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This problem is not solvable by the internet because of the ambiguous notation.


Do you think clearer notation can solve issues like these for mathematicians and "the internet"?


These kinds of problems are always written to be purposefully ambiguous.  A ploy not just to trick people, but to pit people against each other as they argue how math works.

The correct way to write any math problem is left to right.  I guess that assumes an English speaker and perhaps that's different for another language, but for the purposes of the country I live in, it should go left to right.

I'm about to butcher pemdas, but ignore that in favor of concept here.  In this equation there is a "2(2+2)", the purpose of which is to add the 2s inside together and then multiply them by 2, which is by the rules what is happening here.  But you could've written it 2+2*2, or to still adhere to pemdas, (2+2)*2, because the doubling is supposed to occur after.  If the division is supposed to occur first then that is also still rewriteable, we have readily available tools to tell people what to do first.  (8/2)*(2+2) is correct by order of operations and also not something you can read incorrectly.  It didn't even need the emdas, it only needs the P.  Emdas can all be put in to be done left to right or clarified with more parenthesis.


I see.  You favor converting

8÷2(2+2) = ?


(8/2)*(2+2) = ?

thinking this will cause less confusion.


>Do you think clearer notation can solve issues like these for mathematicians and "the internet"?
Mathematicians have clearer notations, would never write this, and are not usually unclear on ambiguous notation. Non-mathematicians just don't tend to use it.

First, mathematicians would never write an expression as written here. Second, if for whatever reason they did, the meaning of the expression as stated would be clear and ambiguous under the notation universally used by mathematicians. The problem is that that notation is not PEMDAS; it is something with a bit more subtlety to it, of which PEMDAS is an imperfect approximation, which in this particular case disagrees with the system it approximates, hence the confusion.

Which means that no, clearer notation evidently cannot solve these issues. There is a clearer notation, and people aren't using it.




1. Follow PEMDAS.
2. Work left to right.

My Extra Rule: If the spacing clearly indicates to use a different order of operations, then use the spacing to help determine the order of operations.


Spacing: single spaces between each letter/symbol; therefore, work left to right
Parenthesis: 8/2(4)
Working left to right: 8/2 = 4; 4(4) = 16.

The answer is 16.

Other Notes:

Had the problem been written something like:
8  /  2(2+2)=? then I might have done:
8  /  8=?
8/8 = 1.

>Do you think clearer notation can solve issues like these for mathematicians and "the internet"?

The clearer notation would be not using the traditional division symbol. Usually, division is written under a line, so things are made much more clear.

There are a lot of different strategies one might use in order to make one's intention, argument, or idea clear. The point of precise, agreed-upon notation is to make sure everyone understands exactly what the problem is. This is important in Math as well as in everyday life. The more mindful a person is with their words and intentions, the healthier their mind will be.


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Seems easy enough to me.

More seriously, I'd agree with the result due to always doing left first, as with reading.
Parentheses of course being a separate matter that is universally done first.

For those as I who wish to read the article without the bothersome popups;

Fundamentally, I think this is an issue of phonetics.
Too many people refuse to read out the problem.
When you do so, it finds itself very simple.
"Eight times four divided by two" is equivalent to 8x4/2. But it's clear how you'd solve the problem by the verbiage.

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