# How does 1/2x read? [closed]

It is an engineering/computer science/math paper, is 1/2x read as 1/(2x) or x/2?

Can you please let me know if it is clearly one of them, or it is not possible to say which one it is?

• I'm voting to close this question as off-topic because it is not about academia, but about a text ambiguity. – user3209815 Aug 31 '17 at 9:22

If it's correct as written, then it means 1/(2x).

However, it's possible it was a typo, and that (1/2)x was meant. You need to interpret from the context in which it occurs which was intended.

It's ambiguous as written. Technically I would argue that it means (1/2)x; just as if you wrote 1/2*x into a computer system. To say otherwise is to subscribe to the commonly-presumed notion that juxtaposition supersedes the normal order of operations, but that is not something actually written in any official definition. But it's possible that the writer was being sloppy and did in fact mean 1/(2x). You will need to decode from the context, or else contact the author.

My guess. 1/2x is an attempt to write on a defective web forum (like academia.se) not implementing LaTeX. And therefore, it means 1/(2x).

Second guess. If written by a mathematician, 1/2x means 1/(2x), since if she meant (1/2)x she would have written the simpler x/2

Third guess. Grade-school "follow the rule, do not think" method: for multiplication and division, evaluate left to right. In that case 1/2x would be (1/2) x

Fourth guess. Grade-school "follow the rule, do not think" method: multiplication first, then division. in that case 1/2x means 1/(2x).

Summary: unless you are clearly in one of the groups I mention, and writing for others in that group, then do not write 1/2x .

I would read it as 1/(2x), because otherwise I would assume they had written it simply as x/2, whereas there is no easy way of writing 1/(2x).

Of course, if there is some multiplication sign, or simple a space, between 2 and x, then I would interpret it as half x.

Whatever they meant by it, it is poor and ambiguous notation. You really should consider the context and see which option makes sense. (If you are ever in the position of writing mathematics, or teaching others to do so, please guide them away from such ambiguous notation.)

The expression looks ambiguous to me, but it might be because I am unaware of a certain agreement on how to interpret it. I made a simple experiment in Julia, a modern language for numerical computing.

julia> x=2
2

julia> 1/2x
0.25


So obviously, in Julia there is a built-in rule saying that multiplication binds stronger than division, i.e. 1/2x=1/(2x). This could be based on an agreement in engineering and scientific computing fields.