren't going to the theory level, and were completely incorrectly using the order of operations

Implied multiplication is a grey area really, but like radix said, if I don't see it with a monomial that includes a variable, I don't even think twice about it. Also, even then, I'd say it needs to be re-written with parentheses to clarify its intended purpose.

[Crisp]

Originally Posted by radix

I talked to a friend of mine who was at one point a professor of theoretical mathematics at Northwestern and has a PhD in the same field. His basic stance was that it was a problem designed to create an argument, and that either answer was acceptable given the poor structure of the problem. The idea was that strict AMS interpretation of the expression would place multiplication by juxtaposition above division in terms of precedence. E.g., normally:


1 / 2x

is interpreted as

1 / (2 * x)

not

(1 / 2) * x

thus were x = 5 the expression would evaluate to .10 not 2.5. However he went on to say that it is not conventional to use multiplication by juxtaposition with digits where there is no variable involved, i.e. 2(9 +3). His ultimate decision is that it was a problem designed to cause an argument, and that either answer would work depending on the rule being followed. The content of this discussion seems to support my friends interpretation:

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


Specifically:

Is he a mathematician or lawyer/philosopher?!


What his argument boils down to is what looks more pleasing to the eye of the general public.
So, according to him:

10/ 2*2 = 10/(2*2) = 2.5

BUT

10/2 *2 = 10



This is not a mathematical argument, it's an argument to show what people would THINK or interpret it as, but in the end, if you want to be technical (as math is), there is only ONE correct answer; 10!

This guy however is saying that you should account for morons in the world that don't know how to write equations properly, thus, you must think like a moron thinks and answer the equation the way that the morons want you to answer it in order to be in agreement.... EVEN THOUGH BOTH OF YOU ARE WRONG AT THE END OF THE DAY.


To help people clarify this, lets say I'm stupid and think a CAT is a PIG.
Each time I talk to you, I tell you my PIG is sitting on my lap. You know that I am actually referring to my cat being on my lap, and in your mind, you correct my retarded mistake, but there is no way in hell you are actually going to look at me with a CAT on my lap and agree that it's actually a PIG.
You're just going along with my retardedness.


If someone came up to you and put a gun to your head and said: is that a PIG or CAT sitting on his lap... you life depends on it.

What would your answer be sir?

[radix]

Originally Posted by Crisp

Is he a mathematician or lawyer/philosopher?!


What his argument boils down to is what looks more pleasing to the eye of the general public.
So, according to him:

10/ 2*2 = 10/(2*2) = 2.5

BUT

10/2 *2 = 10

No, he said that multiplication by juxtaposition takes precedence over division. The example you listed is not multiplication by juxtaposition. The expression:


2a

is multiplication by juxtaposition. The expression:

10/ 2*2

contains only an explicit multiplicative operation, and is therefore evaluated left to right.

10 / 2x

however is evaluated as

10 / (2 * x)

not

(10 / 2 ) * x

because 2x represents a juxtaposed multiplicative operation. The problem with the question as posed in the OP is that multiplicative operations on juxtaposed quantities are usually only used on expressions involving variables. Thus:

2(3) is not proper syntax.


whereas

2a

is.

Of course all of this was stated in my previous post, but instead of actually listening to not one, but two math PhDs, at least one of whom was a professor of theoretical mathematics at one of the top schools in the U.S., you'd rather insult someone by calling them a philosopher/lawyer.

[Verbiage]

[BTM]

I'm in accounting and google says 288































CSB























Radicks how you been?

[BTM]

http://lmgtfy.com/?q=48%C3%B72(9%2B3)

[Crisp]

Originally Posted by radix

No, he said that multiplication by juxtaposition takes precedence over division. The example you listed is not multiplication by juxtaposition. The expression:


2a

is multiplication by juxtaposition. The expression:

10/ 2*2

contains only an explicit multiplicative operation, and is therefore evaluated left to right.

10 / 2x

however is evaluated as

10 / (2 * x)

not

(10 / 2 ) * x

because 2x represents a juxtaposed multiplicative operation. The problem with the question as posed in the OP is that multiplicative operations on juxtaposed quantities are usually only used on expressions involving variables. Thus:

2(3) is not proper syntax.


whereas

2a

is.

Of course all of this was stated in my previous post, but instead of actually listening to not one, but two math PhDs, at least one of whom was a professor of theoretical mathematics at one of the top schools in the U.S., you'd rather insult someone by calling them a philosopher/lawyer.

I read his entire argument and made one of my own.
Do you have any idea what juxtaposition means or you only know that it looks like '2x'?

"An absence of operators in an expression.
Using juxtaposition for multiplication saves space when writing longer expressions."


Hence why I posted the following comparison:

10/ 2*2 = 10/(2*2) = 2.5

BUT

10/2 *2 = 10

The first one contains a space between the division sign and 2, while the second equation has the two next to the division sign.

10/ 2 Versus 10/2

According to Mr.PHD, people go based on what 'looks' correct not what IS correct. They take the liberty to guess what the person means, not what is actually written. Thus he says when you see 10/2x, we assume the person meant 10/(2x).

Sorry but math is NOT about assuming. As I said many times, you do what is in front of you, which is TEN DIVIDED BY 2, MULTIPLIED BY x.

Most people assume 10/2x was meant to be written as:

10
---------
2 * x


This is what he is saying.

Moral of his story: one must assume in math to account for idiots who don't know how to write the equation they really meant to write.

[Crisp]

Originally Posted by BTM

http://lmgtfy.com/?q=48%C3%B72(9%2B3)

You missed a parenthesis, and google ASSUMED you meant "48÷2(9+3) ="
even though your wrote "48÷2(9+3 ="



This is what this whole thread is about. Good proof. lol

[schoy]

Originally Posted by Crisp

With all due respect, both your opinion and my opinion do not count in math.
It has nothing to do with opinion.

2+2 IS 4 not '2+2 is in my opinion 4' but could be something else also.


I understand that some people do not have math backgrounds or majors, but I do not understand if someone tells you the statement above, and you still continue to argue that it could be a different answer or it's open to interpretation.

Disagree strictly as it applies to the present problem. One thing one should realize is that the syntax of operations (and the order of operations) is entirely man-made. If the entire mathematical community tomorrow decided, for example, that the "+" sign meant multiplication, or that equations must be read from right to left, then the game changes entirely. Thus, how math is communicated can be subject to interpretation.

Here, we have in my mind potential ambiguity in the way the problem was communicated. While my own education supports the 288 answer, I can see how 2 could be a reasonable response.

Edit: One more thing to add regarding the multiplication by juxtaposition issue: Let's say on your final exam of Algebra 101, taught by radix's Mr. Phd, you are presented with the problem 10/2x = 10 (written in that exact linear format). Crisp, based on your understanding, I believe you would answer x = 2. But what would you do if Mr. Phd said your answer was incorrect (because Mr. Phd said the answer was 0.5)? While you could plead your case (and Mr. Phd would bring up the multiplication by juxtaposition counter-argument), ultimately it's Mr. Phd that controls the academic consequences. Moral of this story: while math as it exists in a theoretical vacuum is black-and-white, its consequences in the physical, real world is subject to man's interpretation.

Edit: Another example: Let's say you were building the next Space Shuttle. The engineer/designer hands you the plans for a critical widget. The length of said widget is calculated using the equation 10/2(m length of new Space Shuttle) = mm length of widget. Let's say length of new Space Shuttle is now planned to be 50 meters. Do you blindly adhere your understanding of operations and build a 250mm widget? Or do you scratch your head and ask yourself whether the engineer meant a 0.1 mm widget? For the sake of our astronauts and their families, I would hope you would recognize the potential ambiguity and give the engineer a call to clarify ...

[BTM]

Originally Posted by Crisp

You missed a parenthesis, and google ASSUMED you meant "48÷2(9+3) ="
even though your wrote "48÷2(9+3 ="



This is what this whole thread is about. Good proof. lol

OK:

http://lmgtfy.com/?q=48%C3%B72(9%2B3)


:b onk:

[Crisp]

Originally Posted by schoy

Disagree strictly as it applies to the present problem. One thing one should realize is that the syntax of operations (and the order of operations) is entirely man-made. If the entire mathematical community tomorrow decided, for example, that the "+" sign meant multiplication, or that equations must be read from right to left, then the game changes entirely. Thus, how math is communicated can be subject to interpretation.

Here, we have in my mind potential ambiguity in the way the problem was communicated. While my own education supports the 288 answer, I can see how 2 could be a reasonable response.

Edit: One more thing to add regarding the multiplication by juxtaposition issue: Let's say on your final exam of Algebra 101, taught by radix's Mr. Phd, you are presented with the problem 10/2x = 10 (written in that exact linear format). Crisp, based on your understanding, I believe you would answer x = 2. But what would you do if Mr. Phd said your answer was incorrect (because Mr. Phd said the answer was 0.5)? While you could plead your case (and Mr. Phd would bring up the multiplication by juxtaposition counter-argument), ultimately it's Mr. Phd that controls the academic consequences. Moral of this story: while math as it exists in a theoretical vacuum is black-and-white, its consequences in the physical, real world is subject to man's interpretation.

Edit: Another example: Let's say you were building the next Space Shuttle. The engineer/designer hands you the plans for a critical widget. The length of said widget is calculated using the equation 10/2(m length of new Space Shuttle) = mm length of widget. Let's say length of new Space Shuttle is now planned to be 50 meters. Do you blindly adhere your understanding of operations and build a 250mm widget? Or do you scratch your head and ask yourself whether the engineer meant a 0.1 mm widget? For the sake of our astronauts and their families, I would hope you would recognize the potential ambiguity and give the engineer a call to clarify ...

The bold is true and the teacher would obviously win and has happened to me before, but that's just because they hate admitting that they are wrong or they meant something else than what was written. An honest teacher would accept the mistake or the poorly written format of the equation: 48÷2(9+3) = x, and accept both answers 2 and 288, and say "because the equation was written poorly, I will take 2 and 288, but the true answer is 288 if order of operations was followed strictly".



Your second example:

I don't really see it being related. If the engineer wanted the answer to his equation, it would be a 250mm widget. If he wanted the answer that would make that shuttle fly, it would be different.

I would not however write an answer of 0.1mm for that question though.
I would bring it up and have him correct the equation or let him know that I am answering a different question since I already have prior knowledge about what the answer needs to be in order for the shuttle to fly.

There have been countless examples in grade school that teach you to do what you are told on the test, not what you think is write.

For example:

They gave out a test to us in grade school that had 50 questions and we had 5 minutes to answer.
The directions:

"You have 5 minutes to complete this test. Make sure you read every question before starting the test"

The test had some ridiculous questions that were impossible to solve. If however, the directions were followed and the person read EVERY question before starting, they would see that the last question said something like "you don't have to answer any of these questions for this test, just sign your name".


This is why I think it's important to first answer this question with 288, then state that the format is not what we would see every day so this might be a reason for MISTAKES, but nonetheless, the answer is and will always be 288 to that equation.

No if ands or buts. No "it's 288 but I think it can be 2 also".

That was my whole point.

[Crisp]

Anyway, I feel like I've beaten this topic to death.
Most know where I stand.

On to the next one. lol

[007MCoupe]

Originally Posted by Bavarian III

still pushing them milian pics

[Verbiage]

Originally Posted by 007MCoupe

still pushing them milian pics

I am trying to find a reason as to why this thread should still exist.


And I love her.

[radix]

Originally Posted by Crisp

With all due respect, both your opinion and my opinion do not count in math.
It has nothing to do with opinion.

Then please tell me according to "math" which one of these is definitively correct;

- For any point P not on line L, then there are at least two lines through P that are parallel to L.

- For any point P not on line L, there are no lines through P that are parallel to L.

- For any point P not on line L, there is no more than one line parallel to L.

because they are all contradictory.

[Hawkeye]

Bump. Deal with it.

Radix, when ambiguous letters are involved the rules change a bit.

Say you replace x with 5. 1 / 25 is completely different than what you would be trying to ask. You have to use the same syntax to justify the problem using an ambiguous letter. Maybe 1/2(x) works, but then that just simplifies to x/2.

[Want]

[Blake]

this thread is fucking retarded. lock time.

[bosstones]

Wow....who knew math was controversial. Someone divide it by zero and end the universe already.