48÷2(9+3) = ??? -- VOTE!! Poll Added

[Pine Tar]

Wow this is still going.
Ok now some slove the debate that the Longoria Super does not exist.

 

[CubsFan13]

Has anyone put this, as is, into a TI-85/93/95 calculator?

What does Texas Instrument have to say? You can type that equation in as it's written, hit = and tells us what you get...

My TI-84 Plus Silver Edition calculator says that 48/2(9+3) equals:

288

 

[goblue6919]

Parenthesis
Eexponents
Multiplication
Division
Addition
Subtraction

You do 9+3 since it's inside the parenthesis, then multiply, then divide. i don't see how it couldn't be 2

48÷2(9+3)
48÷2(12)
48÷24
=2

 

[goblue6919]

THINK OUTSIDE THE BOX.

the answer is 288 if you use PEMDAS. anyone who denies this is dumb. most people aren't denying this (i hope).

the answer is 2 if you understand that a precedence is given to the multiplication part of the equation because 2(9+3) is implied to be 2*(9+3)

48÷2(9+3) = 288 via PEMDAS
2(9+3) is equal in priority to 48÷2
2(9+3) is implied to be 2*(9+3) -
2*(9+3) takes precedence over 2(9+3) - 99.99999% of the time this doesn't matter, but it is an absolute fact - look it up.
2*(9+3) therefore takes precedence over 48÷2, which was equal to 2(9+3)
48÷2*(9+3) therefore is 2

Does the question say 48÷2*(9+3)? No. It says 48÷2(9+3).

Therefore, neither answer is wrong. If you want to acknowledge the implication then it's 2. If not it's 288.

Does every person who voted 2 fully understand this concept? Probably not, but subconsciously it just makes sense to us. It is training by PEMDAS which makes us want to eliminate the parentheses. It is human nature to associate the adjacent 2 to the function of eliminating the parentheses.

The problem, quite simply, is missing a set of parentheses. (48÷2)(9+3) is inarguably 288. 48÷(2(9+3)) is inarguably 2. It is a deliberately flawed question as 48÷2(9+3).

Were I a high school math teacher I would never include this question on a quiz/test. Had I foolishly included it I would probably accept 288 as my answer (technically I would accept both, but thats beside the point) as I wouldn't expect mere high school students to understand upper level math concepts as I've outlined today.

Anyone who arrives at 2 using plain PEMDAS is doing it wrong. Anyone who can't see why someone would choose 2 for other reasons is also doing it wrong, whether or not they actually agree with those reasons.

Print out this post and show it to your math teachers, professors or Stephen Gotdam Hawking himself and tell me what they say.

Most of your post makes sense, but explain why 2*(9+3) takes precedence over 48÷2.

A big part of the problem people who argue 2 have been having is that they think 2(9+3) should be done first because Multiply comes before Divide in PEMDAS. But, as several have pointed out, dividing and multiplying are interchangeable in the order of operations (therefore equal) and thus the problem should be done left to right - which gets you 288.

2*(9+3) being of greater significance than 2(9+3) (which is of equal significance to 48÷2) therefore changes your order of operations.

Why would you not do 9+3 first since its inside parenthesis which is the P in PEMDAS?

 

[KC37]

Parenthesis
Eexponents
Multiplication
Division
Addition
Subtraction

You do 9+3 since it's inside the parenthesis, then multiply, then divide. i don't see how it couldn't be 2

48÷2(9+3)
48÷2(12)
48÷24
=2

Because, as has been stated, the "MD" of PEMDAS are equal in rank, and go left to right in order in the problem. In this case, you divide first because it's the leftmost operation.

 

[Fandruw25]

3 days, 18 pages and there is still no clear cut answer...Maybe this is one of those meaning of life type questions.


Oh and the answer is 2 :lol:

 

[vwnut13]

3 days, 18 pages and there is still no clear cut answer...Maybe this is one of those meaning of life type questions.


Oh and the answer is 2 :lol:

I found a forum that had a 100 page thread on this question.

This thread IS going to reach 100 pages.

And to those wondering why it is in baseball, a mod started it.

:lol:

 

[Pills]

*bangs head*

Hi, I'm a pension actuary. I have a BS in actuarial math from one of the top 25 institutions in the land (ok, now it's 29, I think, but it was 24 when I was there). I got a perfect score on my math SAT way back when.

The answer is 288.

You people that are saying 2 are putting the 12 in parenthesis as more important than the order of operations, when it's simply saying multiplication. Multiplication using parenthesis is just another way of writing it. Does writing it with an x take precedence over writing it with a dot? No.

48/2(9+3)
is the same as saying
48/2*(9+3)
48/2*12
According to order of operations, multiplication and division are equal, (as are addition and subtraction) and should be read from left to right. This also explains why, when I've seen this post, people have PEDMAS OR PEMDAS.
Thus, 48/2 = 24 * 12 = 288.

 

[BunchOBull]

*bangs head*

Hi, I'm a pension actuary. I have a BS in actuarial math from one of the top 25 institutions in the land (ok, now it's 29, I think, but it was 24 when I was there). I got a perfect score on my math SAT way back when.

The answer is 288.

You people that are saying 2 are putting the 12 in parenthesis as more important than the order of operations, when it's simply saying multiplication. Multiplication using parenthesis is just another way of writing it. Does writing it with an x take precedence over writing it with a dot? No.

48/2(9+3)
is the same as saying
48/2*(9+3)
48/2*12
According to order of operations, multiplication and division are equal, (as are addition and subtraction) and should be read from left to right. This also explains why, when I've seen this post, people have PEDMAS OR PEMDAS.
Thus, 48/2 = 24 * 12 = 288.

We ain't got no room for that there logic and reason 'round these parts.

 

[aminors]

*bangs head*

Hi, I'm a pension actuary. I have a BS in actuarial math from one of the top 25 institutions in the land (ok, now it's 29, I think, but it was 24 when I was there). I got a perfect score on my math SAT way back when.

The answer is 288.

You people that are saying 2 are putting the 12 in parenthesis as more important than the order of operations, when it's simply saying multiplication. Multiplication using parenthesis is just another way of writing it. Does writing it with an x take precedence over writing it with a dot? No.

48/2(9+3)
is the same as saying
48/2*(9+3)
48/2*12
According to order of operations, multiplication and division are equal, (as are addition and subtraction) and should be read from left to right. This also explains why, when I've seen this post, people have PEDMAS OR PEMDAS.
Thus, 48/2 = 24 * 12 = 288.

Yup.

Multiplying and dividing are treated as equal. The rule is to read them from left to right. Same with addition and subtraction. Left to right when that's all that's left. It's kinda like the i before e rule. It's not just PEMDAS all the time (just like it's not i before e all the time). There is(are) clause(s) for these things that must be minded when using them.

 

[miguelcabrera]

288

 

[scotty21690]

Miggy has spoken.

I now change my answer from "2" to "288".

[/thread]

 

[Therion]

*bangs head*

Hi, I'm a pension actuary. I have a BS in actuarial math from one of the top 25 institutions in the land (ok, now it's 29, I think, but it was 24 when I was there). I got a perfect score on my math SAT way back when.

The answer is 288.

You people that are saying 2 are putting the 12 in parenthesis as more important than the order of operations, when it's simply saying multiplication. Multiplication using parenthesis is just another way of writing it. Does writing it with an x take precedence over writing it with a dot? No.

48/2(9+3)
is the same as saying
48/2*(9+3)
48/2*12
According to order of operations, multiplication and division are equal, (as are addition and subtraction) and should be read from left to right. This also explains why, when I've seen this post, people have PEDMAS OR PEMDAS.
Thus, 48/2 = 24 * 12 = 288.

Distributive property, yo.

If 9 and 3 were unknowns, how would you answer it?

48/2(x+y)

The question is too ambiguous to give a definitive answer.

Logic dictates that the answer would be 288. But when you really boil down the nitty gritty of the rules of mathematics, the answer is less obvious. (No, I did not get a perfect score on my math SAT but my math skillz are considered good enough to get occasional paychecks for them)

 

[scotty21690]

Therion - That is how I solved it as well. 288 doesn't make sense to me UNLESS it is in parenthesis with the 2. I can't take the 2 away from the parenthesis unless it looks like this:

2*(9+3)



Instead it looks like this:

2(9+3)
(18+6)
24
=
2

 

[TramFan3]

The distributive property is multiplication. Therefore you would treat it as such in the order of operations.

 

[Mighty Bombjack]

Are these the same equation?

48÷2 x X

48÷2X

 

[scotty21690]

Are these the same equation?

48÷2 x X

48÷2X

No sir.

"X" referring to the parenthesis, correct?

 

[Mighty Bombjack]

Are these the same equation?

48÷2 x X

48÷2X

No sir.

"X" referring to the parenthesis, correct?

Yep, "multiplication by juxtaposition" as mentioned earlier in the thread. It has always taken precedence in my studies of mathematics, which is how I got to 2.

 

[maxpower]

*bangs head*

Hi, I'm a pension actuary. I have a BS in actuarial math from one of the top 25 institutions in the land (ok, now it's 29, I think, but it was 24 when I was there). I got a perfect score on my math SAT way back when.

The answer is 288.

You people that are saying 2 are putting the 12 in parenthesis as more important than the order of operations, when it's simply saying multiplication. Multiplication using parenthesis is just another way of writing it. Does writing it with an x take precedence over writing it with a dot? No.

48/2(9+3)
is the same as saying
48/2*(9+3)
48/2*12
According to order of operations, multiplication and division are equal, (as are addition and subtraction) and should be read from left to right. This also explains why, when I've seen this post, people have PEDMAS OR PEMDAS.
Thus, 48/2 = 24 * 12 = 288.

Distributive property, yo.

If 9 and 3 were unknowns, how would you answer it?

48/2(x+y)

The question is too ambiguous to give a definitive answer.

Logic dictates that the answer would be 288. But when you really boil down the nitty gritty of the rules of mathematics, the answer is less obvious. (No, I did not get a perfect score on my math SAT but my math skillz are considered good enough to get occasional paychecks for them)

I don't understand why the answer would somehow differ if the problem included unknown variables. 48/2(x+y) could just as easily be (24x+24y) as 48/(2x+2y). The use of x and y (vs. 9 and 3) don't have any bearing on the way that the question should be answered.

What I now realize is that in the absence of any authoritative rule that explicitly states 'multiplication by juxtaposition' is not given priority, most 2Heads will simply continue to argue that the answer is ambiguous. However, no true ambiguity exists. No rule speaks to the priority of multiplication by juxtaposition. Rules do, however, speak to the priority of left operators over rightward operators of equivalent priority (e.g. multiplication and division).

And before anyone presents that AMS quote from the Guide for Reviewers, note that the rule discussed there was a submission/editing rule for their journal, and not a statement of general mathematics rules. In fact, the rule was aimed not at clarifying an ambiguity, but rather simply to shorten long formulas. Finally, the rule is no longer listed in the Guide for Reviewers anyway.

 

[Mighty Bombjack]

I don't understand why the answer would somehow differ if the problem included unknown variables. 48/2(x+y) could just as easily be (24x+24y) as 48/(2x+2y). The use of x and y (vs. 9 and 3) don't have any bearing on the way that the question should be answered.

What I now realize is that in the absence of any authoritative rule that explicitly states 'multiplication by juxtaposition' is not given priority, most 2Heads will simply continue to argue that the answer is ambiguous. However, no true ambiguity exists. No rule speaks to the priority of multiplication by juxtaposition. Rules do, however, speak to the priority of left operators over rightward operators of equivalent priority (e.g. multiplication and division).

The answer should and would not differ if unknown variables were used, it was just put out there as an explanation of how some of us got to 2. Your first statement here makes me think you perfectly understand the ambiguity that exists (though 48/2(x+y) =(24x+24y) looks terribly ugly and wrong to me).

Algebra is a language. When we write 6 x 7, we are not physically stacking items in rows of 6 and columns of 7. We are using a language to represent that stacking (in much the same way that our mouths utter words like "dog" to represent canines-the word is not the thing itself). When a teacher wrote this problem on a test, and saw that they consistently got an answer from their students that they did not expect, they realized that there was an ambiguity. I can understand two teachers who write 48/2(x+y) on a test, with one of them expecting (24x+24y) and the other 48/(2x+2y). Can you? You're ready to call the second a bad teacher? I would, first and foremost, ask the teacher to be consistent.

This ambiguity is one that is represented by the zeitgeist that this internet meme has become, and one that has multiple people who have studied mathematics for multiple years siding with different answers. There are people with math degrees disagreeing. There are math teachers disagreeing.

How do you define ambiguity?