Personally, growing up, I've always been taught that PEMDAS was interchangeable. You would read the problem left to right so if multiplication came first, you would that.

Hi, Adam.

This kind of problem, like 48/2(9+3), is called "ambiguous" here in Brazil. In fact, if you interpret this problem like a fraction, you have two possibilities:

-- 48 is the numerator and 2(9+3) is the denominator. So, multiplication comes first.

-- 48 is the numerator, 2 is the denominator and this fraction, 48/2, multiplies (9+3). In this case, division comes first.

You guys in U.S. "solve" that "ambiguous thing" using PEMDAS (I learn that here, on Khan Academy!): multiplication and division have the same priority. But if someone wrote "48/2(9+3)", the problem have to be solved like OUAT said. We should solve the problem left to right for same priority operations.

Thanks Ouat and Leo.

True, when the problem is ambiguous it does make it difficult to determine the "right" answer - but there's the problem.  Apparently, based on my limited research, in the UK (from an article I read) they determine the answer using Division before Multiplication but the in the US we (from what I was taught) answer Multiplication before Division (everything else being equal).

For math being a "universal language" that would make things a bit difficult at the "high end" of mathematical problem solving if there are no clear cut rules on how to solve problems the "right" way.

You shouldn't be able to come up with two different answers to the same math problem, ambiguous or not.  :)

I've always learned that Addition and Subtraction are on equal grounds, and so are Multiplication and Division. So, if I saw that problem I would evaluate it from left to right.

I think the issue with the ambiguous problem here isn't that it can be interpreted two ways, but rather that it was written in an ambiguous way. In the world of higher mathematics, I don't think you would ever see an expression written like that.

The expression should be written in a clearer form that provides no ambiguity as to what it means, such as

48/(2(9 + 3)) or (48/2)(9+3)

Thanks Evan, I agree; but then how would you solve this problem:

2x/3y-1 if x=9 and y=2

See what answer you come up with and then take a look at this article from Harvard:

http://www.math.harvard.edu/~knill/pedagogy/ambiguity/index.html

Obviously ambiguity is a problem, but it appears not everyone solves the problem from left to right.  I would be interested in hearing your thoughts on the matter.  Thanks. :)

That's definitely an interesting paper! Like the author says, I don't think there really is a right or wrong way to look at this, since both answers can be argued as correct. But like the author says, "There is only one solution: write the parenthesis."

Unless there's no ambiguity in the problem, I don't think one can say there's only one correct answer. So as the author suggests, if problems aren't written in an ambiguous way in the first place, then there wouldn't even need to be the argument of how to interpret the problem. But of course, having everyone write unambiguous expressions 100% of the time is rather unlikely....

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