Can someone explain modulo with fractions?

[maxfails]

so apparently 3^-1 mod 5 = 2 so (1/3) mod 5 = 2
I don't get how this works, can someone explain?

 

[CRGreathouse]

so apparently 3^-1 mod 5 = 2 so (1/3) mod 5 = 2
I don't get how this works, can someone explain?

Sure.

In the rational numbers, 1/3 represents the solution to 3 * x = 1. For integers mod 5, we mean the same thing: 3 * x = 1 mod 5. But you can see that 3 * 2 = 1 mod 5, so 3^-1 is just 2.

 

[qntty]

If gcd(a,m) = 1 and ab = 1 (mod m) then b = 1/a (mod m). If you want to find what integer b is congruent to modulo m and you only know a, then you can first use the euclidean algorithm to find it.

 

[Edgardo]

Hi maxfails,

look up "modular inverse" (see Wiki article and Wolfram article).
There is also an older thread here