Dicey Coordinates :P

The equation $|x| + |y| =3$ is just a square with vertices at $3$ and $-3$ on the $x$ and $y$ axes. Since we are dealing with dice, the coordinates must both be positive. That gives us only three possible coordinates: $(1,1)$ , $(1,2)$ and $(2,1)$ . There is only one way to roll each of these coordinates, so our final fraction is $\frac {3}{36}$ where $3$ is the number of possible coordinates that lie inside our region, and $36$ is the number of total possible coordinates. Finally, we simplify our fraction since the numerator and denominator of our fraction must be co-prime. The result should be $\frac {1}{12}$ . $1 + 12 = 13$ . So our answer is $\boxed{13}$