Yes, but only if the second integer is not zero.
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The quotient of two nonzero integers is the definition of a rational number. There are nonzero numbers other than integers (imaginary, rational non-integers) that the quotient of would not be a rational number. If the two nonzero numbers are rational themselves, then the quotient will be rational. (For example, 4 divided by 2 is 2: all of those numbers are rational).
It is an incomplete definition of a rational number.
Yes.
If a number can be expressed as the quotient of two numbers (a ÷ b) and b is not zero, then it is a rational number.
The definition of a rational number is the quotient of any two nonzero integers.