Question 6451: Exact Ordered Rational Sum and Difference

Original question and givens

Exact rational representations have nonzero denominators; a=1/-2, b=1/3. 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=1/-2, b=1/3. 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=[1, -2];raw b=[1, 3]

a=-1/2;b=1/3

rational sum := sum(-1/2, 1/3)

rational sum = -1/6

rational ordered difference := sub(-1/2, 1/3)

rational ordered difference = -5/6

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

(-1/6, -5/6)

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.