The product of two rational numbers is always a rational number.
If a, b, c, and d are integers, b and d not zero, then
(a/b)*(c/d) = (ac)/(bd)
The set of integers is closed for multiplication (any product of integers is an integer), so any product of rationals will be rational.
If a, b, c, and d are integers, b and d not zero, then
(a/b)*(c/d) = (ac)/(bd)
The set of integers is closed for multiplication (any product of integers is an integer), so any product of rationals will be rational.