Notation for a fraction of $n!$

Question

Suppose I want to write $n!/2$, can I just write $\tfrac{1}{2}n!$ or is that easily confused with $(\tfrac{1}{2}n)!$ and I have to write $\tfrac{1}{2}(n!)$?

Are there precedence rules for these situations (like we have in Computer Programming languages C/C++/Python ...)?

Answer 1

It is a Common Convention that $n!$ is always taken together.

Compare $\sum n!$ , it is $\sum (n!)$ , not $(\sum n)!$

Compare $\log n!$ , it is $\log (n!)$ , not $(\log n)!$

Likewise $mn!$ is $m(n!)$ , not $(mn)!$

Thus $\frac12n!$ is $\frac12(n!)$ , not $(\frac12n)!$

When we want the other way , we have to use the Brackets.
When Context is weird , always use Brackets to aid the readers.

ADDENDUM :

Checked with Wolfram , which agrees with this Convention :

We can see that Wolfram is not taking $3n!$ to mean $(3n)!$ , where $n=2$ will not work.
Wolfram took $3n!$ to mean $3(n!)$ , where $n=2$ will work.

Answer 2

We have precedences rules stating that e.g. multiplication must be evaluated before addition, so $1+2*3$ has a unique meaning. Commonly $!$ is assigned a precedence like all other unary operators, i.e. $\frac12n!$ means $\frac12(n!)$.