yes, 82 is rational. Rational numbers are numbers that can be written as a fraction. Irrational Numbers cannot be expressed as a fraction.
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No.
82 is an integer and not a fraction. It therefore makes little, if any, sense to write it as a mixed number. However, if you must, it can be expressed in rational form as 82/1.
No, it is rational.
It is rational. It is rational. It is rational. It is rational.
"Rational" is an adjective and so there cannot be "a rational" (and certainly not "an rational"). Any answer would depend on whether the question was about a rational number, a rational person, a rational argument or "a rational" combined with some other noun.