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48÷2(9+3) = ? watch

  • View Poll Results: 48/2(9+3)
    2
    117
    52.47%
    288
    106
    47.53%

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    (Original post by timiop2008)
    It is definitely 2 though. And how can you say the distributive law has nothing to do with this!?. Your argument that the distributive law is irrelavent is flawed. You say you can "argue that we distribute multiplication by 48÷2 over the (9+3) bracket". However, you cannot do this. The distributive law only applies to multiplications not divisions/(fractions). Therefore as soon as you split up any term from the 2(9+3) you have broken the distributive law of multiplication.
    The law of distributivity for any field states that if a,b,c are three elements of the field then a(b+c)=ab+ac (in this case the field is just the set of real numbers). Here, we're arguing about whether a=2 or a=\frac{48}{2}, the decision of which isn't clear from the notation, unless you make up a rule to say that it is (which is what you've done). This is why it's nothing to do with the law of distributivity, it's to do with whether the bracket is on the numerator or denominator; i.e. something which isn't clear from the notation here.
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    wow, more surprising than how far this has gone is how evenly split the disagreement is. At the time of writing this exactly 69 people have voted each way
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    (Original post by delllboy)
    Rubbish arguement is rubbish.
    You've just showed that it can go either way due to interpretation.
    Read the bit underneath.
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    (Original post by delllboy)
    Rubbish arguement is rubbish.
    You've just showed that it can go either way due to interpretation.
    i think you'll find that's not what he's done!
    also it seems he(/she) knows a lot more about maths than a LOT of people on this forum who may well lose marks in future examinations if they insist on religiously sticking to the laws of BIDMAS haha.

    the question may be crap, but there's still only one right answer. 2.
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    (Original post by CameraGirl)
    i think you'll find that's not what he's done!
    also it seems he(/she) knows a lot more about maths than a LOT of people on this forum who may well lose marks in future examinations if they insist on religiously sticking to the laws of BIDMAS haha.

    the question may be crap, but there's still only one right answer. 2.
    But by saying 2, you are ASSUMING that the 2 is on the "bottom line" of the fraction. That is not stated in the question.

    We have no other information to go on, except the badly phrased question. We therefore just have to use BIDMAS from left to right. As division and multiplication are equal, we just do division first as it's on the left.

    And can you PLEASE stop saying certain people are right because they "know more maths". Lots of people who are good at maths have expressed how both answers could be correct.
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    (Original post by siwelmail)
    Brackets means what's inside the brackets and multiplying the brackets.
    Yeah, but there are no brackets around the 2 and the (9+3) so you don't have to work it out as 48 ÷ [2(9+3)] = 2.
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    BODMAS... duh?
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    Its 2
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    (Original post by thegodofgod)
    Yeah, but there are no brackets around the 2 and the (9+3) so you don't have to work it out as 48 ÷ [2(9+3)] = 2.
    As I said..it includes EXPANDING THE BRACKETS ie anything Xing added on the brackets..
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    (Original post by Manesh2468)
    you were doing aight up till the 48/2(12) then i think you dont understand what that means it looks like this on paper :

    48
    -----------
    2(12)

    which then turns into

    48
    ----------
    24

    which is 2 erm if u want to go into fractions simplify it lol which would get u

    4
    ----------
    2

    which in a form that u may understand is the same as

    4 ÷ 2 = 2

    lol =/
    I understand what it looks like, im just applying bodmas to determine whether it looks like this:
    48
    ---- (9+3) = 288
    2

    or this:
    48
    -------- = 2
    2(9+3)

    If applying bodmas, you get the first as the multiplication (the only multiplication is with (9+3)) to come AFTER the division of 48/2, and since the division is allready done with, it simply becomes 24 x 12.

    Determining whether it's the first or second goes into **** which i clearly don't understand.
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    are we seriously still discussing this?
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    (Original post by Jonty99)
    But by saying 2, you are ASSUMING that the 2 is on the "bottom line" of the fraction. That is not stated in the question.

    We have no other information to go on, except the badly phrased question. We therefore just have to use BIDMAS from left to right. As division and multiplication are equal, we just do division first as it's on the left.

    And can you PLEASE stop saying certain people are right because they "know more maths". Lots of people who are good at maths have expressed how both answers could be correct.
    yes, including me! i have stated how it is slightly ambiguous and not entirely clear, if you bothered reading my earlier posts, but how the best way to go about it, and the more mathematically correct way, gives the answer of 2.
    even using BIDMAS, the 2 is part of the brackets, if the coefficient of (9+3) were (48/2) then 48/2 would have been put in brackets by whoever wrote the question, as they would have spotted the ambiguity and rewritten it, however had they intended it to be 48/(2*(9+3)), then they may not have spotted the ambiguity within their intent.

    try thinking about it from the point of view of the person who set the question, too. they would have been more likely to notice it was in bad format, had they intended it to be (48/2)(9+3).

    if it were algebra instead, you wouldnt still be debating it, as first instinct would be to expand out the brackets!

    BODMAS could also be interpreted as: brackets first - expand them out. although yes there is ambiguity with what the coefficient is. gah this is so frustrating!
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    (Original post by nuodai)
    it's to do with whether the bracket is on the numerator or denominator
    I agree that It's to do with whether the bracket is on the numerator or the denominator. And the law of distribution clearly states you cannot split the (2(9+3)). You have to consider this as an unbreakable entity. Therefore, the bracket is on the denominator. so the problem is 48/(2((+3)). The second pair of brackets is implied by the law of distribution and the answer is 2
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    For info, I'm going to be out for a few hours - when I get back, if the quality of discussion hasn't improved I'm going to close the thread, since I think we're pretty much done here.
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    This is such a bad question!

    People on TSR can't come to a conclusion as to whether it's 288 or 2! :sad:
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    (Original post by nuodai)
    The reason it "could" be equal to either depends on whether the (9+3) is on the numerator or denominator. If this problem were to be interpreted by a computer [EDIT: most computers, depending on whether the programmers have made concessions precisely for this issue], then because computers follow BIDMAS pretty much accurately, what they'll see is:

    48÷2×(9+3)

    And because of the lack of bracket around 2×(9+3), the computer will interpret this as "take 48, divide it by 2, and then multiply what you get by 9+3", giving the answer 288. This is because, as far as a computer is concerned, "÷2" is the same as "×(1/2)" and then all the multiplications are done sequentially, so you get 48×(1/2)×(9+3).

    However, because we're humans, we might think that the (9+3) lies on the denominator of the fraction, in which case what we do is "take 48, work out 2×(9+3) and then divide 48 by that", giving the answer 2. Alternatively, we might think in the same way as the computer, which is how this whole silly debate started.

    Personally I think the notation is ambiguous. It's unclear whether the 9+3 should be on the numerator or denominator, and whatever the implicit prescribed rules for this sort of thing are, you could forgive anyone for making a notational error.

    However these threads do illustrate why LaTeX is a good idea; far too often people don't make it clear what's on a numerator or denominator, e.g. when people write, say, 1+x/3+x, they might have meant \frac{1+x}{3+x} or 1 + \frac{x}{3} + x or a number of other things, and whether they got the notation right or wrong makes no difference to what they meant. So I think future reference to this thread for such people is probably the only good thing to come out of all this.

    Sigh. The maths forum is usually so nice.

    EDIT: This post might also be useful for:
    Quotes



    I'm going to quote this for exposure, totally agree with this.
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    (Original post by timiop2008)
    I agree that It's to do with whether the bracket is on the numerator or the denominator. And the law of distribution clearly states you cannot split the (2(9+3)). You have to consider this as an unbreakable entity. Therefore, the bracket is on the denominator. so the problem is 48/(2((+3)). The second pair of brackets is implied by the law of distribution and the answer is 2
    If the problem was 48/(2(9+3)) then there would be no ambiguity and everything you say would be correct, but that's not what the problem is. It's the lack of brackets (be it around the denominator or around the 48/2) which creates the ambiguity. The bit in bold is the rule you've made up; you can either consider 2(9+3) as an unbreakable entity (giving 2), or \frac{48}{2}(9+3) as an unbreakable entity (giving 288), and it's not clear from the notation which it is unless some more brackets are inserted. You've arbitrarily chosen to insert them around (2(9+3)), whereas some arbitrarily choose to insert them around (48/2); there is no rule which says which you have to do.

    So again I repeat: nothing to do with distributivity.
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    (Original post by nuodai)
    That's not quite as debatable (as it were) because that has a well-defined answer (7), and writing 1+2x3 is different to pushing [1] [+] [2] [×] [3] on a calculator, the latter of which, on MS Calc at least, is another way of finding (1+2)×3 (since the way it works is to move from left to right regardless of what operations you use). On the other hand, a string of minus or division signs does introduce ambiguity, depending on whether or not you buy the 'left to right' rule, which I certainly don't.
    I'm more concerned with the lack of consistency on the way the two different calculators are programmed - the Standard calculator being one most likely used by those with a lack of knowledge on how they should be using parentheses to calculate sums in the correct procedure...
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    Let 48 = \mathbb{Z}. And everyone can accept that ÷ is synonymous with /. 9 + 3 = 12 is not obvious, but a quick look here should convince you of its truth. Just as timiop or whatever his name applied it, the distributitty law (citation) means 2(12) = (24). So we have \mathbb{Z}/(24) - we are quotienting out by the ideal generated by 24. \mathbb{Z}/(24) = \mathbb{Z}_{24} = \mathbb{48}_{24}. That this substitution is permitted follows from Black's theorem.

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    48/2 (9 + 3)
    48/2(12)
    24(12)
    288

    Multiplication doesn't necessarily come first, nor does division. They're equally weighted. So first we'd divide 48 by 2 and then multiply the result by 12.

    There can't be two answers, by the way.
 
 
 
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