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

[StruckANerve]

This equation has been blowing up all the forums I post on. The correct answer is 288.

 

[benbondu]

and I also willing to bet that even you think 2 is the wrong answer. It merit is very low. Yes I can see how someone can come to that result but does not change the fact that 2 is incorrect and wrong.

Only way it could be 2 is if it was written 48/(2(9+3))

The question is whether the juxtaposition=grouping rule is valid. It's not something any of us were taught in grade school and almost certainly does not have universal acceptance, but maybe it should.

At first glance, I read 2(9+3) as a group. If this wasn't presented to me as a "puzzle", I might have said the answer was 2. Not necessarily because that was the "correct" answer (if you follow all of the OOO rules), but because that's what it appears the author intended it to be (most of the people I work with do not have math degrees). If the author wanted it to equal 288, they probably would have also known enough to realize the expression was not very clear, and instead written it as 48/2*(9+3) to avoid any confusion (assuming the goal wasn't to trick you).

I'm personally in favor of making some kind of official rule governing the order of operations in the context of multiplication by juxtaposition and teaching it to all the 5th graders. Obviously a lot of people currently think it's a rule, regardless of whether or not it actually is.

 

[benbondu]

well, i would be willing to bet good money that a vast majority of people, including mathematicians (and the two of you if you had seen it before this thread) would have quickly said 42, without a second thought, because convention makes you read that as "y over 2x" not as "y over 2, times x".

If both the person asking this question and the person answering it are reasonable people, then the answer is 42 and you move on. You start to have issues if either one of them thinks about it too long.

Nice example.

 

[SidBala]

Multiplication and Division are of equal precedence. Hence the expression given is ambiguous.

 

[TuffLuffJimmy]

Multiplication and Division are of equal precedence. Hence the expression given is ambiguous.

No it isn't. Multiplication and division you do in order of which comes first when reading left to right. Same with addition and subtraction. Please, read the thread before posting.

 

[fireshot91]

The multiplication doesn't take precedence over the division. They are equal in the order of operations.

It would be:

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

24 * 12.


In cases where there are both division and multiplication, the order goes from left -> Right (As one would read it in a logical English manner).

EDIT: Am I the only one who transformed it, in my head, to be [48(9+3)]/2.
And P.S: It's not like I have a math degree or anything. I'm only in Precalculus. But, I would have gotten this right in 7th-8th grade also. I was always taught that when there is ambiguity, you move left->right, as in this case.

 

[McGiord]

The answer is 288.

Anyone with a decent education is taught B.E.D.M.A.S not PEDMAS.

Brackets.Exponents. Division.Addition/Subtraction in that order!

/End thread.

Before Ending Discussion Must Acknowledge Self-Stupidity

 

[McGiord]

i fail to see how the example really represents that rule or has bearing on the discussion at hand.

Here are the two equations:

and

i interpret the integral and dt as an implied bracket that surrounds the integrand and defines the variable and domain of integration, and i can see why the second form is cheaper to print than a displayed equation that uses \over.

Edit: Are they saying that the brackets are needed around the (1/2 \pi i) to stop it from being interpreted as

b

wtf?

Nice find. I'd never heard of the juxtaposition=grouping rule, but I think it makes sense. I originally answered 288, but I'm leaning more towards 2 now.

The expression is better written 48/2*(9+3) if you want it to evaluate to 288.

Finally some common sense.

 

[-aggie-]

Finally some common sense.

If you could get to level 148, it would all be clear to you that the answer is 288.

 

[McGiord]

If you could get to level 148, it would all be clear to you that the answer is 288.

The bunnies don't even get to level 2. Not even during Easter Hunt Season.

 

[McGiord]

This is what Excel does:

It has been demonstrated that those calling for the 288 result are assuming that first there is fraction 48/2, and then it has to be multiplied with (9+3).

Once again, Mac OS X is the Man here.

Using the expression as it is originally written, gives the result of 2.

But if you assume the use of an *, you get your manipulated result of 288.

Call it Bomdas...whatever you want to call it. You guys are assuming something.

In real life, like someone else pointed out, you go back and ask the right questions to clarify the doubts.

Most of the people out there use tools like Excel or a simple calculator to do real life calculations.

Those in the Academic world are sometimes so focused on their theories that they get away from real life practical application of the theories.

Some people are so focused on getting their point made that they slip in questions like: who said that it is an equation? Actually it was written not said.

Also, it has been proven that those who get a big refund from taxes have poor math skills.

Thanks for a fun discussion.

 

[Loge]

In APL the answer to 48/2(9+3) is

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12

or to 48÷2(9+3), the answer is

24 4

But then APL is unusual

 

[JoeG4]

My G5 is defective:

 

[Don't panic]

i am telling you, the answer is always 42!!!!!

 

[McGiord]

i am telling you, the answer is always 42!!!!!

Only in the US.

 

[GimmeSlack12]

If you presented me with the expression "a/b(c+d)" in any form, I'd parse it the same way every time.

If you are intending for the problem to read in such a way to get 288, I'd expect to see "(a/b)(c+d)".

The answer is 2. Because that is how it is written out in the Thread title. There is really no excuse for answering the problem 288, because that is simply wrong. There is no debate here.

48 / 24 = 2

Clear and simple. 11 pages? really?

 

[iJohnHenry]

Clear and simple. 11 pages? really?

No, 16, but that depends on your post per page choice.

 

[McGiord]

No, 16, but that depends on your post per page choice.

Not even on this can we agree?

 

[pianojoe]

There can't be no correct answer because the question is crooked. You can't write a mathematical term like the OP did. The spelling is wrong.

Writing up math requires lots of special symbols and formatting. If you choose to write your equation in ASCII, it's good practice to use "standard BASIC" notation. This means that you can't leave out the multiplication sign after the "2".

This being said, you'll need to construe the meaning of the formula. I think that the daisy-chain version is slightly more probable

48 / 2 * 12 = 48 * 12 / 2 = 288

but there's room for interpretation. If all of the "2(9+3)" should be the divisor, you'd need to indicate this in some way, like

48/(2*(9+3))

Hint: There is no rule that "everything after the / must be the divisor".

 

[chaoticbear]

well, i would be willing to bet good money that a vast majority of people, including mathematicians (and the two of you if you had seen it before this thread) would have quickly said 42, without a second thought, because convention makes you read that as "y over 2x" not as "y over 2, times x".

What a good example. You know, it'd totally clear up any ambiguity to just take the suggestion upthread and express it as 48(9+3)/2

 

[balamw]

wtf?

Read the AMS link and then the discussion with benbondu later https://forums.macrumors.com/posts/12371018/.

Only in the US.

DNA was a Brit though he made the US his adopted home.

B

 

[Tomorrow]

...convention makes you read that as "y over 2x" not as "y over 2, times x".

Unless you read it as "y divided by two times x."

 

[Don't panic]

Unless you read it as "y divided by two times x."

which still means two different things depending whether you pause before or after the "two".

which brings it back to the original concept that, no matter how much either side is "absolutely certain" they are correct, the expression is ambiguous.

for example, the people at purplemath seem to think that the lack of the 'times' operator (multiplication by juxtaposition) implies a stronger connection that supersedes the left-to-right order, so in my example it would be "y divided by _ two times x" and not "y divided by two _ times x" and, in the original example, the answer would be 2 and not 288.

 

[darkcurse]

If both the person asking this question and the person answering it are reasonable people, then the answer is 42 and you move on. You start to have issues if either one of them thinks about it too long.

Nice example.

The question and the answer are mutually exclusive though. If both are found together, the universe might reorient itself in a more bizarre and unexplainable way!

 

[Tomorrow]

which still means two different things depending whether you pause before or after the "two".

1. How do you figure that? What does a "pause" mean in mathematics?

2. Why would you pause in that equation?

for example, the people at purplemath seem to think that the lack of the 'times' operator (multiplication by juxtaposition) implies a stronger connection that supersedes the left-to-right order

Implied parentheses? That's a new one on me.