Is the ratio of two natural numbers always a positive?

No.Natural numbers by definition are whole: integers. However, if the numerator cannot be divided evenly by the denominator, or even if the numerator is less than the denominator, then it is impossible for such a ratio to result in an integer. Such ratiOS cannot simplify into natural numbers.

(Note: This assumes that 0 is not a natural number--there is a disagreement over its membership. If 0 is considered a natural number, than any ratio with a 0 in the numerator but anything else in the denominator results in 0. A ratio with a nonzero numerator and a zero denominator is undefined. A 0/0 ratio is considered an indeterminate form and goes into calculus).