Order of operations - why are they in the order they're in? 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. :-)

I am sorry that I am over a year late in reading these posts.  It is a great pitty that so few people understand that order of operations is derived from the basic rules of mathematics.  Let us look at a simple example:  $2 + 3 \times 4$.  Because multiplication is by definition repeated addition, $3 \times 4$ is the same as $4 + 4 + 4$.  So I could rewrite $2 + 3 \times 4$ as $2 + 4 + 4 + 4$.  Then I just add left to right and get $14$.  That is the same as using the natural order of operations and performing the multiplication first.  $2 + 3 \times 4 = 2 + 12 = 14$.  Because exponents are simply repeated multiplication, they are performed before multiplication.  Parentheses are used to form groupings that are to be performed before other operations.  Thus $2(3+4)$ indicates that $3+4$ must be done before multiplying by $2$.  Thus the order:  parentheses first, exponents second,  mutiplication and division third, and save the lowest level operations of addition and subtraction for last.
