# Question 34829: Valid Rational Representation

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This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth.

R0068-34829 · q-20260920-rational-valid-representation-0004



## Original question and givens

Both p=-9 and q=4 are explicitly integers. Is p/q a valid rational-number representation?


- G001 — Both p=-9 and q=4 are explicitly integers. Is p/q a valid rational-number representation?





## 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.


- [mko-rational-number](https://ocme.evemisslab.com/en/mko/mko-rational-number/)





## Step-by-step derivation

S001 · impliesBefore

source roles = [qf-rational-valid-representation, [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 dependenciesRule: R68_BANK_specific_keys_operations_and_numeric_guards · Uses: G001





S002 · impliesBefore

source roles = [-9, 4]

After

derived = [Yes]

Conditions: none

A rational representation needs INTEGER p,q and q≠0.Zero denominator is a LEGAL No,including0/0.This branch does NOT divide or fabricate a numeric value.

Step identifiers and dependenciesRule: Rational_RAW_integer_pair_NONzero_DEN_before_any_division · 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

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.

Source hashes and review receipts
- input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
- original question SHA-256: e663227dcfe94b1e50cd0582bda5819a408db246f8de6c8687eb1e38286ab450
- candidate record SHA-256: 53be94b2f717cb010cb6f71748a6a943eb7a29fc8a5288c45308f46f3d27cbe5
- semantic review receipt SHA-256: e7a54104fa02c235f7591329bd6db8d626dd74bf0fae29c557b1f269c85066ed
- question-first witness SHA-256: 8401a3c2064c1275a6a7ea8f00412fa12286cec7b2db6c305ff9dba3724ae229
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20260920-rational-valid-representation-0004.json)