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Q: Is the quotion of any two nonzero integers is a rational number true?

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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).

Yes.

Actually the product of a nonzero rational number and another rational number will always be rational.The product of a nonzero rational number and an IRrational number will always be irrational. (You have to include the "nonzero" caveat because zero times an irrational number is zero, which is rational)

of course

yes, as it can be expressed as the quotient of two (nonzero) integers (for example, 875 divided by 1000)

All integers are rational numbers.

It is always irrational.

It is irrational.

Integers are aproper subset of rational numbers.

An irrational number.

It is an irrational number.

Yes.

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