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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.

Q: Is the quotient of two nonzero numbers always a rational number?

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A rational number is always the result of dividing an integer when the divisor is nonzero.

Yes, a rational number is a real number. A rational number is a number that can be written as the quotient of two integers, a/b, where b does not equal 0. Integers are real numbers. The quotient of two real numbers is always a real number. The terms "rational" and "irrational" apply to the real numbers. There is no corresponding concept for any other types of numbers.

A real number is any number so yes it is always a real number * * * * * Except if the second number is 0, in which case the quotient is not defined.

The product of an irrational number and a rational number, both nonzero, is always irrational

All integers are rational numbers, but not all rational numbers are integers.2/1 = 2 is an integer1/2 is not an integerRational numbers are sometimesintegers.

Related questions

No.

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

Yes, it is.

Yes.

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

yes

Not if the second rational number is 0: in that case the quotient is not defined. Otherwise the answer is 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)

No. If we let x be irrational, then 0/x = 0 is a counterexample. However, if we consider nonzero rational numbers, then our conjecture is true. We shall prove this by contradiction. Suppose we have nonzero rational numbers x and y, and an irrational number z, such that x/z = y. Since z is not equal to 0, x = yz. Since y is not equal to 0, x/y = z. Since x/y is a quotient of rational numbers, x/y is rational. Therefore, z is rational, contradicting our assumption that z was irrational. QED.