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 \(0.25~+~7/10\) rational or irrational?
Big Picture
What this problem is really about
Numbers expressible as integer ratios remain in that class when added. We’ll rewrite the terminating decimal as a fraction, place both fractions over a common denominator, and observe that their sum is still a quotient of integers with nonzero denominator. This closure argument determines the classification without relying only on the decimal appearance.
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