That's correct.For example if i am using Z7, then first and foremost are the following correct?

-25 = 3

23 = 2

By definition, , so the problem is to find the reciprocal of 2 in . It is easy to see that because . In general, reciprocals can be found using Bézout's identity.Then if i need to simplify 1/2 and 37/2 in Z7, then do i proceed the same? Im just wondering if the numbers have to be integers to use modulo?