Thread: 6÷2(1+2) = ? View Single Post
May 9th, 2011, 12:32 PM   #191 (permalink)
Ichapp
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I'm no longer at all interested in the original question, as it's an interpretation question: basically does the (x+y) term belong to the numerator or denominator. This is the difference between evaluating to 9 and to 1, respectively. The problem is it's missing a set of parentheses and left up to the reader to decide where they ought to fit.

Quote:
 Originally Posted by novox77 To me, left-to-right takes precedence, so 9 is the only correct answer.
I can assure you, left and right has absolutely no precedence because of the commutative property of addition and multiplication. Since subtracting term y from term x (seen as (x-y))is nothing more than the addition of the negative value of term y to term x (seen as (x+(-1)*y)), we can force subtraction to commutativity through addition. Similarly, division can be forced to commutativity through the use of fractions and multiplication (yes, this doesn't completely remove the need for division, but it does help me in what I'm looking to illustrate).

Once we have reached this, we can work through (useful iterations) of this type of problem from left to right, from right to left, or from the centre out if desired as long as we remember to give good respect to the order of operations (and though it has been stated a couple of times already, I think it merits repeating that multiplication and division are on an equal order, as are addition and subtraction (this is why we see several different flavours of PEMDAS)).