Use legal integer fraction representations with nonzero original denominators; negative denominators are allowed. Representation and value remain distinct. Four ordered values=[1/-3, 0/1, 1/2, 12/2]. Give (three following-minus-previous differences, their sum, last−first, are those last two results equal?); do not sort.
G001 — Use legal integer fraction representations with nonzero original denominators; negative denominators are allowed. Representation and value remain distinct. Four ordered values=[1/-3, 0/1, 1/2, 12/2]. Give (three following-minus-previous differences, their sum, last−first, are those last two results equal?); do not sort.
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.
original integer numerator/denominator representations;original denominators nonzero
After
representation and rational value are distinct data
Conditions: none
Negative denominators are valid,but reduced values do not replace original representations.Candidate algorithms about raw numerators/denominators must use those raw data.This finite audit is not a general proof of quotient well-definedness.
S007 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
S006 · premise_and_result_audit — Recompute direct final minus initial with exact rational arithmetic, not rounded decimals.
S005 · premise_and_result_audit — Recompute adjacent difference chain sum with exact rational arithmetic, not rounded decimals.
S004 · premise_and_result_audit — Recompute ordered adjacent difference2 with exact rational arithmetic, not rounded decimals.
S003 · premise_and_result_audit — Recompute ordered adjacent difference1 with exact rational arithmetic, not rounded decimals.
S002 · premise_and_result_audit — Recompute ordered adjacent difference0 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
([1/3, 1/2, 11/2], 19/3, 19/3, Yes)
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.