{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0001","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=0、分母 q=0，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"分母條件為 q≠0；此處 q=0，因此答案為否。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301001,"parameters":{"operation":"representation_validity","p":0,"q":0,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":0,\"q\":0}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0002","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=0、分母 q=5，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"分母條件為 q≠0；此處 q=5，因此答案為是。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301002,"parameters":{"operation":"representation_validity","p":0,"q":5,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":0,\"q\":5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0003","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=-10、分母 q=3，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"分母條件為 q≠0；此處 q=3，因此答案為是。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301003,"parameters":{"operation":"representation_validity","p":-10,"q":3,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":-10,\"q\":3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0004","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=-9、分母 q=-4，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"分母條件為 q≠0；此處 q=-4，因此答案為是。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301004,"parameters":{"operation":"representation_validity","p":-9,"q":-4,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":-9,\"q\":-4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0005","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=-8、分母 q=5，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"分母條件為 q≠0；此處 q=5，因此答案為是。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301005,"parameters":{"operation":"representation_validity","p":-8,"q":5,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":-8,\"q\":5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0006","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=-7、分母 q=0，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"分母條件為 q≠0；此處 q=0，因此答案為否。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301006,"parameters":{"operation":"representation_validity","p":-7,"q":0,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":-7,\"q\":0}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0007","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=-6、分母 q=-7，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"分母條件為 q≠0；此處 q=-7，因此答案為是。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301007,"parameters":{"operation":"representation_validity","p":-6,"q":-7,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":-6,\"q\":-7}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0008","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=-5、分母 q=1，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"分母條件為 q≠0；此處 q=1，因此答案為是。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301008,"parameters":{"operation":"representation_validity","p":-5,"q":1,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":-5,\"q\":1}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0009","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=-4、分母 q=2，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"分母條件為 q≠0；此處 q=2，因此答案為是。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301009,"parameters":{"operation":"representation_validity","p":-4,"q":2,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":-4,\"q\":2}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0010","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=-3、分母 q=-3，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"分母條件為 q≠0；此處 q=-3，因此答案為是。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301010,"parameters":{"operation":"representation_validity","p":-3,"q":-3,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":-3,\"q\":-3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0011","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=-2、分母 q=0，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"分母條件為 q≠0；此處 q=0，因此答案為否。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301011,"parameters":{"operation":"representation_validity","p":-2,"q":0,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":-2,\"q\":0}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0012","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=-1、分母 q=5，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"分母條件為 q≠0；此處 q=5，因此答案為是。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301012,"parameters":{"operation":"representation_validity","p":-1,"q":5,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":-1,\"q\":5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0013","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=0、分母 q=-6，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"分母條件為 q≠0；此處 q=-6，因此答案為是。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301013,"parameters":{"operation":"representation_validity","p":0,"q":-6,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":0,\"q\":-6}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0014","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=1、分母 q=7，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"分母條件為 q≠0；此處 q=7，因此答案為是。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301014,"parameters":{"operation":"representation_validity","p":1,"q":7,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":1,\"q\":7}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0015","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=2、分母 q=1，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"分母條件為 q≠0；此處 q=1，因此答案為是。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301015,"parameters":{"operation":"representation_validity","p":2,"q":1,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":2,\"q\":1}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0016","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=3、分母 q=0，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"分母條件為 q≠0；此處 q=0，因此答案為否。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301016,"parameters":{"operation":"representation_validity","p":3,"q":0,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":3,\"q\":0}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0017","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=4、分母 q=3，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"分母條件為 q≠0；此處 q=3，因此答案為是。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301017,"parameters":{"operation":"representation_validity","p":4,"q":3,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":4,\"q\":3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0018","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=5、分母 q=4，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"分母條件為 q≠0；此處 q=4，因此答案為是。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301018,"parameters":{"operation":"representation_validity","p":5,"q":4,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":5,\"q\":4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0019","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=6、分母 q=-5，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"分母條件為 q≠0；此處 q=-5，因此答案為是。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301019,"parameters":{"operation":"representation_validity","p":6,"q":-5,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":6,\"q\":-5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0020","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=7、分母 q=6，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"分母條件為 q≠0；此處 q=6，因此答案為是。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301020,"parameters":{"operation":"representation_validity","p":7,"q":6,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":7,\"q\":6}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0021","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=8、分母 q=0，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"否","explanation_zh":"分母條件為 q≠0；此處 q=0，因此答案為否。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301021,"parameters":{"operation":"representation_validity","p":8,"q":0,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":8,\"q\":0}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0022","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=9、分母 q=-1，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"分母條件為 q≠0；此處 q=-1，因此答案為是。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301022,"parameters":{"operation":"representation_validity","p":9,"q":-1,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":9,\"q\":-1}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0023","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=10、分母 q=2，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"分母條件為 q≠0；此處 q=2，因此答案為是。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301023,"parameters":{"operation":"representation_validity","p":10,"q":2,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":10,\"q\":2}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0024","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=11、分母 q=3，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"分母條件為 q≠0；此處 q=3，因此答案為是。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301024,"parameters":{"operation":"representation_validity","p":11,"q":3,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":11,\"q\":3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-representation-validity-0025","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"合法分數表示","stem_zh":"對整數分子 p=12、分母 q=-4，p/q 是合法的有理數表示嗎？回答是或否。","answer":{"kind":"short_text","value":"是","explanation_zh":"分母條件為 q≠0；此處 q=-4，因此答案為是。零分子不會取消分母條件。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零分母","整數表示"]},"variant":{"family_id":"qf-fraction-representation-validity","seed":202609301025,"parameters":{"operation":"representation_validity","p":12,"q":-4,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":12,\"q\":-4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0001","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 -12/(1) 與 24/(-2) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 24, 24；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301101,"parameters":{"operation":"equivalence","p":-12,"q":1,"r":24,"s":-2,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-12,\"q\":1,\"r\":24,\"s\":-2}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0002","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 -11/(-2) 與 -32/(-6) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 66, 64；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301102,"parameters":{"operation":"equivalence","p":-11,"q":-2,"r":-32,"s":-6,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-11,\"q\":-2,\"r\":-32,\"s\":-6}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0003","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 -10/(3) 與 -40/(12) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 -120, -120；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301103,"parameters":{"operation":"equivalence","p":-10,"q":3,"r":-40,"s":12,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-10,\"q\":3,\"r\":-40,\"s\":12}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0004","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 -9/(-4) 與 46/(20) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 -180, -184；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301104,"parameters":{"operation":"equivalence","p":-9,"q":-4,"r":46,"s":20,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-9,\"q\":-4,\"r\":46,\"s\":20}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0005","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 -8/(5) 與 -16/(10) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 -80, -80；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301105,"parameters":{"operation":"equivalence","p":-8,"q":5,"r":-16,"s":10,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-8,\"q\":5,\"r\":-16,\"s\":10}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0006","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 -7/(-6) 與 -20/(-18) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 126, 120；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301106,"parameters":{"operation":"equivalence","p":-7,"q":-6,"r":-20,"s":-18,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-7,\"q\":-6,\"r\":-20,\"s\":-18}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0007","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 -6/(7) 與 24/(-28) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 168, 168；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301107,"parameters":{"operation":"equivalence","p":-6,"q":7,"r":24,"s":-28,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-6,\"q\":7,\"r\":24,\"s\":-28}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0008","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 -5/(-1) 與 -24/(-5) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 25, 24；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301108,"parameters":{"operation":"equivalence","p":-5,"q":-1,"r":-24,"s":-5,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-5,\"q\":-1,\"r\":-24,\"s\":-5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0009","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 -4/(2) 與 -8/(4) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 -16, -16；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301109,"parameters":{"operation":"equivalence","p":-4,"q":2,"r":-8,"s":4,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-4,\"q\":2,\"r\":-8,\"s\":4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0010","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 -3/(-3) 與 10/(9) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 -27, -30；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301110,"parameters":{"operation":"equivalence","p":-3,"q":-3,"r":10,"s":9,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-3,\"q\":-3,\"r\":10,\"s\":9}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0011","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 -2/(4) 與 -8/(16) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 -32, -32；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301111,"parameters":{"operation":"equivalence","p":-2,"q":4,"r":-8,"s":16,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-2,\"q\":4,\"r\":-8,\"s\":16}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0012","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 -1/(-5) 與 -4/(-25) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 25, 20；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301112,"parameters":{"operation":"equivalence","p":-1,"q":-5,"r":-4,"s":-25,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-1,\"q\":-5,\"r\":-4,\"s\":-25}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0013","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 0/(6) 與 0/(-12) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 0, 0；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301113,"parameters":{"operation":"equivalence","p":0,"q":6,"r":0,"s":-12,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":0,\"q\":6,\"r\":0,\"s\":-12}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0014","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 1/(-7) 與 4/(-21) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 -21, -28；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301114,"parameters":{"operation":"equivalence","p":1,"q":-7,"r":4,"s":-21,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":1,\"q\":-7,\"r\":4,\"s\":-21}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0015","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 2/(1) 與 8/(4) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 8, 8；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301115,"parameters":{"operation":"equivalence","p":2,"q":1,"r":8,"s":4,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":2,\"q\":1,\"r\":8,\"s\":4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0016","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 3/(-2) 與 -14/(10) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 30, 28；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301116,"parameters":{"operation":"equivalence","p":3,"q":-2,"r":-14,"s":10,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":3,\"q\":-2,\"r\":-14,\"s\":10}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0017","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 4/(3) 與 8/(6) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 24, 24；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301117,"parameters":{"operation":"equivalence","p":4,"q":3,"r":8,"s":6,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":4,\"q\":3,\"r\":8,\"s\":6}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0018","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 5/(-4) 與 16/(-12) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 -60, -64；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301118,"parameters":{"operation":"equivalence","p":5,"q":-4,"r":16,"s":-12,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":5,\"q\":-4,\"r\":16,\"s\":-12}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0019","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 6/(5) 與 -24/(-20) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 -120, -120；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301119,"parameters":{"operation":"equivalence","p":6,"q":5,"r":-24,"s":-20,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":6,\"q\":5,\"r\":-24,\"s\":-20}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0020","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 7/(-6) 與 36/(-30) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 -210, -216；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301120,"parameters":{"operation":"equivalence","p":7,"q":-6,"r":36,"s":-30,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":7,\"q\":-6,\"r\":36,\"s\":-30}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0021","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 8/(7) 與 16/(14) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 112, 112；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301121,"parameters":{"operation":"equivalence","p":8,"q":7,"r":16,"s":14,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":8,\"q\":7,\"r\":16,\"s\":14}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0022","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 9/(-1) 與 -26/(3) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 27, 26；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301122,"parameters":{"operation":"equivalence","p":9,"q":-1,"r":-26,"s":3,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":9,\"q\":-1,\"r\":-26,\"s\":3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0023","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 10/(2) 與 40/(8) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 80, 80；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301123,"parameters":{"operation":"equivalence","p":10,"q":2,"r":40,"s":8,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":10,\"q\":2,\"r\":40,\"s\":8}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0024","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 11/(-3) 與 56/(-15) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 -165, -168；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301124,"parameters":{"operation":"equivalence","p":11,"q":-3,"r":56,"s":-15,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":11,\"q\":-3,\"r\":56,\"s\":-15}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-equivalence-0025","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數等值判定","stem_zh":"整數構成的兩個合法分數 12/(4) 與 -24/(-8) 是否等值？兩個分母均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 -96, -96；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["合法分母","交叉乘積"]},"variant":{"family_id":"qf-fraction-equivalence","seed":202609301125,"parameters":{"operation":"equivalence","p":12,"q":4,"r":-24,"s":-8,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":12,\"q\":4,\"r\":-24,\"s\":-8}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0001","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 -24/(2) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"-12/1","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 -12/1；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301201,"parameters":{"operation":"reduction","p":-24,"q":2,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-24,\"q\":2}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0002","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 -33/(-6) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"11/2","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 11/2；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301202,"parameters":{"operation":"reduction","p":-33,"q":-6,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-33,\"q\":-6}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0003","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 -40/(12) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"-10/3","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 -10/3；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301203,"parameters":{"operation":"reduction","p":-40,"q":12,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-40,\"q\":12}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0004","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 -45/(-20) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"9/4","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 9/4；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301204,"parameters":{"operation":"reduction","p":-45,"q":-20,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-45,\"q\":-20}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0005","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 -16/(10) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"-8/5","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 -8/5；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301205,"parameters":{"operation":"reduction","p":-16,"q":10,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-16,\"q\":10}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0006","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 -21/(-18) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"7/6","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 7/6；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301206,"parameters":{"operation":"reduction","p":-21,"q":-18,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-21,\"q\":-18}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0007","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 -24/(28) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"-6/7","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 -6/7；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301207,"parameters":{"operation":"reduction","p":-24,"q":28,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-24,\"q\":28}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0008","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 -25/(-5) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"5/1","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 5/1；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301208,"parameters":{"operation":"reduction","p":-25,"q":-5,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-25,\"q\":-5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0009","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 -8/(4) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"-2/1","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 -2/1；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301209,"parameters":{"operation":"reduction","p":-8,"q":4,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-8,\"q\":4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0010","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 -9/(-9) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"1/1","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 1/1；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301210,"parameters":{"operation":"reduction","p":-9,"q":-9,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-9,\"q\":-9}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0011","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 -8/(16) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"-1/2","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 -1/2；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301211,"parameters":{"operation":"reduction","p":-8,"q":16,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-8,\"q\":16}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0012","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 -5/(-25) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"1/5","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 1/5；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301212,"parameters":{"operation":"reduction","p":-5,"q":-25,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-5,\"q\":-25}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0013","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 0/(12) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"0/1","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 0/1；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301213,"parameters":{"operation":"reduction","p":0,"q":12,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":0,\"q\":12}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0014","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 3/(-21) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"-1/7","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 -1/7；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301214,"parameters":{"operation":"reduction","p":3,"q":-21,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":3,\"q\":-21}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0015","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 8/(4) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"2/1","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 2/1；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301215,"parameters":{"operation":"reduction","p":8,"q":4,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":8,\"q\":4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0016","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 15/(-10) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"-3/2","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 -3/2；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301216,"parameters":{"operation":"reduction","p":15,"q":-10,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":15,\"q\":-10}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0017","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 8/(6) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"4/3","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 4/3；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301217,"parameters":{"operation":"reduction","p":8,"q":6,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":8,\"q\":6}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0018","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 15/(-12) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"-5/4","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 -5/4；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301218,"parameters":{"operation":"reduction","p":15,"q":-12,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":15,\"q\":-12}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0019","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 24/(20) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"6/5","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 6/5；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301219,"parameters":{"operation":"reduction","p":24,"q":20,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":24,\"q\":20}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0020","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 35/(-30) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"-7/6","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 -7/6；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301220,"parameters":{"operation":"reduction","p":35,"q":-30,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":35,\"q\":-30}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0021","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 16/(14) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"8/7","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 8/7；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301221,"parameters":{"operation":"reduction","p":16,"q":14,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":16,\"q\":14}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0022","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 27/(-3) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"-9/1","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 -9/1；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301222,"parameters":{"operation":"reduction","p":27,"q":-3,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":27,\"q\":-3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0023","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 40/(8) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"5/1","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 5/1；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301223,"parameters":{"operation":"reduction","p":40,"q":8,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":40,\"q\":8}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0024","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 55/(-15) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"-11/3","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 -11/3；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301224,"parameters":{"operation":"reduction","p":55,"q":-15,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":55,\"q\":-15}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-reduction-0025","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數正規化與約分","stem_zh":"把整數構成的合法分數 24/(8) 約成最簡正分母形式；答案用 p/q，包括整數與零。","answer":{"kind":"short_text","value":"3/1","explanation_zh":"先把分母符號移到分子，再同除分子分母的最大公因數，得到 3/1；零的正規形式為 0/1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["正分母","最大公因數"]},"variant":{"family_id":"qf-fraction-reduction","seed":202609301225,"parameters":{"operation":"reduction","p":24,"q":8,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":24,\"q\":8}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0001","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 0/(1)+(0)/(-1)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"0/1","explanation_zh":"通分的分子為 0，分母為 -1；正規化並約分得到 0/1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301301,"parameters":{"operation":"addition","p":0,"q":1,"r":0,"s":-1,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":0,\"q\":1,\"r\":0,\"s\":-1}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0002","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 -11/(-2)+(9)/(2)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"10/1","explanation_zh":"通分的分子為 -40，分母為 -4；正規化並約分得到 10/1。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301302,"parameters":{"operation":"addition","p":-11,"q":-2,"r":9,"s":2,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":-11,\"q\":-2,\"r\":9,\"s\":2}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0003","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 -10/(3)+(6)/(3)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"-4/3","explanation_zh":"通分的分子為 -12，分母為 9；正規化並約分得到 -4/3。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301303,"parameters":{"operation":"addition","p":-10,"q":3,"r":6,"s":3,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":-10,\"q\":3,\"r\":6,\"s\":3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0004","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 -9/(-4)+(3)/(-4)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"3/2","explanation_zh":"通分的分子為 24，分母為 16；正規化並約分得到 3/2。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301304,"parameters":{"operation":"addition","p":-9,"q":-4,"r":3,"s":-4,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":-9,\"q\":-4,\"r\":3,\"s\":-4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0005","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 -8/(5)+(0)/(5)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"-8/5","explanation_zh":"通分的分子為 -40，分母為 25；正規化並約分得到 -8/5。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301305,"parameters":{"operation":"addition","p":-8,"q":5,"r":0,"s":5,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":-8,\"q\":5,\"r\":0,\"s\":5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0006","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 -7/(-6)+(-3)/(1)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"-11/6","explanation_zh":"通分的分子為 11，分母為 -6；正規化並約分得到 -11/6。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301306,"parameters":{"operation":"addition","p":-7,"q":-6,"r":-3,"s":1,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":-7,\"q\":-6,\"r\":-3,\"s\":1}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0007","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 -6/(7)+(-6)/(-2)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"15/7","explanation_zh":"通分的分子為 -30，分母為 -14；正規化並約分得到 15/7。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301307,"parameters":{"operation":"addition","p":-6,"q":7,"r":-6,"s":-2,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":-6,\"q\":7,\"r\":-6,\"s\":-2}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0008","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 -5/(-1)+(-9)/(3)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"2/1","explanation_zh":"通分的分子為 -6，分母為 -3；正規化並約分得到 2/1。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301308,"parameters":{"operation":"addition","p":-5,"q":-1,"r":-9,"s":3,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":-5,\"q\":-1,\"r\":-9,\"s\":3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0009","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 -4/(2)+(-12)/(4)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"-5/1","explanation_zh":"通分的分子為 -40，分母為 8；正規化並約分得到 -5/1。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301309,"parameters":{"operation":"addition","p":-4,"q":2,"r":-12,"s":4,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":-4,\"q\":2,\"r\":-12,\"s\":4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0010","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 -3/(-3)+(10)/(-5)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"-1/1","explanation_zh":"通分的分子為 -15，分母為 15；正規化並約分得到 -1/1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301310,"parameters":{"operation":"addition","p":-3,"q":-3,"r":10,"s":-5,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":-3,\"q\":-3,\"r\":10,\"s\":-5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0011","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 -2/(4)+(7)/(1)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"13/2","explanation_zh":"通分的分子為 26，分母為 4；正規化並約分得到 13/2。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301311,"parameters":{"operation":"addition","p":-2,"q":4,"r":7,"s":1,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":-2,\"q\":4,\"r\":7,\"s\":1}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0012","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 -1/(-5)+(4)/(2)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"11/5","explanation_zh":"通分的分子為 -22，分母為 -10；正規化並約分得到 11/5。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301312,"parameters":{"operation":"addition","p":-1,"q":-5,"r":4,"s":2,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":-1,\"q\":-5,\"r\":4,\"s\":2}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0013","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 0/(6)+(1)/(-3)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"-1/3","explanation_zh":"通分的分子為 6，分母為 -18；正規化並約分得到 -1/3。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301313,"parameters":{"operation":"addition","p":0,"q":6,"r":1,"s":-3,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":0,\"q\":6,\"r\":1,\"s\":-3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0014","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 1/(-7)+(-2)/(4)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"-9/14","explanation_zh":"通分的分子為 18，分母為 -28；正規化並約分得到 -9/14。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301314,"parameters":{"operation":"addition","p":1,"q":-7,"r":-2,"s":4,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":1,\"q\":-7,\"r\":-2,\"s\":4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0015","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 2/(1)+(-5)/(5)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"1/1","explanation_zh":"通分的分子為 5，分母為 5；正規化並約分得到 1/1。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301315,"parameters":{"operation":"addition","p":2,"q":1,"r":-5,"s":5,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":2,\"q\":1,\"r\":-5,\"s\":5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0016","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 3/(-2)+(-8)/(-1)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"13/2","explanation_zh":"通分的分子為 13，分母為 2；正規化並約分得到 13/2。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301316,"parameters":{"operation":"addition","p":3,"q":-2,"r":-8,"s":-1,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":3,\"q\":-2,\"r\":-8,\"s\":-1}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0017","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 4/(3)+(-11)/(2)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"-25/6","explanation_zh":"通分的分子為 -25，分母為 6；正規化並約分得到 -25/6。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301317,"parameters":{"operation":"addition","p":4,"q":3,"r":-11,"s":2,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":4,\"q\":3,\"r\":-11,\"s\":2}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0018","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 5/(-4)+(11)/(3)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"29/12","explanation_zh":"通分的分子為 -29，分母為 -12；正規化並約分得到 29/12。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301318,"parameters":{"operation":"addition","p":5,"q":-4,"r":11,"s":3,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":5,\"q\":-4,\"r\":11,\"s\":3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0019","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 6/(5)+(8)/(-4)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"-4/5","explanation_zh":"通分的分子為 16，分母為 -20；正規化並約分得到 -4/5。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301319,"parameters":{"operation":"addition","p":6,"q":5,"r":8,"s":-4,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":6,\"q\":5,\"r\":8,\"s\":-4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0020","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 7/(-6)+(5)/(5)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"-1/6","explanation_zh":"通分的分子為 5，分母為 -30；正規化並約分得到 -1/6。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301320,"parameters":{"operation":"addition","p":7,"q":-6,"r":5,"s":5,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":7,\"q\":-6,\"r\":5,\"s\":5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0021","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 8/(7)+(2)/(1)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"22/7","explanation_zh":"通分的分子為 22，分母為 7；正規化並約分得到 22/7。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301321,"parameters":{"operation":"addition","p":8,"q":7,"r":2,"s":1,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":8,\"q\":7,\"r\":2,\"s\":1}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0022","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 9/(-1)+(-1)/(-2)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"-17/2","explanation_zh":"通分的分子為 -17，分母為 2；正規化並約分得到 -17/2。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301322,"parameters":{"operation":"addition","p":9,"q":-1,"r":-1,"s":-2,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":9,\"q\":-1,\"r\":-1,\"s\":-2}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0023","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 10/(2)+(-4)/(3)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"11/3","explanation_zh":"通分的分子為 22，分母為 6；正規化並約分得到 11/3。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301323,"parameters":{"operation":"addition","p":10,"q":2,"r":-4,"s":3,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":10,\"q\":2,\"r\":-4,\"s\":3}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0024","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 11/(-3)+(-7)/(4)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"-65/12","explanation_zh":"通分的分子為 65，分母為 -12；正規化並約分得到 -65/12。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301324,"parameters":{"operation":"addition","p":11,"q":-3,"r":-7,"s":4,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":11,\"q\":-3,\"r\":-7,\"s\":4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r01-fraction-exact-addition-0025","batch_id":"batch-20260930-r01-fraction-foundations","language":"zh-Hant","source_mko_ids":["mko-fraction"],"title_zh":"分數精確加法","stem_zh":"對整數構成的合法分數，精確計算 12/(4)+(-10)/(-5)，寫成最簡正分母 p/q。","answer":{"kind":"short_text","value":"5/1","explanation_zh":"通分的分子為 -100，分母為 -20；正規化並約分得到 5/1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["通分","精確有理數"]},"variant":{"family_id":"qf-fraction-exact-addition","seed":202609301325,"parameters":{"operation":"addition","p":12,"q":4,"r":-10,"s":-5,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":12,\"q\":4,\"r\":-10,\"s\":-5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}