Question 7026: Forward Ratio and Independent Reverse Guard

Original question and givens

Use exact numeric ratios in Q; the second component must be nonzero. A zero cross-product defect cannot legalize a zero second component. a=0, b=-5≠0. Give (a/b, is the reverse ratio legal?, b/a or undefined, forward*reverse or undefined).

• G001 — Use exact numeric ratios in Q; the second component must be nonzero. A zero cross-product defect cannot legalize a zero second component. a=0, b=-5≠0. Give (a/b, is the reverse ratio legal?, b/a or undefined, forward*reverse or undefined).

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-ratio-proportion

Step-by-step derivation

exact rational numerical ratios;each denominator needs its own guard

cross-multiplied equality does not legalize a zero ratio denominator

forward ratio a/b := div(0, -5)

forward ratio a/b = 0

a=0;b=-5;forward=0/1

reverse defined=No;reverse=undefined

Reverse checks

• S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S002 · premise_and_result_audit — Recompute forward ratio a/b 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

(0/1, No, undefined, undefined)

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.