6/2(1+2) = X

[GORDON]

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.

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.

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.

[thibodeaux]

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.



Edited By thibodeaux on 1333130559

[GORDON]

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.

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

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

Edited By GORDON on 1333131496

[thibodeaux]

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.

[TPRJones]

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).



Edited By TPRJones on 1333136099

[GORDON]

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.



Edited By GORDON on 1333136094

[thibodeaux]

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.

[Troy]

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

[TPRJones]

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.



Edited By TPRJones on 1333136811

[thibodeaux]

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.

[TPRJones]

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.



Edited By TPRJones on 1333137699

[Leisher]

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:

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))

[thibodeaux]

Here, maybe this will help.

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

[TPRJones]

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.

[GORDON]

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.

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

[TPRJones]

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.



Edited By TPRJones on 1333140352

[Leisher]

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.

[GORDON]

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

[TPRJones]

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.



Edited By TPRJones on 1333141346

[GORDON]

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