Pair a dice

There are 14 ways that the six sided die could be bigger than the four sided die, and 6 ways that the four sided die could be bigger than the six sided die, out of a total of 24 possible outcomes.

And, there is a 50% chance that the four sided die was rolled first and a 50% chance that the six sided die was rolled first.

So, the probability is given by:

$P = \frac{1}{2} \cdot \frac{6}{24} + \frac{1}{2} \cdot \frac{14}{24} = \frac{20}{48} = \frac{5}{12}$

$5 + 12 = \boxed{17}$

There is a 5/6 chance that the rolls are different (assume to see this that the 4 sided is rolled first). The chance of the second roll being higher is half of this as the order is random.