Thread: How do i deal with fractions when using Modulo?

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

-25 = 3

23 = 2

(just want to check im using modulo ok)

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?

At the minute i am thinkin that:

1/2 = 1/2 and
37/2 = 9/2

are these correct?

Thanks :-)

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

-25 = 3

23 = 2

That's correct.

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?

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.

Ah i see, so in this case would i find that:

1/2 = 4

and

37/2 = 1

?

Yes.