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Forum: General Stuff
Topic: 6/2(1+2) = X
started by: GORDON

Posted by GORDON on Mar. 30 2012,07:50

6/2(1+2) = X

Solve for X.

Because this is a big controversy at the moment.

Posted by TPRJones on Mar. 30 2012,08:02

It can't be properly interpreted as written. Is that supposed to be:

6
-------------
2 * (1 + 2)

Or is it

6
-- * (1 + 2)
2

As written it could be either one and therefor has no specific answer. Or, if you prefer, has two equally valid answers.

Posted by GORDON on Mar. 30 2012,08:05

And here's another answer:

6 / 2(1+2)
6 / (2+4)
6 / 6
1

I just pulled out of a big ol' flamewar on Fark because 99% of them were saying, "The answer is 9, it couldn't be more clear," and I was saying that the original question was written sloppily, and there is room for interpretation.

- edit - I guess that isn't another answer, I just rewrote yours.

But still. Flamewar over math, on Fark.

Posted by TPRJones on Mar. 30 2012,08:08

.... but 6 is not a valid answer at all! There's no way it can be 6 no matter which way you interpret it. It can either be 1 or 9, but not 6.

Fark are stupid.

EDIT: Wait, I could swear you said 6 there. Okay, yeah, 9 is a valid choice. Fark are less stupid, but still a little stupid.

Posted by GORDON on Mar. 30 2012,08:08

I typoed 6, before. I meant 9.

Posted by GORDON on Mar. 30 2012,08:09

I am sad that I am the only one there saying the answer is ambiguous, but I am not surprised, and another part of me is a little happy that I am not yet agreeing with the majority of Farkers.

Posted by TPRJones on Mar. 30 2012,08:09

Too many edits!

Posted by GORDON on Mar. 30 2012,08:10

... on the dance floor.

Posted by TPRJones on Mar. 30 2012,08:16

If it were written as 6÷2*(1+2) then they would be right. Order of operations would imply that you would interpret it as 9. However the slanted nature of / for the division sign which can imply that everything to the right is a divisor coupled with the lack of specific inclusion of the multiplications sign to provide clearer separation between the 2 and the (1+2) results in it being open to a bit of interpretation.

Posted by GORDON on Mar. 30 2012,08:17

Exactly.

Posted by Leisher on Mar. 30 2012,08:20

QUOTE

6/2(1+2) = X

Math was always my weakest subject as I find it insanely boring, but my first impression of that equation was that the solution was 9.

6 divided by 2 is 3, 1+2 is 3, 3x3 is 9.

QUOTE

6 / 2(1+2)
6 / (2+4)
6 / 6
1

I always thought you had to do the math outside of the parentheses first...?

Since editing is the thing here...I think the last time I touched this stuff was 7th grade.

Posted by Cakedaddy on Mar. 30 2012,08:43

Math fail. Parentheses come first, always.

Gordon over thought the problem by multiplying 2x1 then 2x2 to come up with (2+4). The only time you do that type of 'double multiplying' is if there are variables in there 2(a+b) = 2a+2b, so that you can continue to solve for one or more of them. Otherwise, you do the parenthesis first. 2(3)=6. Yes the answer is the same no matter which way you do it, but technically, you did break the order of operations.

It is of my opinion that the question does not have enough information to definitively say if it is 1 or 9.

And I love math. Math is awesome. Math was one of my favorite subjects because it is what it is. There's no room for interpretation. Where history, English, etc was all about convincing someone you knew what you were talking about. So, math is easy and straight forward. I liked science for the same reason.

Posted by TPRJones on Mar. 30 2012,08:48

The problem here is not that the math is vague, but that the way it is written it is not really math problem.

It's like asking someone a history question: "what important event happened on 12175"? Is that 12/1/1975 or 1/21/0075, or what? Until you clarify that date, it's not yet a history question.

Posted by Leisher on Mar. 30 2012,09:02

QUOTE

Math fail. Parentheses come first, always.

Dammit.

Posted by GORDON on Mar. 30 2012,09:04

(Cakedaddy @ Mar. 30 2012,11:43)

QUOTE

I wasn't overthinking it, I was saying that the problem, as stated, is vague.

Farkers were trying to say that it wasn't vague at all, and was obvious. They are stupid and wrong.

Posted by GORDON on Mar. 30 2012,09:07

(Cakedaddy @ Mar. 30 2012,11:43)

QUOTE

Gordon over thought the problem by multiplying 2x1 then 2x2 to come up with (2+4).

What do you think the answer to this problem is?

(3 + x)(4 + 2x)

Because the answer to that is why the problem, as stated, is vague. If you understand how to do the above problem, then you understand why there may not be a definitive answer to the original question, and "Order of Operations" may not apply, as taught up through the 6th grade.

Posted by GORDON on Mar. 30 2012,09:08

BTW, the answer is 12 + 10x + 2x^2.

- edit - Oops, 2x^2.

Posted by TPRJones on Mar. 30 2012,09:47

The answers are -3 and -1. And that one's not vague at all.

Posted by thibodeaux on Mar. 30 2012,09:59

(Cakedaddy @ Mar. 30 2012,11:43)

QUOTE

You're wrong. The answer is the same because it's the same. "Order of operations" doesn't matter because multiplication is distributive over addition. And it's not called "double multiplying," is called "distribution."

It's not "math fail" to distribute over constants, it's just not usually very useful.

Posted by thibodeaux on Mar. 30 2012,10:01

On the original question, I'm inclined to agree with the "it's obviously 9, dummy" party. If you MEAN for your expression to be
6/(2*(1+2))

then write it like that, n00b.

Posted by GORDON on Mar. 30 2012,10:32

(thibodeaux @ Mar. 30 2012,12:59)

QUOTE

(Cakedaddy @ Mar. 30 2012,11:43)

QUOTE

I told them in the Fark thread that it was the Distributive Property that made it questionable, but that was completely ignored and I was called an idiot who didn't know nothin about nothin.

Posted by thibodeaux on Mar. 30 2012,11:01

(GORDON @ Mar. 30 2012,13:32)

QUOTE

I told them in the Fark thread that it was the Distributive Property that made it questionable, but that was completely ignored and I was called an idiot who didn't know nothin about nothin.

I disagree with you, too. "Distributive property" doesn't mean "magic parentheses." It just means that a*(b+c) is the same as (a*b) + (a*c). That's it. It doesn't mean that in d/a*(b+c) you evaluate a*(b+c) first.

Maybe it's the implicit multiplication that's confusing people. When you see a(b+c), your brain needs to re-write it as a*(b+c). That's all it means.

Posted by GORDON on Mar. 30 2012,11:17

(thibodeaux @ Mar. 30 2012,14:01)

QUOTE

(GORDON @ Mar. 30 2012,13:32)

QUOTE

I told them in the Fark thread that it was the Distributive Property that made it questionable, but that was completely ignored and I was called an idiot who didn't know nothin about nothin.

Isn't that exactly what I wrote on the first page? Twice?

QUOTE

6 / 2(1+2)
6 / (2+4)
6 / 6
1

Posted by thibodeaux on Mar. 30 2012,12:15

Yeah, except you're supposed to divide first. Tell me the truth: If you saw 6/2*(1+2), you'd have said 9 for sure, wouldn't you? I think it's pretty unambiguous.

Posted by TPRJones on Mar. 30 2012,12:31

The implied multiplication leads me to group the (1+2) as part of the divisor. Because if I were to write it down on paper with it intended that way, it would look something like this:

/
6 /
/ 2(1+2)
/

When you smush it down into one line as 6/2(1+2) I am inclined to put the (1+2) into the divisor for that reason - or at least to consider it somewhat indeterminate. However if you wrote it as 6/2*(1+2) I would take it as (1+2) being outside the divisor.

All in all, this is why () were added to math notation to begin with. In order to avoid any confusion, if forced into a single line it should be written as 6/(2(1+2)) or (6/2)(1+2).

Posted by GORDON on Mar. 30 2012,12:34

edit - was responding to Thib.

And I fully understand that, but the original problem was not written that way.

The first thing I thought when I saw it was to use the Distributive Property. I remember it well because it threw me for a loop in Algebra 2 in 11th grade, and I had to work an extra 10 minutes to learn it.

I didn't fall victim to the Fallacy of Magic Parenthesis.

Posted by thibodeaux on Mar. 30 2012,12:34

(TPRJones @ Mar. 30 2012,15:31)

QUOTE

When you smush it down into one line as 6/2(1+2) I am inclined to put the (1+2) into the divisor...however if you wrote it as 6/2*(1+2) I would certainly take it as (1+2) being outside the divisor.

That's very interesting, considering that 6/2(1+2) and 6/2*(1+2) are the EXACT SAME EXPRESSION.

On a related note, < this page > says that the iPhone says the answer is "2." Somebody parse that one for me.

Posted by Troy on Mar. 30 2012,12:40

Earlier in the day I thought the answer was 9. I still do.

Posted by TPRJones on Mar. 30 2012,12:45

(thibodeaux @ Mar. 30 2012,14:34)

QUOTE

That's very interesting, considering that 6/2(1+2) and 6/2*(1+2) are the EXACT SAME EXPRESSION.

Actually, no, they aren't. The second one has a * while the first one does not.

This isn't a problem of mathematics and operations, it's one of perception and typography. If not restricted to a single line in height in order to express the equation, then there wouldn't be any doubt as to the intent. This is why math textbooks don't do it that way, they clearly put dividends above a horizontal line and divisors below.

You are absolutely correct in how the operations should be interpreted if you read it as being all one straight line of operations. The problem is that the exact nature of the equation being shown for solving is itself indeterminate because it's one-dimensional nature is forced rather than understood to be a part of the problem. This is why math isn't usually performed in text messages.

And this isn't a new debate. People have been arguing about this stuff since at least back when I was in college and telnet math chat groups would often devolve into flame wars over it.

Posted by thibodeaux on Mar. 30 2012,12:51

(TPRJones @ Mar. 30 2012,15:45)

QUOTE

(thibodeaux @ Mar. 30 2012,14:34)

QUOTE

That's very interesting, considering that 6/2(1+2) and 6/2*(1+2) are the EXACT SAME EXPRESSION.

Actually, no, they aren't. The second one has a * while the first one does not.

Actually, YES, they are. Because you SOMEHOW know to multiply the 2 by the sum of 1 and 2.

Posted by TPRJones on Mar. 30 2012,12:52

Here, maybe this will help. Tell me, how would you write this in a single-line simple piece of text:

2
------
5x

Would you perhaps write it as

2/5x

as I know many people that would. But if you use your interpretation that it can never be doubted then that would be wrong, as that would be

2x
------
5

However if you would always only write that as 2/(5x) then this example was no help.

Posted by Leisher on Mar. 30 2012,13:02

QUOTE

Maybe it's the implicit multiplication that's confusing people. When you see a(b+c), your brain needs to re-write it as a*(b+c). That's all it means.

Hey, I did that! I did learn something in school!

By the way, I just entered the equation into Google, and got the following result:
(6 / 2) * (1 + 2) = 9

I also found < a Yahoo Answers thread on the subject. >

< Here's an interesting Google thread > with the following tidbit:

QUOTE

If you want the result of your example to be 1, you'll need to override the equal left-to-right precedence of multiplication and division by including an extra set of parentheses (and preferably also include the implied multiplication): 6/(2*(1+2))

Posted by thibodeaux on Mar. 30 2012,13:04

(TPRJones @ Mar. 30 2012,15:52)

QUOTE

Here, maybe this will help.

I understand perfectly what you're saying. You're just wrong, that's all.

Posted by TPRJones on Mar. 30 2012,13:07

For the record I am not contending that the interpretation leading to 1 is more correct than the one leading to 9. I am only contending that as written it is feasible to interpret it two different ways leading to potential confusion.

I think that the fact that there has already been several decades of arguing on that very point proves me correct that it can be potentially ambiguous. No real mathematician would ever use that specific string of text for a formula for that very reason.

Posted by GORDON on Mar. 30 2012,13:20

(TPRJones @ Mar. 30 2012,16:07)

QUOTE

This thread and the Fark one tell me that some people won't see both sides of it.

Posted by TPRJones on Mar. 30 2012,13:42

Ultimately, 6/2(1+2) is just mathematical trolling. There's no reason to write it like that instead of 6(1+2)/2 except so that you can point and laugh at anyone that misinterprets it. And while the trolls are technically correct, that doesn't make them any less trollish.

EDIT: Not that I mean to imply anyone here is trolling. But whoever posted the thread to Fark probably is. Or was trolled by someone else and is still confused.

Oh, and I have no idea how to get 2 from that. That's just weird.

Posted by Leisher on Mar. 30 2012,13:47

One question, and please understand that I'm not a math person by any means, but that last quote I mentioned from the Google thread on the subject...

Is there a "left to right precedence" in math?

If so, wouldn't that prove that 9 is the correct answer or does it get ignored in this equation, and why?

It just seems that without that rule, a starting point other than the far left, once you got done with the parentheses, would be arbitrary?

And again, if you wanted the 2 to be multiplied by the result of the 1+2 PRIOR to the division, wouldn't your equation have to look like this: 6/(2*(1+2))

Just curious so don't destroy me here.

Posted by GORDON on Mar. 30 2012,13:58

I was wondering about the left-to-right precedence, as well.

Posted by TPRJones on Mar. 30 2012,13:58

I have a question for you, Thib. Solve this equation for me:

x/2x=? where x=4

After you have done that, and not before, please check out < this link >.

Posted by GORDON on Mar. 30 2012,14:04

That's what I had in my head... is there a trick?

Posted by TPRJones on Mar. 30 2012,14:06

Yes. The correct answer following the strict interpretation we have been discussing would be 8 if you do the division before the multiplication (left to right precedence). Yet Wolfram Alpha chooses do it wrong. Why? Because it's a vague way to write it to begin with.

EDIT: < Like this >. Technically the same, yet still different answers.

Posted by GORDON on Mar. 30 2012,14:12

Well blow me down.

Posted by TPRJones on Mar. 30 2012,14:15

If you decide to take those links back to Fark, let me know what they say.

EDIT: Although, the fact that Wolfram Alpha chooses to do < this > weakens that argument slightly. They've clearly coded it with input mistakes in mind to begin with, not because it's a proper way to read it.

Posted by GORDON on Mar. 30 2012,14:19

Nooooooo. The thread structure on their forums is NOT conducive to making a point, having it challenged, and rebuttal. There's no point arguing a point there... which is why 99% of the time I just seagull troll, because it amuses me making hippies get upset.

I love saying things in January like, "We've got 9 inches of global warming on the ground." Yeah, I know it isn't any kind of argument, but it makes a lot of Greens exasperated because they think I am seriously mocking them...... I bored myself in the middle of that sentence. Sorry.

Posted by TPRJones on Mar. 30 2012,14:24

(Leisher @ Mar. 30 2012,15:47)

QUOTE

Is there a "left to right precedence" in math?

If so, wouldn't that prove that 9 is the correct answer or does it get ignored in this equation, and why?

It just seems that without that rule, a starting point other than the far left, once you got done with the parentheses, would be arbitrary?

Yes. And 9 is indeed technically correct. The thing is, in a properly written equation you should be able to do the associative operations in any order you want and still get the same result. The original equation being discussed is poorly expressed, like the math equivalent of awkward grammar. At least, that's my stance on the matter. Some others would disagree.

Posted by TPRJones on Mar. 30 2012,14:43

Heh. I was just curious about what WA would do with the difference between implicit and explicit multiplication:

< x/2x where x=4 > results in 1/4

< x/2*x where x=4 > results in 8

Posted by Cakedaddy on Mar. 30 2012,20:14

(thibodeaux @ Mar. 30 2012,04:59)

QUOTE

(Cakedaddy @ Mar. 30 2012,11:43)

QUOTE

Except that you do whatever is inside the parenthesis first. Period. You add them, then move on. Applying distribution is incorrect. You do what's in the parenthesis first. Yes, I said that twice for emphasis.

And what this argument is coming down to is what is perceived as general practice. Do people generally see it one way over the other? In my opinion, that's not acceptable in math. If you write an ambiguous problem, then neither answer is correct because the problem is broken. And this leads to you stealing $237,000 from your company over night instead of $2.37 because someone/thing perceived it differently than you intended.

The equation is unanswerable as written.