Tough one Gilbert.
X + Y = X - Y. Hmmm.
X * Y = Y. Wtf?
I'm gonna say Y = 0 xD
A similar problem actually came up on my Facebook the other day in one of those new polls they have. I was surprised how many people got it wrong. It was a ratio of about 6:2.5 with the majority getting it right. However, there was about ten-to-a-hundred thousand votes cast (from what I remember). I never thought that order of operations was that difficult to understand.
EDIT: I found the Facebook poll. Kind of astonishing the ratio is A LOT closer than I remembered:
6 / 2 (1 + 2) = ?
1 - 1,546,659 votes
9 - 1,996,151 votes
It's obviously 9:
1 + 2 = 3: 6 / 2 (3) = ?
6 / 2 = 3: 3(3) = ?
3 * 3 = 9
People get 1 because they do the parentheses first, which is right (look at my first step). But then they distribute the 2 into the parentheses before dividing the six by it. This is the wrong way:
1 + 2 - 3: 6 / 2 (3) = ?
2 * 3 = 6: 6 / 6 = ?
6 / 6 = 1
Another way is people might be distributing the 2 early and then adding it:
2 * 2 = 4; 2 * 1 = 2: 6 / (4 + 2) = ?
4 + 2 = 6: 6 / (6) = ?
6 / 6 = 1
However you don't distribute the number into the parentheses unless there's variables. As VR said, you got to use that PEMDAS. Once you do what's in the parentheses you start over from left to right and do multiplication/division. After that you start over from left to right and do addition/subtraction.
EDIT: Found some other guy's explanation if anyone's interested. Apparently this is why people get it wrong:
Team 9: THE ANSWER IS 9
Those who argue that the answer is 9 follow standard order of operations:
6/2(1+2)
First you do whatever is in the parentheses which is (1+2):
6/2(3)
Next, you do multiplication and division in order from left to right, so you devide 6 by 2 and then multiply the result by 3. The parentheses are not needed as 2(3) only indicates 2x3:
3(3) = 9
Team 1: THE ANSWER IS 1
Those who argue that the answer is 1 follow order of operations, but accept that multiplication by juxtaposition indicates that the juxtaposed values must be multiplied together before processing other operations:
6/2(1+2)
First you do whatever is in the parentheses which is (1+2):
6/2(3)
Next you must do 2(3) because multiplying by just putting things next to each other (multiplication by juxtaposition), rather than using the "x" sign indicates that the juxtaposed values must be multiplied together before other operations.
6/6 = 1
As I have demonstrated here both answers can be argued for and the problem lies with what your view on multiplication by juxtaposition is:
Whether or not you believe 6/2(3) is different than 6/2x(3)
From what Ive been able to find, there is no definitive answer or consensus on this matter (even different calculators will calculate them differently), Therefore it is up to the one writing the expression to clearly indicate what he means without any ambiguity by writing:
6/2x(1+2) or 6/(2(1+2))
In conclusion I would like to state that the person who wrote the expression 6/2(1+2) is an absolute dick-headed moron who does not know how to make it clear what he means and just likes pissing people off. Learn some math fool!
That makes complete sense to me. I still vote for 9 though because I only multiply through the parentheses when there's a variable present.