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REPLY TO THREAD
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6÷2(1+2)=? SOLVED by the Professor of Mathematics at California State University [video]
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Original Message
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Hopefully this will end this debate.
The other OP removed this video from his thread as the answers differed.
This is from a math professor and a very well respected one at that.
***UPDATE***
I received this e-mail from Dr. Stein about 20 minutes ago
Russell,
I just researched this in several places, AND I'M WRONG!!! I'd appreciate it if you posted this answer. Here's a nice explanation.
[link to chilimath.com]
While the acronym PEMDAS is correct, the problem comes with the confusion about how M and D are treated.
I have always thought that it meant that M (multiplication) is to precede D (division). On reading several sources, M and D are treated at the same level of hierarchy, and are to be done left to right.
In other words, 6/2 x 3 really is 9, because M and D are at the same hierarchy level, and so M no longer PRECEDES D, but should be done left to right. The division is encountered first in reading 6/2 x 3, and so is done first.
Jim
***2nd e-mail update***
Hi Russell,
One of the things that I've always believed is that one should admit to one's mistakes. I just made one, and the important thing is to get it right.
Most mathematicians are aware of the possibility of error in such a situation (I'm willing to bet I'm not the only mathematician who would make this mistake). As a result, they will usually parenthesize to avoid potential misinterpretation. For instance, I would write the problem as either
6 / (2(1+2)) if I wanted the answer to be 1
or
(6/2) (1+2) if I wanted the answer to be 9
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