How many different numbers can you roll with a one dot cue What fraction of those numbers are less than 3?

Assuming you mean a standard die and not a cube with one dot on it; it has six sides, each with a different number (1-6) on it, so there are six possible outcomes, ie 6 different numbers that can be obtained with one roll of it.

Of these the two numbers "1" and "2" are less than 3, so the fraction less than 3 are:

wanted_outcomes/total_possible_outcomes = 2/6 = 1/3