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.

No, they are not because fractions can be negative also. fractions aren't integers

All integers are rational numbers.

It is an irrational number.

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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)

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

of course

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.

It is always irrational.

No, they are not because fractions can be negative also. fractions aren't integers

It is irrational.

All integers are rational numbers.

An irrational number.

It is an irrational number.