Solve this equation > 48÷2(9+3) = ?

14546485051108

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  • gemma-the-huskygemma-the-husky Posts: 18,116
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    I wonder if the over-40s got 288 and the under-40s got 2.

    OP ... maybe you need to do a companion poll.

    Edit: I got 288 (aged 42), and I've never heard of BODMAS.

    truthfully - I am older than you, and my first reaction was that the answer was 2. To me, it takes a lot of work, and some counter-intuition to get it to be 288.

    To me, 2 looks right, and 288 looks wrong - because I see
    2(9+3) as a single expression, that needs to be evaluated as 24.
  • Mark.Mark. Posts: 84,804
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    truthfully - I am older than you, and my first reaction was that the answer was 2. To me, it takes a lot of work, and some counter-intuition to get it to be 288.

    To me, 2 looks right, and 288 looks wrong - because I see
    2(9+3) as a single expression, that needs to be evaluated as 24.
    It doesn't matter what you see; you're wrong.
  • [Deleted User][Deleted User] Posts: 10,625
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    288
    I see it as 48÷2=24
    24x12=288

    Elke (age 48)
  • [Deleted User][Deleted User] Posts: 3,566
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    Hmm. I just saw it as 24 times 12. The really surprising thing to me is that there seem to be two equally valid answers. I thought the whole point of maths notation was to eliminate this kind of ambiguity.

    Someone should be told! (I suggest the queen).
  • d'@ved'@ve Posts: 45,452
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    truthfully - I am older than you, and my first reaction was that the answer was 2. To me, it takes a lot of work, and some counter-intuition to get it to be 288.

    To me, 2 looks right, and 288 looks wrong - because I see
    2(9+3) as a single expression, that needs to be evaluated as 24.

    This problem has been around for a long time. Here is a Q&A from 1999 (Drexel University Pa. USA):

    About giving priority to implied multiplication
    http://mathforum.org/library/drmath/view/54341.html
    On the TI Web site I learned that they deliberately put this "feature" into the TI 82, and then took it out of the TI 83, probably because they decided it was not a standard rule and would confuse people.

    So to answer your question, I think both answers can be considered right - which means, of course, that the question itself is wrong. I prefer the standard way (your first answer) when talking to students, unless their own text gives the "implicit multiplication first" rule; but in practice if I came across that expression, I would probably first check where it came from to see if I could tell what was intended. The main lesson to learn is not which rule to follow, but how to avoid ambiguity in what you write yourself. Don't give other people this kind of trouble.

    "The main lesson to learn is not which rule to follow, but how to avoid ambiguity in what you write yourself. Don't give other people this kind of trouble."

    And more recently, from Texas Instruments (Equation Operating System) last year http://epsstore.ti.com/OA_HTML/csksxvm.jsp?nSetId=96969&nUsePub=NO&jttst0=6_23871,23871,-1,0,&jtfm0=&etfm1=&jfn=ZG3AEAB5681D93CBEC1515EC1500BD26265D20D1C0C0B04625CC35016B6B3F6767F7143BEA10305F415219C8E57F6A356019 :
    1. Functions that precede the argument, such as square root(, sin(, or log(.
    2. Functions that are entered after the argument, such as exponents, factorials, r (radians), ° (degrees), and unit conversions.
    3. Powers and roots, such as 2^5.
    4. Permutations (nPr) and combinations (nCr).
    5. Multiplication, implied multiplication and division.
    6. Addition and subtraction.
    7. Relational functions, such as > or <.
    8. Logic operator "and".
    9. Other logic operators, such as "or", "not" and "xor".

    Within a priority level, EOS evaluates from left to right. Calculations within parenthesis are always evaluated first.

    So I still say the expression as written, without any context, is ambiguous. And because implied multiplication is not universally accepted, certainly not by Texas Instruments who must have thought a lot about it, those who argue that it automatically trumps the conflicting part of BODMAS are wrong. Mostly. :D

    So the answer is 288, unless the context states or implies priority for implied multiplication. There, I'm finally off the fence - nice one John259, those of a similar view, and everyone who argued that a context is needed.
  • gemma-the-huskygemma-the-husky Posts: 18,116
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    Mark. wrote: »
    It doesn't matter what you see; you're wrong.

    well, that's must be the final word then. thanks for the clarification.
  • Doctor_WibbleDoctor_Wibble Posts: 26,580
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    Keiō Line wrote: »
    so 100/2x is 100/14
    This is my reasoning too. And none of my books show terms like '2x' being treated as anything other than a single item.

    So what would anyone make of '100/2π' ?
    (assuming correct display of 'pi' here...)
    I wonder if the over-40s got 288 and the under-40s got 2.
    Nice try! but I don't think that's it.
    Edit: I got 288 (aged 42), and I've never heard of BODMAS.
    Similar-ish age, got '2', was taught (PB)(OIE)(MD)(SA) but no explicit 'left-to-right' rule that I recall. Though it's possible this is simply due to not being presented with such oddities as in the OP.


    "But since really it's a trick question, the correct answer is 'potentially either, but only if you can coherently justify your conclusion. Always state your assumptions and show your working.'"
  • Kei&#333; LineKei&#333; Line Posts: 12,979
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    d'@ve wrote: »
    This problem has been around for a long time. Here is a Q&A from 1999 (Drexel University Pa. USA):

    From Texas Instruments
    Implied multiplication vs. explicit multiplication.
    We spend a great deal of time talking to educators about the features that are included in our instructional calculators, and implied multiplication is no exception.

    Implied multiplication was given a higher priority than explicit multiplication to allow users to enter expressions as they would write them on paper. For example, the TI-80, 81, 82, 85 evaluates 1/2X as 1/(2*X), while other products may evaluate the same expression as 1/2*X from left to right. Without this feature, you would need to group 2X in parentheses, something you would not typically do when writing the expression on paper.

    This order of precedence has been changed for the TI-83, 86, and 92. Implied and explicit multiplication are given the same priority.

    So there are definitely two schools of thought. and TI have been switching between the two (note the ti-85 compared to ti-83 and ti-86)
  • Doctor_WibbleDoctor_Wibble Posts: 26,580
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    d'@ve wrote: »
    So the answer is 288, unless the context states or implies priority for implied multiplication.
    Or the answer is 2, unless the context states or implies no priority for implied multiplication.

    :p


    Good find, BTW - I had a feeling this wasn't anything particularly new.

    Seems like a reasonable place to attempt an exit I think though if I get drawn back in I will probably take to re-quoting my 'show your working' remark in the hope that it puts people off!
  • neelianeelia Posts: 24,186
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    Keiō Line wrote: »
    Amazing isn;t it?

    Forum after forum all split 50:50, and in addition the vast majority of posts reject the "compromise" that the the equation is ambiguous (as do I).

    After so many days and so many posts its clear there is no authoritative answer. It's like to two people fighting over which is better Rugby League or Rugby Union.

    Of course this is maths, so why does opinion come into it? Well the opinion is on what the rules/convention/notation actually say.

    I am surprised that we are in this position you woud have thought it was clear.


    as Donad Trump said in series 4 of the american apprentices. There comes a point when the weight of opinion on the other side is such that you have to question what you regard as true as being true. The truth in this case is that the we appear to have different rules.

    Bloody well is not a compromise!!!!! It is ambigous and thus unsolvable as for those who voted either option - a plague on both your houses:p
  • d'@ved'@ve Posts: 45,452
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    Or the answer is 2, unless the context states or implies no priority for implied multiplication.
    :p

    Good find, BTW - I had a feeling this wasn't anything particularly new.
    OK, I concede that. Maybe.

    What it boils down to is that both answers may be right but in the absence of context, only the originator of that expression knows which one.

    Whoever first came up with it could be the perfect troll. :eek: :D
  • jrajra Posts: 48,325
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    Final answer.

    Equation is ambiguous, therefore either 2 or 288 is correct.

    Equation is ambiguous, therefore neither answer is correct.

    Did you see what I just did there.

    There again, I expect most people are losing the will to live in this thread.
  • KJ44KJ44 Posts: 38,093
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    CCLXXXVIII innit?
  • Sea_saltSea_salt Posts: 466
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    There again, I expect most people are losing the will to live in this thread.
    Yep

    288 is the number of posts I've probably read about this
    2 is the number when I probably should have stopped

    ;-)
  • MoonyMoony Posts: 15,093
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    d'@ve wrote: »
    So I still say the expression as written, without any context, is ambiguous. And because implied multiplication is not universally accepted, certainly not by Texas Instruments who must have thought a lot about it, those who argue that it automatically trumps the conflicting part of BODMAS are wrong. Mostly. :D

    I personally don't see why it should. Having a different calculation order for the same operator (multiplication) based on whether or not its symbol is explicitly stated would only serve to confuse things and wouldn't bring any real benefit since we already have brackets to allow the calculation order to be dictated.
  • Doctor_WibbleDoctor_Wibble Posts: 26,580
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    Sea_salt wrote: »
    ...
    :eek: DS poster in quote mis-attribution shocka!!!
  • [Deleted User][Deleted User] Posts: 4,922
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    I voted 2, because it seems to me that A / BC is not the same as A / B x C
  • John259John259 Posts: 28,325
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    Sea_salt wrote: »
    Try reading some books written by mathematicians or scientists - you'll see what I mean.
    Can you give links to some examples please, because at that level wouldn't books use maths typsetting with horizontal bars?
  • Sea_saltSea_salt Posts: 466
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    :eek: DS poster in quote mis-attribution shocka!!!
    Sorry Dr Wibble (and jra). Not sure what happened there.
  • Doctor_WibbleDoctor_Wibble Posts: 26,580
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    Sea_salt wrote: »
    Sorry Dr Wibble
    Hardly a problem since I pretty much agree with what jra said there...
  • John259John259 Posts: 28,325
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    So what would anyone make of '100/2π' ?
    100/2π is 100π/2 but if it was laid in a mathematical style with 100, a horizontal line below it, and 2π below the horizontal line then it would be 100/(2π) of course.
  • [Deleted User][Deleted User] Posts: 4,138
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    you all still at it?

    Still, better to have you all banging away at your keyboards : keeps you away from the real world and bothering the rest of us folks
  • Sea_saltSea_salt Posts: 466
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    John259 wrote: »
    Can you give links to some examples please, because at that level wouldn't books use maths typsetting with horizontal bars?
    There were a couple of links I posted a few pages back to translations of a work by Gauss but I'm not sure if you'll find the others on the web.

    You're right about the typesetting - generally the horizontal bar will be present, but particularly in explanatory text I found examples with the '/' character or obelus. Most books appeared to always use the horizontal bar as far as I could see so it took a little while to find these examples:

    Simon Singh "Fermat's Last Theorem", pp335, 336:
    sqrt(2) = p/q = 2m/2n
    sqrt(2) = m/n

    GCE O'Level Passbook A.J. Sly (in the chapter on basic algebra):
    16x^8 ÷ 8x^2 can be written
    16x^8
    8x^2
    = 2x^6

    "What to Solve" J Cofman p229, 230:
    n
    C = n!/(n-r)!r!
    r
    and
    "The trinomial coefficients are the numbers n!/r1!r2!r3! where r1, r2, r3 are the non-negative integers ...."

    There are a few notational changes made for sub- and superscripts and the square root symbol, but otherwise they're as printed.

    [Edit]

    Just noticed http://www.amazon.co.uk/Fermats-Last-Theorem-confounded-greatest/dp/1841157910#reader_1841157910
    p290 for some reason
  • [Deleted User][Deleted User] Posts: 4,922
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    Keiō Line wrote: »
    Amazing isn;t it?

    Forum after forum all split 50:50, and in addition the vast majority of posts reject the "compromise" that the the equation is ambiguous (as do I).

    After so many days and so many posts its clear there is no authoritative answer. It's like to two people fighting over which is better Rugby League or Rugby Union.

    Of course this is maths, so why does opinion come into it? Well the opinion is on what the rules/convention/notation actually say.

    I am surprised that we are in this position you woud have thought it was clear.


    as Donad Trump said in series 4 of the american apprentices. There comes a point when the weight of opinion on the other side is such that you have to question what you regard as true as being true. The truth in this case is that the we appear to have different rules.
    Rugby League. Obviously.
  • Doctor_WibbleDoctor_Wibble Posts: 26,580
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    John259 wrote: »
    100/2π is 100π/2
    Is there nothing about '2π' that might give pause for thought as to whether bludgeoning away with the BODMAS hammer is the right thing to do?
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