TITLE: What does the modulo of a non-integer mean?
QUESTION [5 upvotes]: For example, in the equation
$ x=\frac{3}{5} \bmod 11$
The value of $x$ is $5$ according to wolfram alpha. I know how to manipulate the equation to to get the value but I dont understand what the modulo of a non-integer means.

REPLY [5 votes]: The notation is ambiguous and requires context to interpret.
Additively $x=11n+\frac 35$ - the language of modulus is used in this way often with trigonometric functions mod $\pi$ or mod $2\pi$ and in similar contexts.
Multiplicatively it can be equivalent to $5x\equiv 3 \mod 11$.
In the absence of other information, with $11$ being prime, the most obvious interpretation would be the second, assuming that the context would be integer arithmetic modulo $11$, and noting that division is the inverse of multiplication, so the multiplicative interpretation is likely.