Solve the rational proportion 12/(4)=x/(-6). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.
G001 — Solve the rational proportion 12/(4)=x/(-6). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.
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.
Proportion missing ORIGINAL a times d := mul(12, -6)
After
Proportion missing ORIGINAL a times d = -72
Conditions: none
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.
Proportion missing ORIGINAL ad divided by nonzero b := div(-72, 4)
After
Proportion missing ORIGINAL ad divided by nonzero b = -18
Conditions: none
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.
Proportion missing ORIGINAL solved x divided by nonzero d := div(-18, -6)
After
Proportion missing ORIGINAL solved x divided by nonzero d = 3
Conditions: none
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.
From a/b=x/d,FIRST require b,d≠0.Cross-multiply to bx=ad and divide by b for the UNIQUE x=ad/b.Substitute back into x/d=a/b.Reduce the result with positive denominator and RETAIN/1 for integers;do not alter original negative denominators.
S005 · 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.
S004 · premise_and_result_audit — Recompute Proportion missing ORIGINAL solved x divided by nonzero d with exact rational arithmetic, not rounded decimals.
S003 · premise_and_result_audit — Recompute Proportion missing ORIGINAL ad divided by nonzero b with exact rational arithmetic, not rounded decimals.
S002 · premise_and_result_audit — Recompute Proportion missing 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
-18/1
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.