#21




So we're still no closer to agreeing on whether 1/4x is equivelant to (1/4)x or 1/(4x)...

#22




I think that as you've written it, the answer is always 9 since 6/2 is a fraction which would be resolved before other calculations. but 6÷2(1+2) is ambiguous.

#23




How is the latter ambiguous?
Parenthesis first gives you 6 (divided by, dunno how to do the sign) 2 * 3. Since there are only operations of equal magnitude left, you solve left to right. 6 divided by 2 is 3, and 3 * 3 is 9. That is actually less ambiguous than the other. 
#24




It would be ambiguous if you interpret the 1+2 as inside of the divider (which is possible) making it 6 divided by 6. The bottom being calculated first of course.
That's not what is going on, but it could look that way if it was written out ambiguously which is why when they write this stuff out they make it clear where parenthesis are located so it can be calculated correct  which in this case is (I agree) 9. 
#25




If the order of operations were always the same for all mathematics and programming languages then it would not be ambiguous. Unfortunately, they are not, as described in this wiki:
http://en.wikipedia.org/wiki/Order_of_operations Quote:

#26




Quote:

#27




Quote:

#28




The binding for Wolfram Alpha described in that wiki seems to only work for variables, not for parentheses. (So Google and Wolfram Alpha both give the same answer, 9. They also return any expression in an unambiguous form before the answer, which is welcome feedback.)

#29




Oddly (to my mind anyway) Alpha doesn't respect the same binding for two constants separated by a space, even though it does recognize that form as an implied multiplication. So 6÷2 4 (with a space between 2 and 4) is parsed as (6/2)*4 whereas 6÷2x is parsed as 6/(2*x). So the question is what's 6÷2 x (with a space between 2 and x)? Well, according to Alpha that's (6/2)*x!

#30




The "ambiguity" is when people imagine the portion in brackets to be part of the denominator of a fraction  if the slash is replaced by a division sign, it would be harder to envision this. I doubt that there would be any ambiguity if this is drawn by hand and the (1+2) in the OP is clearly in the numerator.

#31




Playing around with Word and equations. Since there were two possible ways to look at the equation I wanted to see how Word would handle them.
The first was: Word transfers that as 6/2 (1+2) when it is put on a single line. The next was Word saw that as to be 6/(2(1+2)) when on a single line. It has been many years since I had to work much with written math equations. I seem to remember it was a space between number that made a difference. 6/2 are separated by a space from (1+2) and therefore not part of the fraction. If there was no space or dot then they were together. So 2(1+2) would have been 2*(1+2) for the denominator. Since it has been more than 20 years since I had to study and use math equations. Take no notice of my silly idea. 
#32




If it ever comes down to a difference in whitespace you should add parentheses. The point is to communicate something effectively, not to try to trip up your audience by assuming they agree on the finer points of order of operations.

#33




In C, some of the order of operations that trip me up are that bitwise operators come after compares. If you do "x%4 == 0", you're checking if x is evenly divisible by 4. If you do "x&3 == 0", that looks like it should be doing the same operation except possibly more efficiently. But actually it evaluates unconditionally to 0, because it's "x&(3==0)" > "x&0".
Quote:

#34




And if you'll note the original post, that's the way it appears in the Facebook graphic, with the standard division symbol. It's not ambiguous at all, it's a simple test of the order of operations.
Gibbie 
#35




Quote:
The best thing is not to use unclear notation, and use more parentheses in situations where it's possible that it could easily be misinterpreted. 
#36




I was addressing this part of your post:
Quote:
Gibbie 
#37




I did use the ÷ sign when testing this on Alpha but it makes no difference. 6÷2x and 6/2x are both interpreted as 6/(2*x), which is correct according to many authorities, as the wiki I cited points out. You may agree with Alpha that the multiplication in 2x has a different precedence than that in 2(1+2) but it's still no less ambiguous for real communication with anything other than a compiler. That's what this question comes down to: communication between people, not rules of the game.

#38




I think the real lesson of this exercise isn't that people don't know the correct order of operations, nor that the order is ambiguous, but simply don't mix operators from different mathematical languages. The division operation (whether you prefer / or ÷) doesn't mix with the implied multiplication in 2x or 2(1+2). That's why once we get into any kind of math that uses the implied multiplication we stop using the division symbol and switch to the horizontal division bar. It's especially to avoid this kind of mess. (Also, I can't understand why anyone would want this kind of thing to be decided by a bunch of memorized rules. Communication doesn't have to be difficult.)

#39




the PEMDAS method is reffered to as BEDMAS around here 
Brackets Exponents Division Multiplication Addition Subtraction 
#40




I for one can't get any other answer than 9. How about this one: (also shared on Facebook):
4*4+4*4+44*4= ? 
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