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6÷2(1+2)=?

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    #62
    28064212
    Registered Users Posts: 10,494 ✭✭✭✭28064212


    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)?

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    #63
    Turtwig
    Registered Users Posts: 26,578 ✭✭✭✭Turtwig


    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]


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    #64
    HxGH
    Closed Accounts Posts: 767 ✭✭✭HxGH


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


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    #65
    Yahew
    Closed Accounts Posts: 2,491 ✭✭✭Yahew


    This calls for a Pole.


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    #66
    muboop1
    Registered Users Posts: 1,025 ✭✭✭muboop1


    Yahew wrote: »
    This calls for a Pole.

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


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    #67
    [Deleted User]
    Posts: 0 ✭✭✭✭ [Deleted User]


    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


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    #68
    abelard
    Registered Users Posts: 1,837 ✭✭✭abelard


    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


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    #69
    Yahew
    Closed Accounts Posts: 2,491 ✭✭✭Yahew


    No I meant a Polish scientist. Fierce smart lads.


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    #70
    Yahew
    Closed Accounts Posts: 2,491 ✭✭✭Yahew


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


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    #71
    abelard
    Registered Users Posts: 1,837 ✭✭✭abelard


    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.


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    #72
    nickcave
    Registered Users Posts: 300 ✭✭nickcave


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

    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...


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    #73
    singingstranger
    Registered Users Posts: 2,270 ✭✭✭singingstranger


    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.


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    #74
    28064212
    Registered Users Posts: 10,494 ✭✭✭✭28064212


    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)? :confused:
    ...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

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    #75
    Yahew
    Closed Accounts Posts: 2,491 ✭✭✭Yahew


    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.


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    #76
    abelard
    Registered Users Posts: 1,837 ✭✭✭abelard


    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) ?


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    #77
    iii Stevo iii
    Registered Users Posts: 285 ✭✭iii Stevo iii


    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


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    #78
    Yahew
    Closed Accounts Posts: 2,491 ✭✭✭Yahew


    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.


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    #79
    [Deleted User]
    Posts: 0 ✭✭✭✭ [Deleted User]


    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.


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    #80
    abelard
    Registered Users Posts: 1,837 ✭✭✭abelard


    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.....


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    #81
    abelard
    Registered Users Posts: 1,837 ✭✭✭abelard


    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)


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    #82
    28064212
    Registered Users Posts: 10,494 ✭✭✭✭28064212


    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

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    #83
    Keen2win
    Registered Users Posts: 153 ✭✭Keen2win


    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! :)


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    #84
    iii Stevo iii
    Registered Users Posts: 285 ✭✭iii Stevo iii


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

    or

    6
    _____ = 1

    2(1+2)


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    #85
    abelard
    Registered Users Posts: 1,837 ✭✭✭abelard


    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.


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    #86
    Fremen
    Registered Users Posts: 2,481 ✭✭✭Fremen


    The correct answer is

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


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    #87
    im invisible
    Closed Accounts Posts: 4,372 ✭✭✭im invisible


    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


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    #88
    Hootanany
    Registered Users Posts: 5,477 ✭✭✭Hootanany


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


    Put the original sum in to this then


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    #89
    28064212
    Registered Users Posts: 10,494 ✭✭✭✭28064212


    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

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    #90
    abelard
    Registered Users Posts: 1,837 ✭✭✭abelard


    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.


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    #91
    Irish_Elect_Eng
    Registered Users Posts: 1,260 ✭✭✭Irish_Elect_Eng


    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


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