Under the usual real order, compare (7)/3 and (7)/3. Both denominators are positive. Give <, =, or > in that order.
G001 — Under the usual real order, compare (7)/3 and (7)/3. Both denominators are positive. Give <, =, or > in that order.
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.
Order ORIGINAL first numerator times second positive denominator := mul(7, 3)
After
Order ORIGINAL first numerator times second positive denominator = 21
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.
Order ORIGINAL second numerator times first positive denominator := mul(7, 3)
After
Order ORIGINAL second numerator times first positive denominator = 21
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.
Both denominators are POSITIVE,so multiplying by q*s preserves direction.Compare p*s with r*q.Equality includes unreduced equivalent fractions.Derived cross products are not recapped at RAW SAFE.
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 Order ORIGINAL second numerator times first positive denominator with exact rational arithmetic, not rounded decimals.
S002 · premise_and_result_audit — Recompute Order ORIGINAL first numerator times second positive denominator 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
=
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.