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Question 34801: Reduced Rational Form

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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R0068-34801 · q-20260920-rational-reduced-form-0001

Original question and givens

Reduce 0/12 to an exact lowest-terms form with a positive denominator.

  • G001 — Reduce 0/12 to an exact lowest-terms form 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.

Step-by-step derivation

S001 · implies

Before

source roles = [qf-rational-reduced-form, [p, q]]

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.

Step identifiers and dependencies

Rule: R68_BANK_specific_keys_operations_and_numeric_guards · Uses: G001

S002 · implies

Before

source roles = [0, 12]

After

derived = [0/1]

Conditions: none

With nonzero denominator,a zero numerator represents0.THIS reduced-form protocol uses0/1,unlike sign-only0/|q|.

Step identifiers and dependencies

Rule: Rational_REDUCED_zero_CANONICAL0over1 · Uses: G001, S001

Reverse checks

  • S002 · 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.
  • 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.

Result

0/1

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.

Source hashes and review receipts
  • input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
  • original question SHA-256: 953d3d6c88aea7d946f393787a5a60734c1cc485f85beaa733711a6a9f1951da
  • candidate record SHA-256: 9591e4bebc489a814ada43bdfa946595a23e3d1c88431665838728d3a7fbce76
  • semantic review receipt SHA-256: e7a54104fa02c235f7591329bd6db8d626dd74bf0fae29c557b1f269c85066ed
  • question-first witness SHA-256: 8401a3c2064c1275a6a7ea8f00412fa12286cec7b2db6c305ff9dba3724ae229
  • Lean: NOT_RUN · human review: NOT_PERFORMED
Same-source full JSON