{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0001","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ee6667b28414d090c6c2b883b3ac3e36bad999499967d70aa994a823b7727041","family_id":"qf-rational-valid-representation","seed":20260921,"semantic_template":"qf-rational-valid-representation/{\"p\":-12,\"q\":0}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=-12 and q=0 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"q=0, so the denominator is zero and no ordinary rational value is defined."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0002","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9c50590cec6ef406427fc1b4807a289546d50a9fff7bb5f085482aea725430f9","family_id":"qf-rational-valid-representation","seed":20260922,"semantic_template":"qf-rational-valid-representation/{\"p\":-11,\"q\":2}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=-11 and q=2 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=2≠0, so -11/2 is a valid representation."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0003","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"416e28143792fa8b9d00a232c5e3b2e71f3e7846e5959e24a0ee095540866d49","family_id":"qf-rational-valid-representation","seed":20260923,"semantic_template":"qf-rational-valid-representation/{\"p\":-10,\"q\":3}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=-10 and q=3 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=3≠0, so -10/3 is a valid representation."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0004","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e663227dcfe94b1e50cd0582bda5819a408db246f8de6c8687eb1e38286ab450","family_id":"qf-rational-valid-representation","seed":20260924,"semantic_template":"qf-rational-valid-representation/{\"p\":-9,\"q\":4}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=-9 and q=4 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=4≠0, so -9/4 is a valid representation."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0005","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"025d0ea2251961ace4a9c354149b36255ef24266fc9c0fe46d4165efaaa19864","family_id":"qf-rational-valid-representation","seed":20260925,"semantic_template":"qf-rational-valid-representation/{\"p\":-8,\"q\":5}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=-8 and q=5 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=5≠0, so -8/5 is a valid representation."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0006","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5b36841ecaf6c0af2583cab99129767803720c6dadf8eeb0faf8ffea077a8e0b","family_id":"qf-rational-valid-representation","seed":20260926,"semantic_template":"qf-rational-valid-representation/{\"p\":-7,\"q\":0}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=-7 and q=0 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"q=0, so the denominator is zero and no ordinary rational value is defined."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0007","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"884f8a81b4cd826ec86458c8466ef64485fb03daea8754e1dd7b1bf80393cffc","family_id":"qf-rational-valid-representation","seed":20260927,"semantic_template":"qf-rational-valid-representation/{\"p\":-6,\"q\":7}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=-6 and q=7 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=7≠0, so -6/7 is a valid representation."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0008","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"04c7757fd39c6c1131b6721d1c8b6fbf2df79bea7c1eaa9a4457946aed8b26a9","family_id":"qf-rational-valid-representation","seed":20260928,"semantic_template":"qf-rational-valid-representation/{\"p\":-5,\"q\":1}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=-5 and q=1 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=1≠0, so -5/1 is a valid representation."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0009","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"78292ee19b1897e88b90e2fcc1b0e0d4b92b8eb9dcb5c4c28e40ae0b5c8e491c","family_id":"qf-rational-valid-representation","seed":20260929,"semantic_template":"qf-rational-valid-representation/{\"p\":-4,\"q\":2}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=-4 and q=2 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=2≠0, so -4/2 is a valid representation."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0010","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d85db51d86c09fe22d5afc3a31c57fd1e3ee5718448c2e8951e3bcd9ac51dd26","family_id":"qf-rational-valid-representation","seed":20260930,"semantic_template":"qf-rational-valid-representation/{\"p\":-3,\"q\":3}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=-3 and q=3 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=3≠0, so -3/3 is a valid representation."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0011","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a302778b6691729f42b94ae8c6c047a9f3676b132e4b00490ced947cd22d04fc","family_id":"qf-rational-valid-representation","seed":20260931,"semantic_template":"qf-rational-valid-representation/{\"p\":-2,\"q\":0}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=-2 and q=0 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"q=0, so the denominator is zero and no ordinary rational value is defined."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0012","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d3cbd4fcc1fee6a1a8586ab59ad445fd74a578c05a4444e78c13d8cf700a01fe","family_id":"qf-rational-valid-representation","seed":20260932,"semantic_template":"qf-rational-valid-representation/{\"p\":-1,\"q\":5}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=-1 and q=5 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=5≠0, so -1/5 is a valid representation."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0013","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"60b05afee06d6570eb97ffc033e22af9fd7ae587296b8784f1c29766ff935965","family_id":"qf-rational-valid-representation","seed":20260933,"semantic_template":"qf-rational-valid-representation/{\"p\":0,\"q\":6}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=0 and q=6 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=6≠0, so 0/6 is a valid representation."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0014","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8d7c0a2be5c4cd1ac92f75f0318011f12b168a29c94a829d17173e29757c61ee","family_id":"qf-rational-valid-representation","seed":20260934,"semantic_template":"qf-rational-valid-representation/{\"p\":1,\"q\":7}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=1 and q=7 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=7≠0, so 1/7 is a valid representation."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0015","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e77861d0f946f78e3f2e7487f66821d747b20bfb5d7dd8e67a95e3cd03655f50","family_id":"qf-rational-valid-representation","seed":20260935,"semantic_template":"qf-rational-valid-representation/{\"p\":2,\"q\":1}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=2 and q=1 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=1≠0, so 2/1 is a valid representation."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0016","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7bb3038c1a02b886b6b2ff42bc290be5eeeafcab61e4cb96530d3d929b8bba9e","family_id":"qf-rational-valid-representation","seed":20260936,"semantic_template":"qf-rational-valid-representation/{\"p\":3,\"q\":0}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=3 and q=0 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"q=0, so the denominator is zero and no ordinary rational value is defined."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0017","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6a8428576b1b62574b0870e52aa56aa41190078a7fe7bd23378a2d6cfd906a79","family_id":"qf-rational-valid-representation","seed":20260937,"semantic_template":"qf-rational-valid-representation/{\"p\":4,\"q\":3}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=4 and q=3 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=3≠0, so 4/3 is a valid representation."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0018","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ece6f6cf497bab28fa6d151df1355c209badb394c2f075b11ba8f66caa93a172","family_id":"qf-rational-valid-representation","seed":20260938,"semantic_template":"qf-rational-valid-representation/{\"p\":5,\"q\":4}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=5 and q=4 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=4≠0, so 5/4 is a valid representation."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0019","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3183a5eb115b8bb549a571da4adeaa1f911d3ca062a34bbfefee86472b467f99","family_id":"qf-rational-valid-representation","seed":20260939,"semantic_template":"qf-rational-valid-representation/{\"p\":6,\"q\":5}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=6 and q=5 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=5≠0, so 6/5 is a valid representation."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0020","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7ef1bf3cb4c3ff76cd98b4dc010a2577cbfb063e6d13a756d80f782085b7f50b","family_id":"qf-rational-valid-representation","seed":20260940,"semantic_template":"qf-rational-valid-representation/{\"p\":7,\"q\":6}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=7 and q=6 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=6≠0, so 7/6 is a valid representation."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0021","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"596bfe64312e112c4c9e3ae57aef59fd9f0c534e7365ed21b06df0b3986df640","family_id":"qf-rational-valid-representation","seed":20260941,"semantic_template":"qf-rational-valid-representation/{\"p\":8,\"q\":0}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=8 and q=0 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"q=0, so the denominator is zero and no ordinary rational value is defined."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0022","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"730c87f74024a6bb6c4bff3081438ed635337d82002da42202a9095bee7b8eac","family_id":"qf-rational-valid-representation","seed":20260942,"semantic_template":"qf-rational-valid-representation/{\"p\":9,\"q\":1}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=9 and q=1 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=1≠0, so 9/1 is a valid representation."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0023","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5a9168cf26d581dd230fdf39d6cf8d8b55c2aeed7a77ea8c4758414737302ee6","family_id":"qf-rational-valid-representation","seed":20260943,"semantic_template":"qf-rational-valid-representation/{\"p\":10,\"q\":2}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=10 and q=2 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=2≠0, so 10/2 is a valid representation."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0024","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2472454b1d066a3592a1c9677e4c219b3e9718047740894e7e0d0406a64e80b5","family_id":"qf-rational-valid-representation","seed":20260944,"semantic_template":"qf-rational-valid-representation/{\"p\":11,\"q\":3}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=11 and q=3 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=3≠0, so 11/3 is a valid representation."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-valid-representation-0025","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eed596244711974dd329c3b95067d4b87ff927bcc181d0c313e752604a261f4e","family_id":"qf-rational-valid-representation","seed":20260945,"semantic_template":"qf-rational-valid-representation/{\"p\":12,\"q\":4}"},"fields":{"title":"Valid Rational Representation","stem":"Both p=12 and q=4 are explicitly integers. Is p/q a valid rational-number representation?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"q=4≠0, so 12/4 is a valid representation."},"skills":["rational representation","nonzero denominator"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0001","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2cac519981a99267c3c4e255da6bb040166cbe4877f732ed04d3ca8572e17278","family_id":"qf-rational-denominator-sign-normalization","seed":20261021,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":-12,\"q\":-1}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize -12/-1 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"12/1","explanation":"Because q=-1 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0002","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"24f9227834bd74dcc4531b394a091ed91d12d7e408d90eccdc4bf0cbbc4ebdbe","family_id":"qf-rational-denominator-sign-normalization","seed":20261022,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":-11,\"q\":-2}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize -11/-2 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"11/2","explanation":"Because q=-2 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0003","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f46eed9db301ebe448e9a8198d3965c758553cfbff7307f1a129cf6592ad12aa","family_id":"qf-rational-denominator-sign-normalization","seed":20261023,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":-10,\"q\":-3}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize -10/-3 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"10/3","explanation":"Because q=-3 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0004","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2499225c3053fc8931ce306b2fa2de817f1d143a63a2974eaaaf6eb4f2fe80ba","family_id":"qf-rational-denominator-sign-normalization","seed":20261024,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":-9,\"q\":-4}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize -9/-4 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"9/4","explanation":"Because q=-4 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0005","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"74b75ab20f33180a106c53aa0026f64a319b997343a5f5d8a829c989017b5ed8","family_id":"qf-rational-denominator-sign-normalization","seed":20261025,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":-8,\"q\":-5}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize -8/-5 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"8/5","explanation":"Because q=-5 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0006","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3897a33ca8b044b64cf4416f483a6852e646d2adb6c159bac63ce4b97e4ce8ae","family_id":"qf-rational-denominator-sign-normalization","seed":20261026,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":-7,\"q\":-6}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize -7/-6 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"7/6","explanation":"Because q=-6 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0007","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"81464f1e5d66b62c512c5c6ee36286704beaaefde66d309b06d0ccb2626fafc9","family_id":"qf-rational-denominator-sign-normalization","seed":20261027,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":-6,\"q\":-7}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize -6/-7 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"6/7","explanation":"Because q=-7 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0008","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a56697e791cda91beb7a69f5841d2492358f6128da811b8703b3fad45aea48e9","family_id":"qf-rational-denominator-sign-normalization","seed":20261028,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":-5,\"q\":-8}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize -5/-8 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"5/8","explanation":"Because q=-8 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0009","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"aad7ade3b4d2d8cc49c7bb944a72b8490944320220d7e461a59f77244ede48c7","family_id":"qf-rational-denominator-sign-normalization","seed":20261029,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":-4,\"q\":-9}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize -4/-9 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"4/9","explanation":"Because q=-9 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0010","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9d406143bbdccf159d3fba6ee1e998585ba4d98fc307a896d1057395fb862a16","family_id":"qf-rational-denominator-sign-normalization","seed":20261030,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":-3,\"q\":-1}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize -3/-1 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"3/1","explanation":"Because q=-1 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0011","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"019afebda4807d7b2d9ac308065233e7b3fcdd76d24bdf0939bc939de6581ee9","family_id":"qf-rational-denominator-sign-normalization","seed":20261031,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":-2,\"q\":-2}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize -2/-2 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"2/2","explanation":"Because q=-2 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0012","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"70db39ddcf71820cea9be5934a8442ebbbc51554c5772ed6164dd5787667cf26","family_id":"qf-rational-denominator-sign-normalization","seed":20261032,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":-1,\"q\":-3}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize -1/-3 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"1/3","explanation":"Because q=-3 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0013","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"317a0d26bccec2febde5cebc89e90b2b09c952a2318559c65eb3690192729b3f","family_id":"qf-rational-denominator-sign-normalization","seed":20261033,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":0,\"q\":-4}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize 0/-4 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"0/4","explanation":"Because q=-4 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0014","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ba45616fa8c3ee3a72f22576d780248827b0a34695563c3abb2ff2190b19a176","family_id":"qf-rational-denominator-sign-normalization","seed":20261034,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":1,\"q\":-5}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize 1/-5 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"-1/5","explanation":"Because q=-5 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0015","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2c7a4ae29e05b767b4b7da258d432db131835d01ed2337ea65a0f338622ca5c7","family_id":"qf-rational-denominator-sign-normalization","seed":20261035,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":2,\"q\":-6}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize 2/-6 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"-2/6","explanation":"Because q=-6 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0016","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2a30f85d74b98c26a7e0550eea8067be031b852580461ac06229813ef28e392c","family_id":"qf-rational-denominator-sign-normalization","seed":20261036,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":3,\"q\":-7}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize 3/-7 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"-3/7","explanation":"Because q=-7 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0017","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9294bbbbf30db34c60d5e8e1ec3174dd42b93cff6cae8b26b8e3715934ba52f8","family_id":"qf-rational-denominator-sign-normalization","seed":20261037,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":4,\"q\":-8}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize 4/-8 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"-4/8","explanation":"Because q=-8 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0018","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"714f3517eea2fb996a5c8ba747e5593157e4984809ecc6cc2247bd97cb6b9eaf","family_id":"qf-rational-denominator-sign-normalization","seed":20261038,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":5,\"q\":-9}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize 5/-9 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"-5/9","explanation":"Because q=-9 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0019","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dd96b3f90ec4d2c5f96aa71a40c7add4b472059af39df49f1cf78316dbe9115a","family_id":"qf-rational-denominator-sign-normalization","seed":20261039,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":6,\"q\":-1}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize 6/-1 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"-6/1","explanation":"Because q=-1 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0020","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"152424e361162ba618c7bb5d8d18e70a1025e20d08a27cd918c490c18dca92ae","family_id":"qf-rational-denominator-sign-normalization","seed":20261040,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":7,\"q\":-2}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize 7/-2 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"-7/2","explanation":"Because q=-2 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0021","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"436fc14313585759aad17fa0ec08e22872929b9cde7852cae9389740d5914916","family_id":"qf-rational-denominator-sign-normalization","seed":20261041,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":8,\"q\":-3}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize 8/-3 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"-8/3","explanation":"Because q=-3 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0022","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"696095d22185845990be1c656bbcdf616ac27d70bf53469860d2e6c27ac8ea0f","family_id":"qf-rational-denominator-sign-normalization","seed":20261042,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":9,\"q\":-4}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize 9/-4 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"-9/4","explanation":"Because q=-4 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0023","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8c44fb3cfd774adf8cab7a0b8427508ddc5400ed64acaf3058086561601c506d","family_id":"qf-rational-denominator-sign-normalization","seed":20261043,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":10,\"q\":-5}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize 10/-5 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"-10/5","explanation":"Because q=-5 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0024","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"28c819538ddb4e987271e4f7f02f843b5cddc58c6376825ab12533a03775c3c7","family_id":"qf-rational-denominator-sign-normalization","seed":20261044,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":11,\"q\":-6}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize 11/-6 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"-11/6","explanation":"Because q=-6 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-denominator-sign-normalization-0025","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"144f07fbc625419235963afab800fcf0d52b9264d0829a52593a759487b718de","family_id":"qf-rational-denominator-sign-normalization","seed":20261045,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":12,\"q\":-7}"},"fields":{"title":"Denominator-Sign Normalization","stem":"Normalize 12/-7 to an exact representation with a positive denominator.","answer":{"kind":"short_text","value":"-12/7","explanation":"Because q=-7 is negative, move only the sign to the numerator. The value is unchanged; no gcd reduction is performed."},"skills":["denominator-sign normalization"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0001","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b37454c7e1073d639d1a3f039a1ad2056748164dc42a4245c7195a01f5f4e167","family_id":"qf-rational-equivalent-fractions","seed":20261121,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":-11,\"q\":1,\"r\":-22,\"s\":2}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=1 and s=2 are nonzero. Are -11/1 and -22/2 equivalent?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"-11×2 = -22×1; the fractions are equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0002","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dd66229560581a6fef6b3927b07b938c3ff6fb85782cc7a3c78f2b0d170a4378","family_id":"qf-rational-equivalent-fractions","seed":20261122,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":-10,\"q\":2,\"r\":-19,\"s\":4}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=2 and s=4 are nonzero. Are -10/2 and -19/4 equivalent?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"-10×4 ≠ -19×2; the fractions are not equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0003","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cf4ed0cf64c4f58725ece726dba9cee299f31d8de18006a4628ec30ec6189dea","family_id":"qf-rational-equivalent-fractions","seed":20261123,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":-9,\"q\":3,\"r\":-18,\"s\":6}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=3 and s=6 are nonzero. Are -9/3 and -18/6 equivalent?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"-9×6 = -18×3; the fractions are equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0004","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d4d90c4a8e1b7cfc35d13aa38dfd0852794088c1e73cfeb7cd45a6e758737ef7","family_id":"qf-rational-equivalent-fractions","seed":20261124,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":-8,\"q\":4,\"r\":-15,\"s\":8}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=4 and s=8 are nonzero. Are -8/4 and -15/8 equivalent?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"-8×8 ≠ -15×4; the fractions are not equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0005","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c74a9ac358845f90b3518d52426c060fb8cc26443e4ae1643e23cdcfb39f160d","family_id":"qf-rational-equivalent-fractions","seed":20261125,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":-7,\"q\":5,\"r\":-14,\"s\":10}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=5 and s=10 are nonzero. Are -7/5 and -14/10 equivalent?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"-7×10 = -14×5; the fractions are equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0006","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"05ac1d63aac2b4b74f2e1f03940e8c60f8a075e45c59874d7aeb8f542bdaabba","family_id":"qf-rational-equivalent-fractions","seed":20261126,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":-6,\"q\":6,\"r\":-11,\"s\":12}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=6 and s=12 are nonzero. Are -6/6 and -11/12 equivalent?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"-6×12 ≠ -11×6; the fractions are not equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0007","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"92eae0212a695222e59076d7cdeba71e1515a9baa303278ce3fd4bed524e209d","family_id":"qf-rational-equivalent-fractions","seed":20261127,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":-5,\"q\":7,\"r\":-10,\"s\":14}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=7 and s=14 are nonzero. Are -5/7 and -10/14 equivalent?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"-5×14 = -10×7; the fractions are equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0008","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5886e552bdf614d9b288200f40b62d3f6471b6f59d9a98a1116089d34536607e","family_id":"qf-rational-equivalent-fractions","seed":20261128,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":-4,\"q\":1,\"r\":-7,\"s\":2}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=1 and s=2 are nonzero. Are -4/1 and -7/2 equivalent?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"-4×2 ≠ -7×1; the fractions are not equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0009","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"59e6195162675f367b1847797f88905b6e05582712721ea91a585f421bc985f1","family_id":"qf-rational-equivalent-fractions","seed":20261129,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":-3,\"q\":2,\"r\":-6,\"s\":4}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=2 and s=4 are nonzero. Are -3/2 and -6/4 equivalent?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"-3×4 = -6×2; the fractions are equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0010","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"077185e9fc7a08c90f7d9002d666e102832647f808bb92eacc636a52a88170c1","family_id":"qf-rational-equivalent-fractions","seed":20261130,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":-2,\"q\":3,\"r\":-3,\"s\":6}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=3 and s=6 are nonzero. Are -2/3 and -3/6 equivalent?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"-2×6 ≠ -3×3; the fractions are not equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0011","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e5255a0278c209705ab7311c1bb1b13ed87813a22f445347786d974216b422a6","family_id":"qf-rational-equivalent-fractions","seed":20261131,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":-1,\"q\":4,\"r\":-2,\"s\":8}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=4 and s=8 are nonzero. Are -1/4 and -2/8 equivalent?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"-1×8 = -2×4; the fractions are equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0012","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"36fdfb5a2f272c83ea8e8d87841d2367e22ef7b7fe2eee43028ecc00053c2604","family_id":"qf-rational-equivalent-fractions","seed":20261132,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":0,\"q\":5,\"r\":1,\"s\":10}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=5 and s=10 are nonzero. Are 0/5 and 1/10 equivalent?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"0×10 ≠ 1×5; the fractions are not equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0013","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"67d64cc740ccac672bcabd95f9b3b3626856cb8e95186f3536f2a4496b8dbbc0","family_id":"qf-rational-equivalent-fractions","seed":20261133,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":1,\"q\":6,\"r\":2,\"s\":12}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=6 and s=12 are nonzero. Are 1/6 and 2/12 equivalent?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"1×12 = 2×6; the fractions are equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0014","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"09a131d359751c77628ecde81d629595d654405f4f86ac576cc205a13e49bf0c","family_id":"qf-rational-equivalent-fractions","seed":20261134,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":2,\"q\":7,\"r\":5,\"s\":14}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=7 and s=14 are nonzero. Are 2/7 and 5/14 equivalent?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"2×14 ≠ 5×7; the fractions are not equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0015","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"39b924b738cffbdb744456ae5d6e7df17737c460dd9748370ad0a025f801a82c","family_id":"qf-rational-equivalent-fractions","seed":20261135,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":3,\"q\":1,\"r\":6,\"s\":2}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=1 and s=2 are nonzero. Are 3/1 and 6/2 equivalent?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"3×2 = 6×1; the fractions are equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0016","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"aacca76ad352f9e8b9554bddc3fed177ba4e56ea484bd467786040824bcf7bb4","family_id":"qf-rational-equivalent-fractions","seed":20261136,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":4,\"q\":2,\"r\":9,\"s\":4}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=2 and s=4 are nonzero. Are 4/2 and 9/4 equivalent?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"4×4 ≠ 9×2; the fractions are not equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0017","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8ace197f091f1e220130c354e3d46289cb00a99395abc0f81d8c2fc3cde031db","family_id":"qf-rational-equivalent-fractions","seed":20261137,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":5,\"q\":3,\"r\":10,\"s\":6}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=3 and s=6 are nonzero. Are 5/3 and 10/6 equivalent?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"5×6 = 10×3; the fractions are equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0018","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"342b1721a2d7ef63da1e569b57e1d9bab031fa5f45201ceb5a4d46ca30ec8a28","family_id":"qf-rational-equivalent-fractions","seed":20261138,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":6,\"q\":4,\"r\":13,\"s\":8}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=4 and s=8 are nonzero. Are 6/4 and 13/8 equivalent?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"6×8 ≠ 13×4; the fractions are not equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0019","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d417d09c297b13adaf231221320e2eef2b6471f89e8ec963f788dd76769dd7b8","family_id":"qf-rational-equivalent-fractions","seed":20261139,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":7,\"q\":5,\"r\":14,\"s\":10}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=5 and s=10 are nonzero. Are 7/5 and 14/10 equivalent?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"7×10 = 14×5; the fractions are equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0020","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"771822941e29241a01516effeae609c94f65b952286b4be03606261611f64de5","family_id":"qf-rational-equivalent-fractions","seed":20261140,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":8,\"q\":6,\"r\":17,\"s\":12}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=6 and s=12 are nonzero. Are 8/6 and 17/12 equivalent?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"8×12 ≠ 17×6; the fractions are not equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0021","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"309ad8e124f82820673516b6a8dcbb7560068f63d9c4046fde8d2889a045be44","family_id":"qf-rational-equivalent-fractions","seed":20261141,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":9,\"q\":7,\"r\":18,\"s\":14}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=7 and s=14 are nonzero. Are 9/7 and 18/14 equivalent?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"9×14 = 18×7; the fractions are equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0022","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8a8813f09941943524a34867eb3a329ccc7372245c859b4f838edd01399edf47","family_id":"qf-rational-equivalent-fractions","seed":20261142,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":10,\"q\":1,\"r\":21,\"s\":2}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=1 and s=2 are nonzero. Are 10/1 and 21/2 equivalent?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"10×2 ≠ 21×1; the fractions are not equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0023","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"26445792c08c0f433e4f1271cbdd113464b5a66cb0ebf8090bed0e11af436df0","family_id":"qf-rational-equivalent-fractions","seed":20261143,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":11,\"q\":2,\"r\":22,\"s\":4}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=2 and s=4 are nonzero. Are 11/2 and 22/4 equivalent?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"11×4 = 22×2; the fractions are equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0024","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9993ba7721d1915a4c7ca2ffffa45ae21eb38dac941586a93271ffb63fc39625","family_id":"qf-rational-equivalent-fractions","seed":20261144,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":12,\"q\":3,\"r\":25,\"s\":6}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=3 and s=6 are nonzero. Are 12/3 and 25/6 equivalent?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"12×6 ≠ 25×3; the fractions are not equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-equivalent-fractions-0025","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7dbfba4e8592c0eb5ba1226c41ab0be361966906ba2f7b5b4142588f7a25c100","family_id":"qf-rational-equivalent-fractions","seed":20261145,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":13,\"q\":4,\"r\":26,\"s\":8}"},"fields":{"title":"Equivalent Fractions","stem":"The denominators q=4 and s=8 are nonzero. Are 13/4 and 26/8 equivalent?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"13×8 = 26×4; the fractions are equivalent. This uses exact cross products rather than decimal appearance."},"skills":["cross multiplication","equivalent fractions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0001","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"953d3d6c88aea7d946f393787a5a60734c1cc485f85beaa733711a6a9f1951da","family_id":"qf-rational-reduced-form","seed":20261221,"semantic_template":"qf-rational-reduced-form/{\"p\":0,\"q\":12}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce 0/12 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"0/1","explanation":"The canonical reduced form of zero is 0/1."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0002","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dfe4795987ff5db7c7b9ddc28a3e4c225a362cca7731eec4397b7037cf6b93e2","family_id":"qf-rational-reduced-form","seed":20261222,"semantic_template":"qf-rational-reduced-form/{\"p\":-12,\"q\":8}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce -12/8 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"-3/2","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is -3/2."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0003","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"88f2ba40d89babe7c9af2b1c13b5d0348869f90c3d45bcbc85dab57570c3a5f1","family_id":"qf-rational-reduced-form","seed":20261223,"semantic_template":"qf-rational-reduced-form/{\"p\":27,\"q\":12}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce 27/12 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"9/4","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is 9/4."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0004","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"937b85f32ea9598e31ce18c0e8fe65d30f50506488f7fc01806dfb88fb9075c5","family_id":"qf-rational-reduced-form","seed":20261224,"semantic_template":"qf-rational-reduced-form/{\"p\":-24,\"q\":8}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce -24/8 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"-3/1","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is -3/1."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0005","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c2b87bb0714e27d08b5f045fe0dda87a32fb100ad2b0160b522b7c11baad4a99","family_id":"qf-rational-reduced-form","seed":20261225,"semantic_template":"qf-rational-reduced-form/{\"p\":45,\"q\":12}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce 45/12 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"15/4","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is 15/4."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0006","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"174111125c0ddb37bb80857c2303e3fdba6f78f206de079f22abafd321105da4","family_id":"qf-rational-reduced-form","seed":20261226,"semantic_template":"qf-rational-reduced-form/{\"p\":-36,\"q\":8}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce -36/8 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"-9/2","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is -9/2."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0007","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ab01cf597e13c9c84f1f209a1dfa15d6eb242df17688aecd04fd4621dda746f3","family_id":"qf-rational-reduced-form","seed":20261227,"semantic_template":"qf-rational-reduced-form/{\"p\":63,\"q\":12}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce 63/12 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"21/4","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is 21/4."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0008","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"70d933c7c15fdb3c964c20b966f0b4601bb03c378d968c4e799e5f896808a7cf","family_id":"qf-rational-reduced-form","seed":20261228,"semantic_template":"qf-rational-reduced-form/{\"p\":-48,\"q\":8}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce -48/8 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"-6/1","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is -6/1."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0009","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9f908f8d1ba59f18630f5c5a83494e272319b97cbf57f8cf61c9c60255a65f53","family_id":"qf-rational-reduced-form","seed":20261229,"semantic_template":"qf-rational-reduced-form/{\"p\":81,\"q\":12}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce 81/12 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"27/4","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is 27/4."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0010","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"45773f27d02a2482a509356497e1c053509ce42b40b0ef90ffceec763806dd18","family_id":"qf-rational-reduced-form","seed":20261230,"semantic_template":"qf-rational-reduced-form/{\"p\":-60,\"q\":8}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce -60/8 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"-15/2","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is -15/2."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0011","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"42d54464db781c9e6707b8992dbec6ddd4b79793f58a2e13c0f9318e032c1b73","family_id":"qf-rational-reduced-form","seed":20261231,"semantic_template":"qf-rational-reduced-form/{\"p\":99,\"q\":12}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce 99/12 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"33/4","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is 33/4."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0012","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c6456df9df3ff9f125a36ace186f8b57a2a1dd6c34e46b86e6bceef71692ccec","family_id":"qf-rational-reduced-form","seed":20261232,"semantic_template":"qf-rational-reduced-form/{\"p\":-72,\"q\":8}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce -72/8 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"-9/1","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is -9/1."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0013","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"db370cdbc94d38a79e65dbdf044351951521b85ee828785b80efc44a63f954cc","family_id":"qf-rational-reduced-form","seed":20261233,"semantic_template":"qf-rational-reduced-form/{\"p\":117,\"q\":12}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce 117/12 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"39/4","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is 39/4."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0014","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5e6c12818fb08cf811f2328185dc4d6924cbf899e531c32d97ddcd20b0c4edbe","family_id":"qf-rational-reduced-form","seed":20261234,"semantic_template":"qf-rational-reduced-form/{\"p\":-84,\"q\":8}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce -84/8 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"-21/2","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is -21/2."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0015","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3dd97b0953ebffbc6e920df3c7e001395362fe0d31a0488e27d9b1aadcd1cfd7","family_id":"qf-rational-reduced-form","seed":20261235,"semantic_template":"qf-rational-reduced-form/{\"p\":135,\"q\":12}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce 135/12 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"45/4","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is 45/4."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0016","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"55ca3d7f1f21705654005690150b18fba5d8d7d959c92f20c57ca3c012c931a7","family_id":"qf-rational-reduced-form","seed":20261236,"semantic_template":"qf-rational-reduced-form/{\"p\":-96,\"q\":8}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce -96/8 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"-12/1","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is -12/1."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0017","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c6c0c4e539332be165540649d860bffa655bbb30e247d067f7ade84aa0d6a1f2","family_id":"qf-rational-reduced-form","seed":20261237,"semantic_template":"qf-rational-reduced-form/{\"p\":153,\"q\":12}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce 153/12 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"51/4","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is 51/4."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0018","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6eb0010c09ef34a2816001a838deafcad13ec3a31dec98ac61985850ae895d93","family_id":"qf-rational-reduced-form","seed":20261238,"semantic_template":"qf-rational-reduced-form/{\"p\":-108,\"q\":8}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce -108/8 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"-27/2","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is -27/2."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0019","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"af7fb4c46652039682572baa94d9b4e730ad0be33566f0577e42fa0d6344a97d","family_id":"qf-rational-reduced-form","seed":20261239,"semantic_template":"qf-rational-reduced-form/{\"p\":171,\"q\":12}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce 171/12 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"57/4","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is 57/4."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0020","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"29d7161960b88acf2d6fd5cf2f83aab8a3570b426aea430940d80e040bcf7899","family_id":"qf-rational-reduced-form","seed":20261240,"semantic_template":"qf-rational-reduced-form/{\"p\":-120,\"q\":8}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce -120/8 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"-15/1","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is -15/1."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0021","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"859bbb6b9408cec65912754b0b39c934897e1132eb21fe3b7a97eed849d36b6a","family_id":"qf-rational-reduced-form","seed":20261241,"semantic_template":"qf-rational-reduced-form/{\"p\":189,\"q\":12}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce 189/12 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"63/4","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is 63/4."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0022","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6a9dd7302c0500fe76db5337793409fa1a4569820b331a1610405d163979b687","family_id":"qf-rational-reduced-form","seed":20261242,"semantic_template":"qf-rational-reduced-form/{\"p\":-132,\"q\":8}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce -132/8 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"-33/2","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is -33/2."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0023","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8cc4919b5c4354cbccbf24e9f2a7fffb31bc7130776411df91077122220ea49b","family_id":"qf-rational-reduced-form","seed":20261243,"semantic_template":"qf-rational-reduced-form/{\"p\":207,\"q\":12}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce 207/12 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"69/4","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is 69/4."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0024","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"60a8174ec5326e571543d1408b2af0d0e5ef6ffaa8b7cf4a5b1f1f838946b0d9","family_id":"qf-rational-reduced-form","seed":20261244,"semantic_template":"qf-rational-reduced-form/{\"p\":-144,\"q\":8}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce -144/8 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"-18/1","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is -18/1."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260920-rational-reduced-form-0025","batch_id":"batch-20260920-rational-number-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"37a5a9f61fbc33857ac81fd4282913b7357758482571a13cc924b17105230c2f","family_id":"qf-rational-reduced-form","seed":20261245,"semantic_template":"qf-rational-reduced-form/{\"p\":225,\"q\":12}"},"fields":{"title":"Reduced Rational Form","stem":"Reduce 225/12 to an exact lowest-terms form with a positive denominator.","answer":{"kind":"short_text","value":"75/4","explanation":"Divide numerator and denominator by their gcd and normalize the denominator sign; the result is 75/4."},"skills":["gcd reduction","reduced form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}