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

Updated: 4/28/2022 Wiki User

12y ago

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. Wiki User

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Q: Is the quotient of two nonzero numbers always a rational number?
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No.

### Is the quotient of an integer divided by a nonzero integer always be a rational number Why?

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

Yes, it is.

Yes.

### Is a quotient of an integer divided by a nonzero integer always a rational number?

Because that is how a rational number is defined!

### Why is the quotient of an integer divided by a nonzero integer always a rational number?

Because that is how a rational number is defined!

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

Yes, by definition.

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

I had this name question for homework :| no

yes

### What if two rational numbers are divided is the quotient always going to be a rational number?

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

### Why the product of nonzero rational number and a rational number is an irrational?

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)

### Is a rational number divided by an irrational number always irrational?

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.