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

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yes

yes say you have 5 divided by 2 you get 2.5 or even 5 divided by 7 you get 0.714257142857 which is still rational.

Yes

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

Because that is how a rational number is defined!

Yes.

Yes, it is.

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.

Yes, that's true. * * * * * Unless the second number is 0, in which case the quotient is not defined!

Yes, that is how a rational number is defined.

Yes, by definition.

In general, no. It is possible though. (2pi)/pi is rational. pi2/pi is irrational. The ratio of two rationals numbers is always rational and the ratio of a rational and an irrational is always irrational.

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