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R0068-34731 · q-20260930-r02-ratio-exact-value-0006
In the rational numerical-ratio setting, find the exact value of -7:(-6). The consequent is nonzero; answer as a reduced p/q with a positive denominator.
G001 — In the rational numerical-ratio setting, find the exact value of -7:(-6). The consequent is nonzero; answer as a reduced p/q with a positive denominator.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.
Before
source roles = [qf-ratio-exact-value, [a, b, operation]]
After
derived = [ratio_value, no-invented-domain]
Conditions: none
Separate source banks:legacy RAW SAFE with unbounded derived BigInts versus BASE Number.isInteger without invented SAFE/million caps.Operations,domains and permissive/exact keys follow THIS bank.Keep ORIGINAL JSON intact.
Rule: R68_BANK_specific_keys_operations_and_numeric_guards · Uses: G001
Before
Ratio ORIGINAL antecedent divided by NONzero consequent := div(-7, -6)
After
Ratio ORIGINAL antecedent divided by NONzero consequent = 7/6
Conditions: none
Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer.
Rule: exact_rational_arithmetic · Uses: G001, S001
Before
source roles = [-7, -6]
After
derived = [7/6]
Conditions: none
The ORDERED numerical ratio a:b is a/b,FIRST requiring b≠0.Negative inputs are allowed;reduce by gcd and make the denominator positive,RETAINING/1 for integers.Do not invert the ratio or infer arbitrary dimensional division.
Rule: Ratio_ORDERED_numerical_ratio_reduced_positive_denominator · Uses: G001, S002
S003 · premise_and_result_audit — Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof.S002 · premise_and_result_audit — Recompute Ratio ORIGINAL antecedent divided by NONzero consequent with exact rational arithmetic, not rounded decimals.S001 · premise_and_result_audit — Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof.7/6
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
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.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 74cb8ec276233f8b60bc2c9061076f887890e47c4c3f80fd52d20e320b34bc8acandidate record SHA-256: 941e791e748537d2ada54b76966b4f426c475959a9ad13fc9008b3dbb5a66f33semantic review receipt SHA-256: e7a54104fa02c235f7591329bd6db8d626dd74bf0fae29c557b1f269c85066edquestion-first witness SHA-256: 8401a3c2064c1275a6a7ea8f00412fa12286cec7b2db6c305ff9dba3724ae229Lean: NOT_RUN · human review: NOT_PERFORMED