Explain closure properties of rational numbers and irrational results from rational/irrational sums and products.
Classify the sum of two rational numbers as rational
Problem
Is \(1/3~+~5/6\) rational or irrational?
Big Picture
What this problem is really about
Rational numbers are closed under addition, so classification can be established before arithmetic. We’ll identify both addends as integer ratios with nonzero denominators, invoke closure, compute a common-denominator sum, and use its fraction form as a direct check.
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