Use legal integer fraction representations with nonzero original denominators; negative denominators are allowed. Representation and value remain distinct. a=-1/-2, b=1/3. The naive candidate adds the original numerators and original denominators separately, before reduction. Give (true sum, is naive addition defined?, naive value or undefined, naive−true defect or undefined, is naive addition correct?).
G001 — Use legal integer fraction representations with nonzero original denominators; negative denominators are allowed. Representation and value remain distinct. a=-1/-2, b=1/3. The naive candidate adds the original numerators and original denominators separately, before reduction. Give (true sum, is naive addition defined?, naive value or undefined, naive−true defect or undefined, is naive addition correct?).
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.
raw numerator sum=0;raw denominator sum=1;true sum=5/6
After
naive defined=Yes;naive=0/1;correct=No
Conditions: none
Adding numerators and denominators separately is not fraction addition.Prior reduction may change the specified WRONG algorithm,so retain raw representations.An undefined candidate is not correct even when the true sum is0.
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 naive minus true sum with exact rational arithmetic, not rounded decimals.
S005 · premise_and_result_audit — Recompute defined naive fraction candidate with exact rational arithmetic, not rounded decimals.
S004 · premise_and_result_audit — Recompute naive raw denominator sum with exact rational arithmetic, not rounded decimals.
S003 · premise_and_result_audit — Recompute naive raw numerator sum with exact rational arithmetic, not rounded decimals.
S002 · premise_and_result_audit — Recompute true 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
(5/6, Yes, 0/1, -5/6, No)
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.