Undefined: You cannot divide by zero
Yes, it is.
Yes.
Yes, always. That is the definition of a rational number.
Because that is how a rational number is defined!
Because that is how a rational number is defined!
Yes, by definition.
I had this name question for homework :| 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).
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.
== == The fact is - any nonzero number raised to 0 is always 1. the reason is: suppose a is nonzero. Then by the quotient rule of indices, am/an = am - n Taking m = n we come up with am - m = am/am , which is 1 in view of a nonzero.
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)
Yes.