Yes. Both the additive inverse and the multiplicative inverse would be irrational in this case. For example, if a and b are integers, a/b is rational by definition; in this case, b/a would also be rational, being the ratio of two integers.
An irrational number is a real number that cannot be expressed as a ratio of two integers, x and y, where y>0. In 1761, Johann Heinrich Lambert proved that pi is irrational. His proof and...
The rational numbers form a field. In particular, the sum or difference of two rational numbers is rational. (This is easy to check directly). Suppose now that a + b = c, with a rational and c...