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Q: Should the quotient of an integer divided by nonzero integer always be a rational number?

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Any integer divided by a non-zero integer is rational.

Any fraction p/q where p is an integer and q is a non-zero integer is rational.

No. Division by 0 is not permitted.

2

anything (except zero) divided by zero is infinityzero divided by zero is undefined (there are ways to get definite answers for this using calculus in some cases)

Related questions

Any integer divided by a non-zero integer is rational.

Yes.

Yes, it is.

Because that is how a rational number is defined!

Because that is how a rational number is defined!

Yes, always. That is the definition of a rational number.

I had this name question for homework :| no

No.

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).

No.

Usually not.

Yes, as long as the two nonzero numbers are themselves rational. (Since a rational number is any number that can be expressed as the quotient of two rational numbers, or any number that can be written as a fraction using only rational numbers.) If one of the nonzero numbers is not rational, the quotient will most likely be irrational.

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