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I understand the order of operations, but why are they ordered the way they're ordered? Is there a particular reason why multiplication should have a higher precedence than subtraction, other than to prevent ambiguity?

Edit: I'm a curious software developer that's relatively lousy at math. A simple explanation that your grandma could understand would be very welcome. :-)

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    There's some relevant information here: http://mathforum.org/library/drmath/view/52582.html2011-05-26
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    I believe it is just convention - really one should use brackets. A similar convention exists in "real life": There is a sign on some of the toilets in my maths department which reads "For the use of female staff and postgrads only". Being a male postgrad, I am yet to work up the courage to use these loos!2011-08-26
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    Parentheses are certainly natural enough, and once you accept these, multiplication over addition makes the formula 5*(4 + 2) = 5*4 + 5*2 pretty nice.2014-06-09
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    Multiplication is just shorthand for addition - so 2 x 3 + 4 is actually 2 + 2 + 2 + 4 (alternatively can be written as 3 + 3 + 4). This leaves no ambiguity as to which operation is to be performed first.2016-03-21

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