8/2(2+2) = ?

[Goodygumdrops]

heh Z-man I saw the proof for this just about a month ago, But i forget the exact details.

edit: spoiler removed

[dariv]

I was talking about this with someone else, and the conclusion was, technically, you work from left to right where it is not clear whether divide or multiply are first

hence a/b*c = (a/b)*c

and my answer is 16.

If I saw this written on paper though I wouldn't know because a lot of people will write it to mean a/(b*c) because the backslash makes it look like everything that follows it is in some invisible brackets.

[chrisd]

My math teacher told me that the "/" and "()" are grouping symbols.

Teachers are not always right either. The ones who only teach in middle school may not even have a university degree. Or teachers who have a university degree may not have been the brightest students when they were in university. Another interesting property of teachers to note is that it is far more important to be sure of yourself and to impress this self-confidence on the pupils than to be right. A teacher that is not displaying self-confidence is basically done for, but a teacher who says things that are wrong in a self-confident way can easily be considered a great teacher by everybody. The fact is, the "/" is not a grouping symbol at all.

Using "/" to represent division is "incorrect". Calculators do that because it is their only representation of division, even though it is "incorrect".

It is a notation, so as such it is neither correct nor incorrect. It is just what most people do or are used to. In many cases the notation

a
--
b

is used in scientific papers to indicate division. However, this is a bit large and bulky so it may not look very good typographically, especially in text (the opposite of text being a displayed equation, that is displayed on a line by itself). Therefore, if both the numerator and the denominator are small, often this is written as a/b. So, actually, you find fractions of the form a/b quite a lot in scientific papers.

In that case I would also recommend people to write either (a/b)*c or a/(b*c) to make clear what the order of operations is. The convention of either working from left to right or doing multiplication before division, has varied over time and over countries. Although, it seems that nowadays mostly the convention is in use to work from left to right. Hence, a/b*c means (a/b)*c but not because of grouping, but because multiplications and divisions are done from left to right. However, if one reads a/b*c in a scientific paper, one even has to consider the possibility that the author really has a/(b*c) in mind in which case it does not do any good to stubbornly be set on reading it as (a/b)*c because this is supposed to be "right".

[Tank Program]

If you really want to be clear about division, you should use ^-1. (In superscript of course...)

[Mecca]

[quote="INW"]Using "/" to represent division is "incorrect". Calculators do that because it is their only representation of division, even though it is "incorrect".[quote]

Yeah I also have to disagree with that. How can it possibly be incorrect when everyone that read the equasion in the topic title knew that "/" meant division? Also, what do you mean by the bolded part? I have used calculators that show division with a "/" and calculators that have shown it with the other symbol (too lazy to copy paste or look up the alt code).

[INW]

Using "/" to represent division is "incorrect". Calculators do that because it is their only representation of division, even though it is "incorrect".

Yeah I also have to disagree with that. How can it possibly be incorrect when everyone that read the equasion in the topic title knew that "/" meant division? Also, what do you mean by the bolded part? I have used calculators that show division with a "/" and calculators that have shown it with the other symbol (too lazy to copy paste or look up the alt code).

Some calculators don't have the advancement, if that is the correct term, to provide the "division sign".
So the "/" is used as a substitution.

[Mecca]

What!? The calculators which I have seen the division sign on have been the single 9 or 10 digit line calculators...

[INW]

New doesn't always mean advanced.

Some older calculators are more advanced than newer ones.