Question

Is the difference between two rational numbers always as rational number?

Answer 1

Yes, the difference of rationals is always a rational.

Consider a/b - c/d, where a, b, c, d are integers with bd≠0.

The difference can be written as

... a/b - c/d = (ad - bc)/(bd)

where each product of integers is also an integer, hence this expression is rational.