6÷2(1+2)=?

nickcave · 28-04-2011 5:30pm

muboop1 wrote: »

No.

Nice troll.

nothing · 28-04-2011 5:32pm

I've seen this elsewhere, with the 48/2(9+3), basically the notation is badly written deliberately for trolling purposes... For that one both 288 and 2 are correct answers, but you would need to give more distinction about whether the bracketed part is a denominator or numerator.

Same thing here, both 1 and 9 are correct until more rigorous notation is given.

Keen2win · 28-04-2011 5:32pm

Shane732 wrote: »

Is there a link to the question??

I'd like to laugh at people!!

I was trying to put a link to it and there doesn't seem to be a way...

It was asked by this fella
http://www.facebook.com/home.php#!/mike.carras?sk=questions

Just click "asked" at the top right and you should see it.

Yahew · 28-04-2011 5:33pm

Just use parenthesis to disambiguate - the man speaks sense.

28-04-2011 5:33pm

nickcave wrote: »

No, trust me, if you write A ÷ BCDEFG, you mean A divided by everything to the right of it unless there is delimitation with brackets e.g. (A ÷ BCD)EFG.

So you're saying that 2(1+2) is not the same as 2*(1+2)? It's actually (2*(1+2))?

JustAddWater · 28-04-2011 5:34pm

Deleted User wrote: »

Didn't know that Ronnie Drew knew Math

And nick cave!!

abelard · 28-04-2011 5:38pm

The answer to

6
- (1+2) is obviously 9
2

The answer to

6

is obviously 1
2 (1+2)

Is the whole confusion not just because it had to be represented in an illogical manner on one line? There is no purely logical way of differentiating between the reading which results in 9 and the reading which results in 1 when it is expressed on a single line. Whether you want to rely on rules like BOMDAS or BEDMAS or whatever, since multiplication and division are associative, neither comes first. The BOMDAS rules and their ilk did not develop as there is a single most logical way of performing operations in mathematics, they developed as they represent the most logical way of performing operations ON THE WAY WE NOTATE MATHEMATICS.

The whole problem is in the notation. Surely this is not notated in such a way as to have a single logical way of performing operations in our notation system?

nickcave · 28-04-2011 5:40pm

28064212 wrote: »

So you're saying that 2(1+2) is not the same as 2*(1+2)? It's actually (2*(1+2))?

No, I said that 6÷2(1+2) = (6)÷(2(1+2)) unless there is some other delimitation.

Yahew · 28-04-2011 5:40pm

abelard wrote: »

The answer to

6
- (1+2) is obviously 9
2

The answer to

6
is obviously 1
2 (1+2)

Is the whole confusion not just because it had to be represented in an illogical manner on one line? There is no purely logical way of differentiating between the reading which results in 9 and the reading which results in 1 when it is expressed on a single line. Whether you want to rely on rules like BOMDAS or BEDMAS or whatever, since multiplication and division are associative, neither comes first. The BOMDAS rules and their ilk did not develop as there is a single most logical way of performing operations in mathematics, they developed as they represent the most logical way of performing operations ON THE WAY WE NOTATE MATHEMATICS.

The whole problem is in the notation. Surely this is not notated in such a way as to have a single logical way of performing operations in our notation system?

Yeah, its not a problem with mathematics bit with the notation system, as the answer is ambiguous.

muboop1 · 28-04-2011 5:44pm

nickcave wrote: »

Nice troll.

Hardly I have presented my evidence. Follow bomdas rule thingy. Or (B)(O)(MD)(AS) as it should be presented.

6/2(1+2) = 6/2*(1+2) = 1(6/2*(1+2) same as = (6/2)*(1+2) = 9... hell put it into you calculator just as you see it, then put it into excel, then matlab! I have done all 3 just to verify (meant to be studying better alternative). This is most certainly equal to 9.

You could argue that it means 6/(2*(1+2)) but that seems a little irrational to me. why? because 2(2) has always meant 2*2. I have never witnessed any different. As such the equation would read 6/2*(1+2) = 9

28-04-2011 5:45pm

nickcave wrote: »

No, I said that 6÷2(1+2) = (6)÷(2(1+2)) unless there is some other delimitation.

Why does 2(1+2) have a higher precedence? Why does using the parentheses notation instead of the multiplication symbol give it a higher precedence?

Is 6 ÷ 2(1+2) = 6 ÷ 2 * (1+2)?

Turtwig · 28-04-2011 5:46pm

It's 9

Division and multiplication have equal rank so you take in order of operation from left to right.

[latex]
6\div2*(1+2) [/latex] (brackets first)
[latex]6\div2*(3)[/latex] (division/multiplication decided by left to right rule)
[latex]3*3 = 9[/latex]

HxGH · 28-04-2011 5:47pm

Honours maths isn't working for me here...

Yahew · 28-04-2011 5:48pm

This calls for a Pole.

muboop1 · 28-04-2011 5:53pm

Yahew wrote: »

This calls for a Pole.

Already one on FB 9 is winning... hope for humanity yet...

28-04-2011 5:53pm

28064212 wrote: »

Why does 2(1+2) have a higher precedence? Why does using the parentheses notation instead of the multiplication symbol give it a higher precedence?

Is 6 ÷ 2(1+2) = 6 ÷ 2 * (1+2)?

why do we use toilet paper and not bidets?

It's just the way it's done....

QED

abelard · 28-04-2011 5:54pm

I can't stop myself now. And forgive the following post for sounding condescending.

What is 8*5+1?

You'll say 41. I'll say 41. Pretty much anyone will say 41. But why? Because we multiply before adding. Fair enough, but why? Because of the BOMDAS rule. Ok, but why is that rule there? The thing is it's arbitrary.

The sum 8*5+1 offers no hint on it's own as to which operator should be used first. But we have developed a rule which tells us how to proceed, because we want a standardised mathematical notation that everyone can use to come to the same conclusion.

Mathematics is like a language, and like any language it is simply a social construct (I don't mean the rules of mathematics, just the way we write it). We have developed rules of notation to make sure that when different people look at the same equation, they come up with the same answer. Without these agreed rules, one man's workings could be completely indecipherable to another. This isn't a bad thing, it's the very reason we can be taught and understand mathematics.

Representing the original equation as 6/2(1+2) pretty much just flouts our accepted rules of notation and that's why people have competing answers. There is nothing to make either answer logically more likely than the other, they just result from two possible interpretations of a point of notation which is a little ambiguous

Yahew · 28-04-2011 5:56pm

No I meant a Polish scientist. Fierce smart lads.

Yahew · 28-04-2011 5:59pm

abelard is right - as was the bearded buy. The notation is ambiguous. Which is why we should all use parenthesis.

abelard · 28-04-2011 6:00pm

Yahew wrote: »

abelard is right - as was the bearded buy. The notation is ambiguous. Which is why we should all use parenthesis.

What was his argument? No sound here so can't listen.

nickcave · 28-04-2011 6:00pm

why are people arguing over 2(1+2) = 2*(1+2)?

OK, it's been pointed out that this is an ambiguous question. Software packages and calculators don't deal well with ambiguities so their programmers have taken steps to ensure that there is only one answer, which seems to be universally 9.

How about this: to me, the answer is 1 (see my first post). To others, the answer is either 1 or 9. To guys with calculators, the answer is 9.

Now I'm off to find a very cold beer...

singingstranger · 28-04-2011 6:06pm

I was as equally incredulous and adamant that the answer was one, but it might help to think of it this way:

Replace the (1+2) in the brackets simply with x. You then have 6/2x.

This is sloppy notation, but the widely-held convention (again, as abelard referred to, it's only a convention like BOMDAS, but an authoritative one none the less) is that though you might think otherwise, 6/2x is considered (6/2)x and not 6/(2x). If it's meant to be interpreted as 6/(2x), you say it so. Otherwise, in the absence of brackets, it's to be assumed as (6/2)x.

Therefore, 6/2(1+2) should actually be thought of as (6/2)(1+2), and is therefore 9.

28-04-2011 6:06pm

Deleted User wrote: »

why do we use toilet paper and not bidets?

It's just the way it's done....

QED

Except it's not, it's the way you've chosen to do it this particular time because it "seems" right. 6÷2(1+2) is exactly equivalent to 6÷2*(1+2). That's what it is short for. And 6÷2*(1+2) has a very definite meaning.

abelard wrote: »

Mathematics is like a language, and like any language it is simply a social construct (I don't mean the rules of mathematics, just the way we write it). We have developed rules of notation to make sure that when different people look at the same equation, they come up with the same answer. Without these agreed rules, one man's workings could be completely indecipherable to another. This isn't a bad thing, it's the very reason we can be taught and understand mathematics.

Yes, but 8, *, 5, +, and 1 are all part of that same language. The question is whether the statement is ambiguous or not. I don't believe it is. Using parentheses for multiplication doesn't change the precedence of the statement

nickcave wrote: »

why are people arguing over 2(1+2) = 2*(1+2)?

...because it's the entire point of contention in the argument? If the original question was 6÷2*(1+2), anyone saying 1 would be very, very obviously wrong. Your claim is that multiplication using parentheses changes the precedence

Yahew · 28-04-2011 6:06pm

abelard wrote: »

What was his argument? No sound here so can't listen.

What you said - he never heard of Bomdas, or whatever tis called. Said use parenthesis to disambiguate.

abelard · 28-04-2011 6:13pm

28064212 wrote: »

Yes, but 8, *, 5, +, and 1 are all part of that same language. The question is whether the statement is ambiguous or not. I don't believe it is.

Why isn't it?

We have 6/2(2+1)

What tells us if we first divide 6 by 2 then multiply by 3, or first multiply 2 by 3 and then take 6 divided by the answer to that?

Of the two equations I put in an earlier post, what tells us which one of them is represented by 6/2(2+1) ?

iii Stevo iii · 28-04-2011 6:15pm

How is there 5 pages on this????

6÷2(1+2) Brackets first
6÷2(3) Brackets are still there so we HAVE to multiply the 2(3) first
6÷6
=1

Yahew · 28-04-2011 6:16pm

iii Stevo iii wrote: »

How is there 5 pages on this????

6÷2(1+2) Brackets first
6÷2(3) Brackets are still there so we HAVE to multiply the 2(3) first
6÷6
=1

Because brackets first is bollocks.

28-04-2011 6:16pm

singingstranger wrote: »

I was as equally incredulous and adamant that the answer was one, but it might help to think of it this way:

Replace the (1+2) in the brackets simply with x. You then have 6/2x.

This is sloppy notation, but the widely-held convention (again, as abelard referred to, it's only a convention like BOMDAS, but an authoritative one none the less) is that though you might think otherwise, 6/2x is considered (6/2)x and not 6/(2x). If it's meant to be interpreted as 6/(2x), you say it so. Otherwise, in the absence of brackets, it's to be assumed as (6/2)x.

Therefore, 6/2(1+2) should actually be thought of as (6/2)(1+2), and is therefore 9.

6/2x = 6 / 2x

Its never to be understood as (6/2)x. It would be written that way if it was.

Btw, the BEMDAS thing is a bit of a cop out/joke, because technically Division = Multiplication, and Addition = Subtraction. Essentially Division is multiplication by an inverted number while subtraction is addition of a negative number.

6÷2(1+2) is equivalent to (A)*[(B)(C+D)]^-1,
Where A = 6, B = 2, C= 1, D=2

It's a poorly written equation, but the generally accepted (and correct) way of looking at it is [6 divided by [3 times [1 plus 2]]].

That being said, an equation pulled out of thin air and badly written isn't worth solving. If the equation is based on something, this makes the "problem" far easier to comprehend. e.g 6 eggs split between two families where the Man eats twice what the mother eats.

abelard · 28-04-2011 6:17pm

iii Stevo iii wrote: »

How is there 5 pages on this????

6÷2(1+2) Brackets first
6÷2(3) Brackets are still there so we HAVE to multiply the 2(3) first
6÷6
=1

because brackets first only applies to operations inside the brackets.....

abelard · 28-04-2011 6:19pm

Deleted User wrote: »

That being said, an equation pulled out of thin air and badly written isn't worth solving. If the equation is based on something, this makes the "problem" far easier to comprehend. e.g 6 eggs split between two families where the Man eats twice what the mother eats.

Yep, this is the problem, an equation this ambiguous would never appear in a real setting (be it in applied or abstract mathematics)

The whole point of this equation is to have people argue over the answer (I don't mean to accuse the OP of trolling or something, I just mean that's the point of such an equation)

28-04-2011 6:20pm

abelard wrote: »

Why isn't it?

We have 6/2(2+1)

What tells us if we first divide 6 by 2 then multiply by 3, or first multiply 2 by 3 and then take 6 divided by the answer to that?

Of the two equations I put in an earlier post, what tells us which one of them is represented by 6/2(2+1) ?

The rules of associativity. Multiplication and division are both left-associative. What you're saying is identical to saying we have no way of knowing what 6 - 2 + 3 is, because we don't know whether to add the 3 or subtract the 2 first

iii Stevo iii wrote: »

How is there 5 pages on this????

6÷2(1+2) Brackets first
6÷2(3) Brackets are still there so we HAVE to multiply the 2(3) first
6÷6
=1

Brackets only increase the precedence of what's inside them, not anywhere else. 2(3) is the same as 2 * 3, which doesn't have any brackets

Keen2win · 28-04-2011 6:24pm

abelard wrote: »

Yep, this is the problem, an equation this ambiguous would never appear in a real setting (be it in applied or abstract mathematics)

The whole point of this equation is to have people argue over the answer (I don't mean to accuse the OP of trolling or something, I just mean that's the point of such an equation)

It's not my equation, some fella on facebook is the brainchild... Blame him!

iii Stevo iii · 28-04-2011 6:30pm

Ok the equation is ambiguous.
The way I read the question is:
6÷[2(1+2)] = 1

or

6
_____ = 1

2(1+2)

abelard · 28-04-2011 6:33pm

28064212 wrote: »

The rules of associativity. Multiplication and division are both left-associative. What you're saying is identical to saying we have no way of knowing what 6 - 2 + 3 is, because we don't know whether to add the 3 or subtract the 2 first

Ok, that's a fair point. Left-associativity may be the key. Where there is no other way to order operators, start from the left and work on. Seems ok. It's at least a standardised way of doing it, though again it will amount to nothing but a social construct. But that's fine.

Out of interest what level of acceptance does this principle have? It seems to come from computer science. But I guess that it's a notation that can only really occur in a computer programming environment since we'd be more inclined to write it differently unless we had to. In fact, I'd be very surprised if there aren't papers out there written on this, as it was surely a massive issue when computer programming was in it's infancy, and essentially an arbitrary decision just had to be made, which ended up being left associativity.

If we proceed with left associativity, the answer is 9. But to anyone who says 1, their answer is no less logical. It just seems that when this notational problem arose, someone decided that computers would read that equation and get 9, so that's how it is.

Fremen · 28-04-2011 6:36pm

The correct answer is

"Could you rephrase the question to make it a bit clearer please?".

im invisible · 28-04-2011 6:39pm

Brackets only increase the precedence of what's inside them, not anywhere else. 2(3) is the same as 2 * 3, which doesn't have any brackets

But,,, are you SURE??
I started thinking it was 9, then 1, then 9 again, now im not too sure

Hootanany · 28-04-2011 6:43pm

http://www.coolmath.com/graphit/

Put the original sum in to this then

28-04-2011 6:46pm

abelard wrote: »

Ok, that's a fair point. Left-associativity may be the key. Where there is no other way to order operators, start from the left and work on. Seems ok. It's at least a standardised way of doing it, though again it will amount to nothing but a social construct. But that's fine.

But again, every piece of mathematical notation is a social construct

abelard wrote: »

Out of interest what level of acceptance does this principle have? It seems to come from computer science. But I guess that it's a notation that can only really occur in a computer programming environment since we'd be more inclined to write it differently unless we had to. In fact, I'd be very surprised if there aren't papers out there written on this, as it was surely a massive issue when computer programming was in it's infancy, and essentially an arbitrary decision just had to be made, which ended up being left associativity.

Associativity has been around almost as long as addition and subtraction existed. It certainly didn't come in with computers. And as to where it can occur and be useful? Is 6 - 2 + 3 equal to 7 or 1? That's pretty fundamental, but it's only unambiguous because addition and subtraction are left-associative

abelard wrote: »

If we proceed with left associativity, the answer is 9. But to anyone who says 1, their answer is no less logical. It just seems that when this notational problem arose, someone decided that computers would read that equation and get 9, so that's how it is.

Left-associativity isn't really the problem. Again, if the initial statement was 6÷2*(1+2), the answer would be 9. Saying anything different would be completely incorrect. The confusion is arising because some people think that 2(1+2) has a higher precedence than 2*(1+2). That is the only remotely ambiguous part of it

abelard · 28-04-2011 6:52pm

28064212 wrote: »

But again, every piece of mathematical notation is a social construct

True, and obviously i'm not trying to say any different

28064212 wrote: »

Associativity has been around almost as long as addition and subtraction existed. It certainly didn't come in with computers. And as to where it can occur and be useful? Is 6 - 2 + 3 equal to 7 or 1? That's pretty fundamental, but it's only unambiguous because addition and subtraction are left-associative

Whilst associativity has been around as long as mathematics, are you sure about the idea of left/right associativity (genuine question)? It seems a problem that never would have arisen until it was necessary for computers to calculate.

28064212 wrote: »

Left-associativity isn't really the problem. Again, if the initial statement was 6÷2*(1+2), the answer would be 9. Saying anything different would be completely incorrect. The confusion is arising because some people think that 2(1+2) has a higher precedence than 2*(1+2). That is the only remotely ambiguous part of it

Are you sure? I thought it was because some people were doing the multiplication before division, and some the division before multiplication, and the argument is which comes first?

Maybe I need to just stop looking at this thread

edit: i pretty much understand and agree with everything you say by the way. Just curious as to why left associativity came about. I agree it's the best way to proceed (considering we write language left-right), but wondering who was it that decided it would be the standard.

Irish_Elect_Eng · 28-04-2011 7:05pm

The answer is 9.

Windows Calculator result says its 9
MS Excel Cell Calculation says that the result is 9
Google Calculator result says 9

It translates 6/2(1+2) to (6 / 2) * (1 + 2) = 9

But you could also argue that as the division sigh is stated between 6 and 2 and missing between 2 and ( that the formula actually is as follows

6/2^(1+2) = 1

If you assumer that the person stating the formula is missing the superscript for the (1+2)

Or for the result to be 1 the formula would have to be written as follows:

= 6/(2*(1+2))

http://boards.ign.com/teh_vestibule/b5296/201953531/p1/?76

28-04-2011 7:06pm

I can't believe this has 90 posts already :pac:

google calc is giving 9 because it's adding in extra brackets

sponsoredwalk · 28-04-2011 7:14pm

This is like that spinning dancer with her leg out that supposedly tells
you whether you think with the left side of your brain or your right, if
you push yourself you can see her spin both ways.

0,,5693171,00.gif

Same thing here, you can see it both ways.

http://www.dailymotion.com/video/xf88b5_jean-pierre-serre-writing-mathemati_tech

Eliot Rosewater · 28-04-2011 7:20pm

The answer is neither 1 nor 9; there is no answer because the question is ambiguous. In the absence of both a consensus view and a rigorous abstract algebraic answer (if you want to use BOMDAS, prove it please, stating clearly the axioms of the number system (R, N, Z) you choose to work in) then to pick either 1 or 9 is just to be totally arbitary. Even if the resulting answer you arbitarily chose was subseqeutly proven to be the right one, you would only be as correct as the man who closes his eyes, predicts he will see a naked women when he opens them, and happens to see a naked women when he does. Such a man may be lucky, but he is not acting with any kind of scientific rigour.

28-04-2011 8:01pm

abelard wrote: »

Whilst associativity has been around as long as mathematics, are you sure about the idea of left/right associativity (genuine question)? It seems a problem that never would have arisen until it was necessary for computers to calculate.

How would you calculate 6 - 2 + 3 without associativity?

abelard wrote: »

Are you sure? I thought it was because some people were doing the multiplication before division, and some the division before multiplication, and the argument is which comes first?

Pretty sure. Well, some people are just way, way, way off, but for the ones that have a reasonable argument, that seems to be the sole point of confusion.

abelard wrote: »

Maybe I need to just stop looking at this thread

But someone is wrong on the internet :pac:

abelard wrote: »

edit: i pretty much understand and agree with everything you say by the way. Just curious as to why left associativity came about. I agree it's the best way to proceed (considering we write language left-right), but wondering who was it that decided it would be the standard.

AFAIK, it was similar to the precedence rules, initially every mathematician had their own notation, then a standard grew to save time.

bluewolf wrote: »

I can't believe this has 90 posts already :pac:

google calc is giving 9 because it's adding in extra brackets

It's adding in extra brackets for demonstration purposes, it doesn't change the meaning of the statement. If you put in 1+2*3 it "changes it to 1+(2*3)

Eliot Rosewater wrote: »

The answer is neither 1 nor 9; there is no answer because the question is ambiguous. In the absence of both a consensus view and a rigorous abstract algebraic answer (if you want to use BOMDAS, prove it please, stating clearly the axioms of the number system (R, N, Z) you choose to work in) then to pick either 1 or 9 is just to be totally arbitary. Even if the resulting answer you arbitarily chose was subseqeutly proven to be the right one, you would only be as correct as the man who closes his eyes, predicts he will see a naked women when he opens them, and happens to see a naked women when he does. Such a man may be lucky, but he is not acting with any kind of scientific rigour.

Having to derive everything from first axioms in every post is really going to kill off the Mathematics forum.

But I'll skip a few steps and get to important bits. Here's my "assumptions":

Multiplication and division have equal precedence
Multiplication and division are left-associative
x(y) is exactly equivalent to x * y

I don't think any of those are exactly huge leaps of logic, or entirely new concepts to maths

Yahew · 28-04-2011 8:19pm

Lads.

Let's compromise and call it 5.

Fremen · 28-04-2011 8:23pm

Yahew wrote: »

Lads.

Let's compromise and call it 5.

No, it's 3. You should be taking the geometric mean.

scorn · 28-04-2011 9:02pm

Do the Chinese also use the left-to-right associative 'standard'?

Just putting out there...

TimeToShine · 28-04-2011 9:17pm

Well I was hoping this **** wouldn't infest the intelligent occupants of Boards but here we are, arguing over a fúcking troll question specifically designed to cause disagreement.

This is an AMBIGUOUS QUESTION. IT DOES NOT HAVE A SPECIFIC ANSWER.

Let me EXPLAIN:

ASSUMING NO EXTERNAL BRACKETS, THE BOMDAS RULE:

6 / (2(1+2)) WE GET AN ANSWER OF 1.

NOW, USING THE AMERICAN CONVENTIONAL METHOD:

(6 / 2)(1+2) GIVES AN ANSWER OF 9.

THE DISTRIBUTIVE PROPERTY IS MANIPULATED UNDER THESE CIRCUMSTANCES, SIMILARLY, IMAGINE IF I GAVE THE FOLLOWING QUESTION:

1 (SOMETHING) 2 =

SOME WOULD ASSUME THERE'S A + BETWEEN THE NUMBERS AND OTHER WOULD ASSUME THERE'S A -. THIS IS THE SAME PRINCIPLE, AN AMBIGUOUS STATEMENT WHICH LEAVES PLENTY OF ROOM FOR EXPLOITATION CAUSING THE FEEBLE-MINDED POPULATION OF FACEBOOK TO ARGUE OVER IT.

HOWEVER, DEPENDING ON HOW ONE WAS TAUGHT, ONE ANSWER WILL SEEM INTUITIVELY CORRECT, FOR EXAMPLE FOR ME I WOULD SEE 1 AS THE CORRECT ANSWER. STILL, I, AND HOPEFULLY YOU AS WELL, CAN SEE PAST THIS AMBIGUITY AND ACCEPT THAT BOTH ANSWERS ARE TECHNICALLY CORRECT, RATHER THAN LOOKING FOR EVIDENCE TO BACK UP YOUR ALREADY CORRECT ANSWER.

Bucklesman · 28-04-2011 9:23pm

I think it's fair to say the question was badly phrased.

Chemistry Ftw · 28-04-2011 9:29pm

The answer is 1

6÷2(1+2)=?

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