In the rational numerical-ratio setting, is -6:(-7)=-18:(-21) a valid proportion? Both consequents are nonzero.
G001 — In the rational numerical-ratio setting, is -6:(-7)=-18:(-21) a valid proportion? Both consequents are nonzero.
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.
Check THIS bank’s keys/operation/domain:legacy table underscores,MOD50 local hyphens;permissive BASE data acquires no unknown-field restriction.Keep Number.isInteger and SAFE source guards distinct,while preserving ORIGINAL JSON number representations.
Calculate exactly from ORIGINAL ordered operands.Legacy derived integers are not recapped at the RAW SAFE bound;MOD50 rationals separately retain the NAIVE pre-reduction source envelope.
Calculate exactly from ORIGINAL ordered operands.Legacy derived integers are not recapped at the RAW SAFE bound;MOD50 rationals separately retain the NAIVE pre-reduction source envelope.
FIRST require nonzero b,d.Then a/b=c/d IFF ad=cb.Negative denominators are allowed;equation equivalence survives multiplication by a nonzero number.Never certify undefined ratios using0=0 with zero denominators.
S004 · premise_and_result_audit — Reverse-audit THIS step against the ORIGINAL roles,complete premises and field order.Distinguish implication from equivalence;preserve originals,English,MKOs,ASTs and review states.Finite checks are not independent review or general formal proof.
S003 · premise_and_result_audit — Recompute Proportion ORIGINAL c times b with exact rational arithmetic, not rounded decimals.
S002 · premise_and_result_audit — Recompute Proportion ORIGINAL a times d with exact rational arithmetic, not rounded decimals.
S001 · premise_and_result_audit — Reverse-audit THIS step against the ORIGINAL roles,complete premises and field order.Distinguish implication from equivalence;preserve originals,English,MKOs,ASTs and review states.Finite checks are not independent review or general formal proof.
Result
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.