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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.
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Is the product of a nonzero rational number and an irrational number rational or irrational?
It is always irrational.
Is the product of a rational number and an irrational number rational or irrational?
Such a product is always irrational - unless the rational number happens to be zero.
Why is 4 divided by 9 an irrational number?
0.4444
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)
Can an irrational number divided by an irrational number equals an irrational number?
Yes, an irrational number divided by an irrational number will usually be an irrational number, but not always. For example, pi / (3pi) is 1/3, which is a rational number, but pi/e is an irrational number.
