What set/sets of real numbers does - 54/19 belong to?

That is a rational number since you can write it as a ratio (=fraction).

The fraction - 54/19 is a rational number, so it belongs to the set of rational numbers. It's a rational number because it is a ratio of two integers. An integer is a positive or negative whole number. The value 0 is also included in the set of integers; however, the denominator cannot be 0.