Yes. Rational numbers are numbers that can be written as a fraction. Irrational Numbers cannot be expressed as a fraction.
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No, never.
The way in which the binary functions, addition and multiplication, are defined on the set of rational numbers ensures that the set is closed under these two operations.
Yes. In fact, a rational plus or minus an irrational will always be irrational.
Yes.
Since the sum of two rational numbers is rational, the answer will be the same as for the sum of an irrational and a single rational number. It is always irrational.