Explain closure properties of rational numbers and irrational results from rational/irrational sums and products.
Classify the product of two rational numbers as rational or irrational
Problem
Is \((2/3)(9/5)\) rational or irrational?
Big Picture
What this problem is really about
The product of two rational numbers remains rational by closure, whether or not it is an integer. We’ll classify each factor from its integer-ratio form, multiply numerators and denominators, reduce the result, and verify that the final denominator is nonzero.
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