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If pi is irrational does that mean that pi divided by 2 is irrational?
Yes, it does. If Pi/2 were rational, it could be written as p/q, and then Pi could be written as 2p/q and would be rational as well.
Can the quotient of two irrational numbers be rational?
Yes. 2*pi is irrational, pi is irrational, but their quotient is 2pi/pi = 2: not only rational, but integer.
Is 2 pi a rational number?
No, since Pi is an irrational number, 2(pi) would still be irrational.
Is pi divided by e rational?
A rational number is able to be represented as a ratio of polynomials. pi/e is a ratio of irrational numbers, neither of which can be represented as a ratio of polynomials, and so I would conclude that pi/e is not rational. But it's a good question, because what if two irrational numbers could cancel out their irrationality, like two negative numbers! A quotient of two irrational numbers can be a rational number. Trivial example 2pi/pi = 2.
What is an irrational number that is also rational?
Numbers are either irrational (like the square root of 2 or pi) or rational (can be stated as a fraction using whole numbers). Irrational numbers are never rational.
