Question 6463: Exact Ordered Rational Sum and Difference

Original question and givens

Exact rational representations have nonzero denominators; a=0/1, b=13/5. Negative input denominators are allowed. Give (a+b, a−b). Use exact reduced fractions with positive denominators, retaining /1 for integers.

• G001 — Exact rational representations have nonzero denominators; a=0/1, b=13/5. Negative input denominators are allowed. Give (a+b, a−b). Use exact reduced fractions with positive denominators, retaining /1 for integers.

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-rational-number

Step-by-step derivation

raw a=[0, 1];raw b=[13, 5]

a=0/1;b=13/5

rational sum := sum(0, 13/5)

rational sum = 13/5

rational ordered difference := sub(0, 13/5)

rational ordered difference = -13/5

Reverse checks

• S003 · premise_and_result_audit — Recompute rational ordered difference with exact rational arithmetic, not rounded decimals.
• S002 · premise_and_result_audit — Recompute rational sum with exact rational arithmetic, not rounded decimals.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

(13/5, -13/5)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.