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Six or less? (Posted on 2018-08-09) Difficulty: 2 of 5
This simple math problem went viral (about five million views) on YouTube:

6รท3(1+2)

What is your answer and its justification?

No Solution Yet Submitted by Ady TZIDON    
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re(2): Don't get me started... (but) ... | Comment 4 of 6 |
(In reply to re: Don't get me started... (but) ... by Dej Mar)

"The order given by PEMDAS does not imply that multiplication occurs before division, and addition before substraction."


The people who promote PEMDAS are the first group of people mentioned in the top, short answer, portion of my post: math teachers, for whom I did say the answer is 6. I agree a that among the people who use PEMDAS, they in fact in agreement with what you say, so not imply that multiplication takes precedence over division, and in fact support your answer of 6.

It is not PEMDAS that gives the answer as 2/3. It is, for one, the conventions found in the Physical Review Style and Notation Guide that dictates that in their physics journals:

<blockquote>(e) When slashing fractions, respect the following conventions.In mathematical formulas this is the acceptedorder of operations:
(1) raising to a power,
(2) multiplication,
(3) division,
(4) addition and subtraction.
According to the same conventions, parentheses indicate that the operations within them are to be performed before what they contain is operated upon. Insert parentheses in ambiguous situations. For example, do not write a/b/c; write in an unambiguous form, such as (a/b)/c or a/(b/c).</blockquote>

Note that in this system, not the PEMDAS system, multiplication explicitly takes precedence over division. It also reflects the practices of Richard Feynman and the authors of many college physics texts including Sears and Zemansky, who wrote the one I used in college. It would seem a common-sense system, so that 1/2y is not considered the same as y/2.

The point was, the system was not identified, and it was designed to be ambiguous--not a good thing when trying to communicate in the real world. In the real world in situations like this, put in some "unnecessary" parentheses.

You mention "given that the equation is modern...". Why? The Physical Review submission guidelines are the ones currently in place.

Edited on August 9, 2018, 7:08 pm
  Posted by Charlie on 2018-08-09 19:06:08

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