20210928, 14:05  #1 
Dec 2011
After milion nines:)
1,487 Posts 
8 ÷ 2 (2 + 2)
One group of people say result is 16 another group answer is 1
Since I presume this task can only have one correct answer , what that answer will be? 
20210928, 14:20  #2 
"Oliver"
Sep 2017
Porta Westfalica, DE
2×3×127 Posts 
It can have either of your solutions depending on your choice of operator precedences. (Even more if you allow more peculiar definitions.) I personally would give an implicit multiplication a higher precedence than an explicit one, since the bracket expression is visually grouped with the prefactor. But I never saw that formalised, since it is usually only a shorthand  and in this case they would be of equal precedence. Having said that, if somebody writes an expression like this, it is definitely misleading, maybe deliberately.

20210928, 14:24  #3 
Jun 2003
5,179 Posts 
Wrong. The expression is ambiguous. Hence there can be more than one answer depending on how you interpret.
The ambiguity is due to two incompatible notation styles being used together. Here, the multiplication operator is implicit, but the division operator is explicit. Due to this, we could reasonably interpret as meaning 8 / 2 * (2+2) or Code:
8  2(2+2) 
20210928, 19:27  #4 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{3}×1,201 Posts 
Welcome to the world of semantics!
It is the same as (it sounds better in Russian) a some king's ruling that was passed down to minions: "behead not pardon" Imagine the confusion of the "project managers" of that time. 
20210928, 20:32  #5  
"Rashid Naimi"
Oct 2015
Remote to Here/There
2^{2}·3·181 Posts 
Mathematics is way too old and too perfect for such ambiguity:
Quote:
or just use Parigp, it will give you only the correct answer. Of course you an always rely on Wikipedia to corrupt a beautiful science to nonsense. Democratic sciences anyone? Quote:
Last fiddled with by a1call on 20210928 at 20:45 

20210929, 00:31  #6  
Feb 2017
Nowhere
2^{2}×1,277 Posts 
Quote:
In the error message, the ^ appeared directly under the (. I tried to put it there by inserting  characters, but YMMV. Code:
? 8/2(2+2) *** unused characters: 8/2(2+2) ^ ? 

20210929, 09:00  #7 
"Jacob"
Sep 2006
Brussels, Belgium
1,753 Posts 
IMHO the rule that implicit multiplication should have a higher priority is nonsense : if the sign for a multiplication operation can be omitted, there is still a multiplication to do. Why treat it differently from a multiplication which does use a sign ?
The left to right convention is simple and unambiguous. 
20210929, 10:10  #8 
"Oliver"
Sep 2017
Porta Westfalica, DE
2·3·127 Posts 
Let's take the example of a1call:
Why should someone interpret 1 ÷ 2n as (1 ÷ 2)n i.e. half n? This is really counterintuitive. Giving the implicit operator precedence is also unambiguous, maybe even simpler and definitely selfevident. Edit: Why should we treat something that is written differently inevitably the same? Math is not a conversational language which may have ambiguities etc., math should be well defined and having multiple ways to express the exact same thing is not helpful. Last fiddled with by kruoli on 20210929 at 10:13 Reason: Additions. 
20210929, 13:46  #9 
"刀比日"
May 2018
EB_{16} Posts 
The answer could also be {8} for a finite set containing one element in the range 8 ÷ 8 from 8 to 8.
"In Italy, Poland and Russia, this notation is sometimes used in engineering to denote a range of values." https://en.wikipedia.org/wiki/Obelus 
20210930, 12:06  #10 
Feb 2017
Nowhere
13F4_{16} Posts 
This is a case where punctuation really would be a matter of life and death! "Behead, not pardon" and "Behead not, pardon" have opposite meanings.

20210930, 14:16  #11 
Dec 2011
After milion nines:)
1,487 Posts 
I am very disappointed. I expected the math to be a little better defined after all :)
