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PEMDAS and BODMAS

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    Sorry if this has been mentioned before, but surely they wouldn't give the same answer? According to PEMDAS, multiplication comes before division and BODMAS states the other way.

    So for  6 \div 2 \times 5

    Using PEMDAS gives us 0.6
    Using BODMAS gives us 15

    Any opinions on this?
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    Both.
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    (Original post by InadequateJusticex)

    Any opinions on this?
    Multiplication and division are the same operation and are, therefore, completed left to right

    So the answer is 15
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    What's PEDMAS? Wow everything changes when you leave school

    Oh I spelt it wrong. It's PEMDAS
  5. Offline

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    (Original post by Cephalus)
    What's PEDMAS? Wow everything changes when you leave school
    The american version of BODMAS
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    (Original post by InadequateJusticex)
    Sorry if this has been mentioned before, but surely they wouldn't give the same answer? According to PEMDAS, multiplication comes before division and BODMAS states the other way.

    So for  6 \div 2 \times 5

    Using PEMDAS gives us 0.6
    Using BODMAS gives us 15

    Any opinions on this?
    Strictly speaking, this isn't resolved by BODMAS/PEMDAS. These rules give division and multiplication equal priority, and likewise addition and subtraction: after all, division is just multiplication by a fraction, and subtraction is just addition of a negative. So in this sense, BODMAS, BOMDAS, BODMSA and BOMDSA all give the same rule.

    If you interpret 6 \div 2 \times 5 to be just a sequence of operations to carry out then by default you should work from left to right, to obtain 15.

    But in the strictest sense, this is ambiguous. There are 'hidden brackets', which make it either (6 \div 2) \times 5 or 6 \div (2 \times 5), the former giving 15 and the latter giving 0.6, and without further context it's impossible to say with confidence which it is. In order to disambiguate, brackets should be added, or the fraction should be written in vertical notation to give either \dfrac{6}{2} \times 5 or \dfrac{6}{2 \times 5}.
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    (Original post by InadequateJusticex)
    Sorry if this has been mentioned before, but surely they wouldn't give the same answer? According to PEMDAS, multiplication comes before division and BODMAS states the other way.

    So for  6 \div 2 \times 5

    Using PEMDAS gives us 0.6
    Using BODMAS gives us 15

    Any opinions on this?
    Multiplication & Division are equivalent so saying one comes before the other makes little sense. Why not reduce it down to a product? 6 \div 2 \times 5=6 \times \dfrac{1}{2} \times 5=15
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    (Original post by Lord of the Flies)
    Multiplication & Division are equivalent so saying one comes before the other makes little sense. Why not reduce it down to a product? 6 \div 2 \times 5=6 \times \dfrac{1}{2} \times 5=15
    The real issue is in deciding whether

    (i): 6 \div 2 \times 5 = 6 \times \dfrac{1}{2} \times 5

    or

    (ii): 6 \div 2 \times 5 = 6 \times \dfrac{1}{2 \times 5}

    I'd expect (i) is the most common, and certainly what you'd assume if you were doing a basic (say, pre-A-level) arithmetic without any context to it; but there's no universally accepted reason why the notation couldn't also refer to (ii).
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    (Original post by nuodai)
    there's no universally accepted reason why the notation couldn't also refer to (ii).
    Ah, I wasn't aware. I thought "separating" the operations and substituting with their equivalents made complete sense given the absence of brackets:

     (+6)\;(\div 2)\;(\times 5)=(+6)\;(\times 1/2)\;(\times 5)

    Strange that there is still no universally accepted method for these things!
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    (Original post by Lord of the Flies)
    Ah, I wasn't aware. I thought "separating" the operations and substituting with their equivalents made complete sense given the absence of brackets:

     (+6)\;(\div 2)\;(\times 5)=(+6)\;(\times 1/2)\;(\times 5)

    Strange that there is still no universally accepted method for these things!
    Mhm, there's a facebook question homogeneous to this, and in fact, it's both. Maybe they'll eventually overhaul the problem by just stating that in these scenarios a "left-to-right" approach is the more suitable.

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