Cuantas fracciones son propias e irreductibles y tienen como denominador al 30?

There are 8 proper fractions with a denominator of 30 that are irreducible:

1/30, 7/30, 11/30, 13/30, 17/30, 19/30, 23/30, 29/30

We cannot count any even numerators, as 30 is even and would therefore make the fraction reducible.

We cannot count any numerators that are a multiple of 3, as it is a factor of 30.  Likewise we cannot count any numerators that are a multiple of 5.