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R0068-34791 · q-20260920-rational-equivalent-fractions-0016
The denominators q=2 and s=4 are nonzero. Are 4/2 and 9/4 equivalent?
G001 — The denominators q=2 and s=4 are nonzero. Are 4/2 and 9/4 equivalent?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-rational-equivalent-fractions, [p, q, r, s]]
After
derived = [BASE-no-required-operation, 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
Rational equivalence ORIGINAL p times s := mul(4, 4)
After
Rational equivalence ORIGINAL p times s = 16
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
Rational equivalence ORIGINAL r times q := mul(9, 2)
After
Rational equivalence ORIGINAL r times q = 18
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, S002
Before
source roles = [4, 2, 9, 4]
After
derived = [16, 18, No]
Conditions: none
FIRST qualify BOTH nonzero denominators,THEN compare p*s=r*q.Negative denominators are allowed for EQUATIONS,unlike order-direction issues.Do not compare decimal appearance or accept0=0 with an undefined ratio.
Rule: Rational_EQUIVALENCE_crossmultiply_ONLY_nonzero_denominators · Uses: G001, S003
S004 · 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.S003 · premise_and_result_audit — Recompute Rational equivalence ORIGINAL r times q with exact rational arithmetic, not rounded decimals.S002 · premise_and_result_audit — Recompute Rational equivalence ORIGINAL p times s 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.No
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: aacca76ad352f9e8b9554bddc3fed177ba4e56ea484bd467786040824bcf7bb4candidate record SHA-256: fdf2f506d3ff246c1b53a160ce0ebe9e26060e4b2a89e45de376f9579ff646ebsemantic review receipt SHA-256: e7a54104fa02c235f7591329bd6db8d626dd74bf0fae29c557b1f269c85066edquestion-first witness SHA-256: 8401a3c2064c1275a6a7ea8f00412fa12286cec7b2db6c305ff9dba3724ae229Lean: NOT_RUN · human review: NOT_PERFORMED