Solve this equation > 48÷2(9+3) = ?

15455575960108

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  • FlufanFlufan Posts: 2,544
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    indehed wrote: »
    I'm not one for maths, but I get 2.
    If there's one thing I remember from school, it's that you do the bits with brackets first....

    Just a stab in the dark, but I'm guessing that you haven't read the preceding 1,305 posts in this thread...?

    ======================

    To me, the debate isn't (shouldn't be) over the acceptedness(?) of BODMAS/BEDMAS/BIDMAS at all, it's over whether "a/bc" means (a/b)*c or a/(bc), pure and simple.

    To reiterate my stance: there is a bond in the "bc" expression and hence "a/(bc)" is right. I have never encountered otherwise.
    1/2i = 1/(2i) = -0.5i
    100/2π =100/(2π) = 16ish

    Much as I'm struggling to believe that anyone has really and seriously used these terms (as typographically presented here) to mean (a/b)*c, 0.5i and 157ish respectively, I'll suspend my disbelief - hence my conclusion that "mu" is the answer: "re-ask the question in a better way".

    Writing "2(9+3)" is unorthodox (as they're just numbers, not x's, π's etc) but that "bond" is still there and to be able to do the "48÷2" first, there should be a "*" before the "(" because
    48÷2*(9+3) = 288

    Also, I do believe we were given an equation to solve:

    "48÷2(9+3) = ?"

    (where "?" would normally be "x" or similar). There's an equals sign; it's an equation; solve it for "?".

    Yes, it would be better expressed as "evaluate the expression 48÷2(9+3)", but to bicker over this is, in my book, pure red herringery served with more than a soupçon of pedantry. The main debate is over a different point and I don't think is going to go any further now. Great thread, though - loving how long and fast-growing it's been!

    ETA: "Mathsgate", ROFL!

    EATA: from the referred-to thread:
    But I've been somewhat amazed by the number of people, some at university, who insist that 3x / 2y = 3xy / 2 is standard usage.
    It's not just me, then!
  • John259John259 Posts: 28,328
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    http://www.bbc.co.uk/schools/ks3bitesize/maths/number/order_operation/revise2.shtml
    "Division and Multiplication. Start on the left and work them out in the order that you find them."

    http://www.channel4.com/programmes/dispatches/articles/kids-dont-count-bodmas
    "What it in fact means that brackets are evaluated first, then division and multiplication are to be done before addition and subtraction, but each of these pairs of operations are to be evaluated from left to right."

    http://www.mathematics.me.uk/BODMAS.pdf
    "For operators of the same priority, we simply evaluate left-to-right."

    http://www.mathcentre.ac.uk/resources/workbooks/mathcentre/rules.pdf
    "Anything in brackets must be done first. Then we evaluate any powers. Next we do any divisions and multiplications, working from left to right. And finally we do the additions and subtractions, again working from left to right."

    http://www.uea.ac.uk/polopoly_fs/1.141672!BODMAS.pdf
    "Importantly, when two or more operations of the same order appear one-after-another, the operations should be carried out from left-to-right. "
  • Keiō LineKeiō Line Posts: 12,979
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    Can a 288'er explain this

    http://www3.wolframalpha.com/input/?i=1%2F2x

    How could they have got this so wrong?
  • FlufanFlufan Posts: 2,544
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    John259 wrote: »
    http://www.bbc.co.uk/schools/ks3bitesize/maths/number/order_operation/revise2.shtml
    "Division and Multiplication. Start on the left and work them out in the order that you find them."

    http://www.channel4.com/programmes/dispatches/articles/kids-dont-count-bodmas
    "What it in fact means that brackets are evaluated first, then division and multiplication are to be done before addition and subtraction, but each of these pairs of operations are to be evaluated from left to right."

    http://www.mathematics.me.uk/BODMAS.pdf
    "For operators of the same priority, we simply evaluate left-to-right."

    http://www.mathcentre.ac.uk/resources/workbooks/mathcentre/rules.pdf
    "Anything in brackets must be done first. Then we evaluate any powers. Next we do any divisions and multiplications, working from left to right. And finally we do the additions and subtractions, again working from left to right."

    http://www.uea.ac.uk/polopoly_fs/1.141672!BODMAS.pdf
    "Importantly, when two or more operations of the same order appear one-after-another, the operations should be carried out from left-to-right. "

    cba to look at the links, but from your excerpts it looks like you're just hitting us with definitions of BODMAS. No-one's disputing that, AFAICT.
  • KJ44KJ44 Posts: 38,093
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    This thread is just too gross.
  • FlufanFlufan Posts: 2,544
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    KJ44 wrote: »
    This thread is just too gross.

    Excellent!

    (And wrong, btw :D.)

    What I want to know is how we should evaluate

    http://www.digitalspy.co.uk

    Does the "//" mean just the "www" goes on top, or do we work out the three dot-products first then double-divide the result, or what?
  • Special K_Special K_ Posts: 6,320
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    No wonder this country is in such a mess if the eggheads can't even work out a simple sum like this......it's what you get for leaving out common sense brackets and multiplication signs just to make a simple thing seem clever

    So...what is the answer then?
  • KJ44KJ44 Posts: 38,093
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    Flufan wrote: »
    Excellent!

    (And wrong, btw.)

    I'm glad someone's paying attention.

    I'm not wrong, because the correct answer to a silly question is a silly answer. :D
  • John259John259 Posts: 28,328
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    Flufan wrote: »
    cba to look at the links, but from your excerpts it looks like you're just hitting us with definitions of BODMAS. No-one's disputing that, AFAICT.
    My aim was to stress the left to right rule, which the list of operations specified by BODMAS doesn't cover. This is important because some people here think that when two items are multiplied together without a multiplication sign that multiplication should be done first, even if it follows to the right of a division. Those references all say that is wrong.

    In maths the multiplication sign is always omitted if at least one of the operands is a letter. However, all the references I quoted say to always proceed left to right, and none mention the question of whether there is a multiplication sign or not.

    You'll have noticed that the references aren't just forum postings, wiki articles or blog entries, but from generally more authoritative sources.
  • KJ44KJ44 Posts: 38,093
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    Flufan wrote: »
    Does the "//" mean just the "www" goes on top, or do we work out the three dot-products first then double-divide the result, or what?

    Truth is stranger than fiction:

    http://docs.python.org/reference/lexical_analysis.html#operators

    The following tokens are operators:

    + - * ** / [highlight]//[/highlight] %
    << >> & | ^ ~
    < > <= >= == != <>


    http://docs.python.org/release/2.2.3/whatsnew/node7.html

    A new operator, //, is the floor division operator. (Yes, we know it looks like C++'s comment symbol.) // always performs floor division no matter what the types of its operands are, so 1 // 2 is 0 and 1.0 // 2.0 is also 0.0.
  • John259John259 Posts: 28,328
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    KJ44 wrote: »
    A new operator, //, is the floor division operator. (Yes, we know it looks like C++'s comment symbol.) // always performs floor division no matter what the types of its operands are, so 1 // 2 is 0 and 1.0 // 2.0 is also 0.0.
    That sounds like Int(a/b) in BASIC.
  • Kei&#333; LineKei&#333; Line Posts: 12,979
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    John259 wrote: »
    http://www.uea.ac.uk/polopoly_fs/1.141672!BODMAS.pdf
    "Importantly, when two or more operations of the same order appear one-after-another, the operations should be carried out from left-to-right. "
    Your google is (unintentionally) biased.
    Please take a look at page 6
    http://www.uea.ac.uk/jtm/1/lec1p5.pdf
    I'm not a clever as you. Is the second "basic rule" giving ac/bd correct?
  • KJ44KJ44 Posts: 38,093
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    Just suppose Cameron and Osborne think the National Debt is 288 billion when it's really only 2 billion? :eek:
  • BedlemBedlem Posts: 2,629
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    (2(9+3)) / 2(9+3) / 2 x (9+3) = ??

    :p
  • FlufanFlufan Posts: 2,544
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    John259 wrote: »
    My aim was to stress the left to right rule, which the list of operations specified by BODMAS doesn't cover. This is important because some people here think that when two items are multiplied together without a multiplication sign that multiplication should be done first, even if it follows to the right of a division. Those references all say that is wrong.
    In maths the multiplication sign is always omitted if at least one of the operands is a letter. However, all the references I quoted say to always proceed left to right, and none mention the question of whether there is a multiplication sign or not.

    You'll have noticed that the references aren't just forum postings, wiki articles or blog entries, but from generally more authoritative sources.

    ?? You say on the one hand:
    "When two items are multiplied together without a multiplication sign that multiplication should be done first... Those references all say that is wrong."
    and then
    "none [of the references] mention the question of whether there is a multiplication sign or not"

    How can they say it's wrong without mentioning it?

    I think also that perhaps there's confusion caused by whether "BODMAS" merely means the order of operations with those initial letters (yes, in pairs) OR the rule/convention that talks about that order TOGETHER WITH the left-to-right aspect.
  • John259John259 Posts: 28,328
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    Keiō Line wrote: »
    Your google is (unintentionally) biased.
    Please take a look at page 6
    http://www.uea.ac.uk/jtm/1/lec1p5.pdf
    I'm not a clever as you. Is ac/bd correct?
    I guess you mean page six by page numbers within the document (page 7 by my PDF reader's reckoning) - section 1.5.4?

    As they have it, ac above a horizontal line and bd below it, is correct and abides by the standard.

    As you have it, very differently, ac/bd is wrong as that of course is acd/b.
  • KJ44KJ44 Posts: 38,093
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    Keiō Line wrote: »
    Can a 288'er explain this

    http://www3.wolframalpha.com/input/?i=1%2F2x

    How could they have got this so wrong?


    It's entirely correct, as you'd expect. You're trying to blur the distinction between the horizontal line and the slash; the former groups everything beneath it as if inside an implied set of brackets, the latter does not.

    Indeed, if you hold your mouse over the expression with the horizontal bar, under "Input:", the alt image text shows the expression using a slash and brackets.
  • FlufanFlufan Posts: 2,544
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    John259 wrote: »
    As they have it, ac above a horizontal line and bd below it, is correct and abides by the standard.

    As you have it, very differently, ac/bd is wrong as that of course is acd/b.

    You stirrer, you! There's NO "of course" about it at all!

    If you went up to the board in any of the maths lectures I went to and wrote

    ac/bd = acd/b

    (like that, on one line, with slashes) you'd have been greeted with howls of derisive laughter.

    Well, perhaps not, mathematicians not being known for such extroversion, but you know what I mean.
  • John259John259 Posts: 28,328
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    Flufan wrote: »
    ?? You say on the one hand:
    "When two items are multiplied together without a multiplication sign that multiplication should be done first... Those references all say that is wrong."
    and then
    "none [of the references] mention the question of whether there is a multiplication sign or not"

    How can they say it's wrong without mentioning it?
    Because if that rule existed I would have expected at least one source to mention it. None do, which implies (but does not prove) that there is no such rule.
    I think also that perhaps there's confusion caused by whether "BODMAS" merely means the order of operations with those initial letters (yes, in pairs) OR the rule/convention that talks about that order TOGETHER WITH the left-to-right aspect.
    BODMAS is an acronym for remembering that part of the convention for evaluating expressions that specifies the order of operations. The convention also includes the additional aspects that division and multiplication have the same priority as each other, and that addition and subjtraction have the same priority as each other, and the left to right rule.
  • cartreecartree Posts: 1,562
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    Keiō Line wrote: »
    Can a 288'er explain this

    http://www3.wolframalpha.com/input/?i=1%2F2x

    How could they have got this so wrong?

    Erm... I kinda really hate to do this to you, but...

    http://www3.wolframalpha.com/input/?i=48%2F2%289%2B3%29
  • John259John259 Posts: 28,328
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    Flufan wrote: »
    If you went up to the board in any of the maths lectures I went to and wrote

    ac/bd = acd/b

    (like that, on one line, with slashes) you'd have been greeted with howls of derisive laughter.
    From some quarters perhaps, but those who understood the rule would have nodded in agreement, although probably wondering why the horizontal bar format wasn't being used.
  • FlufanFlufan Posts: 2,544
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    John259 wrote: »
    Because if that rule existed I would have expected at least one source to mention it. None do, which implies (but does not prove) that there is no such rule.

    Which is very different to them actually saying that it's wrong, which is what you said.
  • Special K_Special K_ Posts: 6,320
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    Okay then, as it stands right now, it's 288.
  • FlufanFlufan Posts: 2,544
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    John259 wrote: »
    From some quarters perhaps, but those who understood the rule would have nodded in agreement

    It's not to do with understanding the rule; it's to do with understanding that "ab" has a subtle, yet definite, different meaning than "a*b" does, and using BODMAS on that entity.

    re ac/bd: Most quarters would have thought that if you meant acd/b then you'd write (ac/b)d
  • FlufanFlufan Posts: 2,544
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    Special K_ wrote: »
    Okay then, as it stands right now, it's 288.

    Only according to p% of the votes, where

    p = (48÷2*(9+3))/100+40

    (because happily, as I write, the 288ers have 42.88% in the poll).

    And, just for clarity, 42.88<57.12

    Not that DS polls mean anything, of course. :D
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