Explain closure properties of rational numbers and irrational results from rational/irrational sums and products.
Classify always, sometimes, or never statements about rational and irrational sums and products
Problem
Is this statement always, sometimes, or never true? "The sum of \(\text{two}~\text{rational}~\text{numbers}\) is rational."
Big Picture
What this problem is really about
An always statement needs a proof for arbitrary inputs, not a handful of examples. We’ll represent two rational numbers as integer ratios, add them with a common denominator, prove the new numerator is integral and denominator nonzero, and use that construction to establish closure for every pair.
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