The product of any rational number and one is_
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The product of any rational number and any irrational number will always be an irrational number. This allows us to quickly conclude that 3π is irrational.
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Two rationals is the same as adding two such fractions, which will result in another fraction of this same form since integers are closed under addition and multiplication. Thus, adding two rational numbers produces another rational number. "The product of two rational numbers is rational."
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