{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0001","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 0.5 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"1/2","explanation_zh":"0.5 依小數位數轉為整數分子/10^k，再以 gcd 約成 1/2。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260924,"parameters":{"decimal":"0.5","scale":1,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"0.5\",\"operation\":\"decimal_to_fraction\",\"scale\":1}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0002","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 1.25 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"5/4","explanation_zh":"1.25 依小數位數轉為整數分子/10^k，再以 gcd 約成 5/4。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260925,"parameters":{"decimal":"1.25","scale":2,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"1.25\",\"operation\":\"decimal_to_fraction\",\"scale\":2}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0003","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 -2.4 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"-12/5","explanation_zh":"-2.4 依小數位數轉為整數分子/10^k，再以 gcd 約成 -12/5。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260926,"parameters":{"decimal":"-2.4","scale":1,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"-2.4\",\"operation\":\"decimal_to_fraction\",\"scale\":1}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0004","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 3.125 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"25/8","explanation_zh":"3.125 依小數位數轉為整數分子/10^k，再以 gcd 約成 25/8。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260927,"parameters":{"decimal":"3.125","scale":3,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"3.125\",\"operation\":\"decimal_to_fraction\",\"scale\":3}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0005","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 0.04 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"1/25","explanation_zh":"0.04 依小數位數轉為整數分子/10^k，再以 gcd 約成 1/25。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260928,"parameters":{"decimal":"0.04","scale":2,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"0.04\",\"operation\":\"decimal_to_fraction\",\"scale\":2}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0006","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 -0.75 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"-3/4","explanation_zh":"-0.75 依小數位數轉為整數分子/10^k，再以 gcd 約成 -3/4。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260929,"parameters":{"decimal":"-0.75","scale":2,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"-0.75\",\"operation\":\"decimal_to_fraction\",\"scale\":2}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0007","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 12.5 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"25/2","explanation_zh":"12.5 依小數位數轉為整數分子/10^k，再以 gcd 約成 25/2。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260930,"parameters":{"decimal":"12.5","scale":1,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"12.5\",\"operation\":\"decimal_to_fraction\",\"scale\":1}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0008","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 0.125 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"1/8","explanation_zh":"0.125 依小數位數轉為整數分子/10^k，再以 gcd 約成 1/8。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260931,"parameters":{"decimal":"0.125","scale":3,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"0.125\",\"operation\":\"decimal_to_fraction\",\"scale\":3}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0009","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 2.05 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"41/20","explanation_zh":"2.05 依小數位數轉為整數分子/10^k，再以 gcd 約成 41/20。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260932,"parameters":{"decimal":"2.05","scale":2,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"2.05\",\"operation\":\"decimal_to_fraction\",\"scale\":2}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0010","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 -1.2 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"-6/5","explanation_zh":"-1.2 依小數位數轉為整數分子/10^k，再以 gcd 約成 -6/5。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260933,"parameters":{"decimal":"-1.2","scale":1,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"-1.2\",\"operation\":\"decimal_to_fraction\",\"scale\":1}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0011","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 4.375 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"35/8","explanation_zh":"4.375 依小數位數轉為整數分子/10^k，再以 gcd 約成 35/8。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260934,"parameters":{"decimal":"4.375","scale":3,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"4.375\",\"operation\":\"decimal_to_fraction\",\"scale\":3}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0012","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 0.625 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"5/8","explanation_zh":"0.625 依小數位數轉為整數分子/10^k，再以 gcd 約成 5/8。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260935,"parameters":{"decimal":"0.625","scale":3,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"0.625\",\"operation\":\"decimal_to_fraction\",\"scale\":3}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0013","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 7.01 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"701/100","explanation_zh":"7.01 依小數位數轉為整數分子/10^k，再以 gcd 約成 701/100。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260936,"parameters":{"decimal":"7.01","scale":2,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"7.01\",\"operation\":\"decimal_to_fraction\",\"scale\":2}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0014","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 -3.5 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"-7/2","explanation_zh":"-3.5 依小數位數轉為整數分子/10^k，再以 gcd 約成 -7/2。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260937,"parameters":{"decimal":"-3.5","scale":1,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"-3.5\",\"operation\":\"decimal_to_fraction\",\"scale\":1}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0015","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 8.2 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"41/5","explanation_zh":"8.2 依小數位數轉為整數分子/10^k，再以 gcd 約成 41/5。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260938,"parameters":{"decimal":"8.2","scale":1,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"8.2\",\"operation\":\"decimal_to_fraction\",\"scale\":1}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0016","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 0.09 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"9/100","explanation_zh":"0.09 依小數位數轉為整數分子/10^k，再以 gcd 約成 9/100。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260939,"parameters":{"decimal":"0.09","scale":2,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"0.09\",\"operation\":\"decimal_to_fraction\",\"scale\":2}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0017","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 -0.01 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"-1/100","explanation_zh":"-0.01 依小數位數轉為整數分子/10^k，再以 gcd 約成 -1/100。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260940,"parameters":{"decimal":"-0.01","scale":2,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"-0.01\",\"operation\":\"decimal_to_fraction\",\"scale\":2}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0018","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 15.625 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"125/8","explanation_zh":"15.625 依小數位數轉為整數分子/10^k，再以 gcd 約成 125/8。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260941,"parameters":{"decimal":"15.625","scale":3,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"15.625\",\"operation\":\"decimal_to_fraction\",\"scale\":3}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0019","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 6.4 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"32/5","explanation_zh":"6.4 依小數位數轉為整數分子/10^k，再以 gcd 約成 32/5。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260942,"parameters":{"decimal":"6.4","scale":1,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"6.4\",\"operation\":\"decimal_to_fraction\",\"scale\":1}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0020","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 -9.08 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"-227/25","explanation_zh":"-9.08 依小數位數轉為整數分子/10^k，再以 gcd 約成 -227/25。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260943,"parameters":{"decimal":"-9.08","scale":2,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"-9.08\",\"operation\":\"decimal_to_fraction\",\"scale\":2}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0021","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 0.2 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"1/5","explanation_zh":"0.2 依小數位數轉為整數分子/10^k，再以 gcd 約成 1/5。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260944,"parameters":{"decimal":"0.2","scale":1,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"0.2\",\"operation\":\"decimal_to_fraction\",\"scale\":1}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0022","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 11.25 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"45/4","explanation_zh":"11.25 依小數位數轉為整數分子/10^k，再以 gcd 約成 45/4。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260945,"parameters":{"decimal":"11.25","scale":2,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"11.25\",\"operation\":\"decimal_to_fraction\",\"scale\":2}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0023","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 -4.125 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"-33/8","explanation_zh":"-4.125 依小數位數轉為整數分子/10^k，再以 gcd 約成 -33/8。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260946,"parameters":{"decimal":"-4.125","scale":3,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"-4.125\",\"operation\":\"decimal_to_fraction\",\"scale\":3}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0024","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 2.75 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"11/4","explanation_zh":"2.75 依小數位數轉為整數分子/10^k，再以 gcd 約成 11/4。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260947,"parameters":{"decimal":"2.75","scale":2,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"2.75\",\"operation\":\"decimal_to_fraction\",\"scale\":2}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-terminating-decimal-fraction-0025","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有限小數的精確分數","stem_zh":"把明示十進位字串 0.001 精確轉成最簡正分母分數；不得使用浮點近似。","answer":{"kind":"short_text","value":"1/1000","explanation_zh":"0.001 依小數位數轉為整數分子/10^k，再以 gcd 約成 1/1000。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有限小數","gcd"]},"variant":{"family_id":"qf-real-terminating-decimal-fraction","seed":20260948,"parameters":{"decimal":"0.001","scale":3,"operation":"decimal_to_fraction","semantic_template":"qf-real-terminating-decimal-fraction/{\"decimal\":\"0.001\",\"operation\":\"decimal_to_fraction\",\"scale\":3}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0001","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=-12/1、b=-6/1。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":"<","explanation_zh":"-12×1 < -6×1，故 -12/1 < -6/1。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261024,"parameters":{"left":[-12,1],"right":[-6,1],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[-12,1],\"operation\":\"cross_multiplication_order\",\"right\":[-6,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0002","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=-11/2、b=-5/2。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":"<","explanation_zh":"-11×2 < -5×2，故 -11/2 < -5/2。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261025,"parameters":{"left":[-11,2],"right":[-5,2],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[-11,2],\"operation\":\"cross_multiplication_order\",\"right\":[-5,2]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0003","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=-10/3、b=-4/3。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":"<","explanation_zh":"-10×3 < -4×3，故 -10/3 < -4/3。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261026,"parameters":{"left":[-10,3],"right":[-4,3],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[-10,3],\"operation\":\"cross_multiplication_order\",\"right\":[-4,3]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0004","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=-9/4、b=-3/4。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":"<","explanation_zh":"-9×4 < -3×4，故 -9/4 < -3/4。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261027,"parameters":{"left":[-9,4],"right":[-3,4],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[-9,4],\"operation\":\"cross_multiplication_order\",\"right\":[-3,4]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0005","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=-8/5、b=-2/5。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":"<","explanation_zh":"-8×5 < -2×5，故 -8/5 < -2/5。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261028,"parameters":{"left":[-8,5],"right":[-2,5],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[-8,5],\"operation\":\"cross_multiplication_order\",\"right\":[-2,5]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0006","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=-7/6、b=-1/1。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":"<","explanation_zh":"-7×1 < -1×6，故 -7/6 < -1/1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261029,"parameters":{"left":[-7,6],"right":[-1,1],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[-7,6],\"operation\":\"cross_multiplication_order\",\"right\":[-1,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0007","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=-6/7、b=0/1。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":"<","explanation_zh":"-6×1 < 0×7，故 -6/7 < 0/1。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261030,"parameters":{"left":[-6,7],"right":[0,1],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[-6,7],\"operation\":\"cross_multiplication_order\",\"right\":[0,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0008","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=-5/1、b=1/3。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":"<","explanation_zh":"-5×3 < 1×1，故 -5/1 < 1/3。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261031,"parameters":{"left":[-5,1],"right":[1,3],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[-5,1],\"operation\":\"cross_multiplication_order\",\"right\":[1,3]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0009","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=-2/1、b=1/2。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":"<","explanation_zh":"-2×2 < 1×1，故 -2/1 < 1/2。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261032,"parameters":{"left":[-2,1],"right":[1,2],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[-2,1],\"operation\":\"cross_multiplication_order\",\"right\":[1,2]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0010","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=-1/1、b=3/5。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":"<","explanation_zh":"-1×5 < 3×1，故 -1/1 < 3/5。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261033,"parameters":{"left":[-1,1],"right":[3,5],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[-1,1],\"operation\":\"cross_multiplication_order\",\"right\":[3,5]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0011","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=-1/2、b=4/1。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":"<","explanation_zh":"-1×1 < 4×2，故 -1/2 < 4/1。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261034,"parameters":{"left":[-1,2],"right":[4,1],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[-1,2],\"operation\":\"cross_multiplication_order\",\"right\":[4,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0012","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=-1/5、b=5/2。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":"<","explanation_zh":"-1×2 < 5×5，故 -1/5 < 5/2。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261035,"parameters":{"left":[-1,5],"right":[5,2],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[-1,5],\"operation\":\"cross_multiplication_order\",\"right\":[5,2]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0013","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=0/1、b=2/1。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":"<","explanation_zh":"0×1 < 2×1，故 0/1 < 2/1。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261036,"parameters":{"left":[0,1],"right":[2,1],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[0,1],\"operation\":\"cross_multiplication_order\",\"right\":[2,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0014","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=1/7、b=-3/2。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":">","explanation_zh":"1×2 > -3×7，故 1/7 > -3/2。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261037,"parameters":{"left":[1,7],"right":[-3,2],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[1,7],\"operation\":\"cross_multiplication_order\",\"right\":[-3,2]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0015","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=2/1、b=-1/1。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":">","explanation_zh":"2×1 > -1×1，故 2/1 > -1/1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261038,"parameters":{"left":[2,1],"right":[-1,1],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[2,1],\"operation\":\"cross_multiplication_order\",\"right\":[-1,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0016","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=3/2、b=-4/1。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":">","explanation_zh":"3×1 > -4×2，故 3/2 > -4/1。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261039,"parameters":{"left":[3,2],"right":[-4,1],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[3,2],\"operation\":\"cross_multiplication_order\",\"right\":[-4,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0017","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=4/3、b=-3/2。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":">","explanation_zh":"4×2 > -3×3，故 4/3 > -3/2。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261040,"parameters":{"left":[4,3],"right":[-3,2],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[4,3],\"operation\":\"cross_multiplication_order\",\"right\":[-3,2]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0018","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=5/4、b=-2/3。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":">","explanation_zh":"5×3 > -2×4，故 5/4 > -2/3。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261041,"parameters":{"left":[5,4],"right":[-2,3],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[5,4],\"operation\":\"cross_multiplication_order\",\"right\":[-2,3]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0019","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=6/5、b=-1/4。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":">","explanation_zh":"6×4 > -1×5，故 6/5 > -1/4。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261042,"parameters":{"left":[6,5],"right":[-1,4],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[6,5],\"operation\":\"cross_multiplication_order\",\"right\":[-1,4]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0020","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=7/6、b=0/1。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":">","explanation_zh":"7×1 > 0×6，故 7/6 > 0/1。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261043,"parameters":{"left":[7,6],"right":[0,1],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[7,6],\"operation\":\"cross_multiplication_order\",\"right\":[0,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0021","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=8/7、b=1/1。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":">","explanation_zh":"8×1 > 1×7，故 8/7 > 1/1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261044,"parameters":{"left":[8,7],"right":[1,1],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[8,7],\"operation\":\"cross_multiplication_order\",\"right\":[1,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0022","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=9/1、b=1/1。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":">","explanation_zh":"9×1 > 1×1，故 9/1 > 1/1。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261045,"parameters":{"left":[9,1],"right":[1,1],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[9,1],\"operation\":\"cross_multiplication_order\",\"right\":[1,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0023","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=5/1、b=1/1。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":">","explanation_zh":"5×1 > 1×1，故 5/1 > 1/1。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261046,"parameters":{"left":[5,1],"right":[1,1],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[5,1],\"operation\":\"cross_multiplication_order\",\"right\":[1,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0024","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=11/3、b=1/1。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":">","explanation_zh":"11×1 > 1×3，故 11/3 > 1/1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261047,"parameters":{"left":[11,3],"right":[1,1],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[11,3],\"operation\":\"cross_multiplication_order\",\"right\":[1,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-order-0025","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確排序","stem_zh":"有理點 a=3/1、b=1/1。用交叉乘積判斷 a 與 b 的關係（<、= 或 >）。","answer":{"kind":"short_text","value":">","explanation_zh":"3×1 > 1×1，故 3/1 > 1/1。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","交叉乘積"]},"variant":{"family_id":"qf-real-rational-order","seed":20261048,"parameters":{"left":[3,1],"right":[1,1],"operation":"cross_multiplication_order","semantic_template":"qf-real-rational-order/{\"left\":[3,1],\"operation\":\"cross_multiplication_order\",\"right\":[1,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0001","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [-12, -11] 與有理點 -12/1 均明示。-12/1 是否屬於此閉區間？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"-12≤-12/1≤-11 的精確交叉乘積判定為真；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261124,"parameters":{"a":-12,"b":-11,"point":[-12,1],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":-12,\"b\":-11,\"operation\":\"closed_interval\",\"point\":[-12,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0002","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [-11, -9] 與有理點 -5/1 均明示。-5/1 是否屬於此閉區間？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"-11≤-5/1≤-9 的精確交叉乘積判定為假；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261125,"parameters":{"a":-11,"b":-9,"point":[-5,1],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":-11,\"b\":-9,\"operation\":\"closed_interval\",\"point\":[-5,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0003","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [-10, -7] 與有理點 -8/3 均明示。-8/3 是否屬於此閉區間？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"-10≤-8/3≤-7 的精確交叉乘積判定為假；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261126,"parameters":{"a":-10,"b":-7,"point":[-8,3],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":-10,\"b\":-7,\"operation\":\"closed_interval\",\"point\":[-8,3]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0004","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [-9, -5] 與有理點 -3/2 均明示。-3/2 是否屬於此閉區間？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"-9≤-3/2≤-5 的精確交叉乘積判定為假；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261127,"parameters":{"a":-9,"b":-5,"point":[-3,2],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":-9,\"b\":-5,\"operation\":\"closed_interval\",\"point\":[-3,2]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0005","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [-8, -3] 與有理點 -4/1 均明示。-4/1 是否屬於此閉區間？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"-8≤-4/1≤-3 的精確交叉乘積判定為真；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261128,"parameters":{"a":-8,"b":-3,"point":[-4,1],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":-8,\"b\":-3,\"operation\":\"closed_interval\",\"point\":[-4,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0006","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [-7, -1] 與有理點 -1/1 均明示。-1/1 是否屬於此閉區間？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"-7≤-1/1≤-1 的精確交叉乘積判定為真；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261129,"parameters":{"a":-7,"b":-1,"point":[-1,1],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":-7,\"b\":-1,\"operation\":\"closed_interval\",\"point\":[-1,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0007","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [-6, -5] 與有理點 -2/1 均明示。-2/1 是否屬於此閉區間？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"-6≤-2/1≤-5 的精確交叉乘積判定為假；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261130,"parameters":{"a":-6,"b":-5,"point":[-2,1],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":-6,\"b\":-5,\"operation\":\"closed_interval\",\"point\":[-2,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0008","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [-5, -3] 與有理點 -1/1 均明示。-1/1 是否屬於此閉區間？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"-5≤-1/1≤-3 的精確交叉乘積判定為假；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261131,"parameters":{"a":-5,"b":-3,"point":[-1,1],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":-5,\"b\":-3,\"operation\":\"closed_interval\",\"point\":[-1,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0009","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [-4, -1] 與有理點 -4/1 均明示。-4/1 是否屬於此閉區間？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"-4≤-4/1≤-1 的精確交叉乘積判定為真；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261132,"parameters":{"a":-4,"b":-1,"point":[-4,1],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":-4,\"b\":-1,\"operation\":\"closed_interval\",\"point\":[-4,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0010","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [-3, 1] 與有理點 1/2 均明示。1/2 是否屬於此閉區間？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"-3≤1/2≤1 的精確交叉乘積判定為真；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261133,"parameters":{"a":-3,"b":1,"point":[1,2],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":-3,\"b\":1,\"operation\":\"closed_interval\",\"point\":[1,2]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0011","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [-2, 3] 與有理點 2/3 均明示。2/3 是否屬於此閉區間？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"-2≤2/3≤3 的精確交叉乘積判定為真；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261134,"parameters":{"a":-2,"b":3,"point":[2,3],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":-2,\"b\":3,\"operation\":\"closed_interval\",\"point\":[2,3]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0012","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [-1, 5] 與有理點 3/4 均明示。3/4 是否屬於此閉區間？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"-1≤3/4≤5 的精確交叉乘積判定為真；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261135,"parameters":{"a":-1,"b":5,"point":[3,4],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":-1,\"b\":5,\"operation\":\"closed_interval\",\"point\":[3,4]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0013","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [0, 1] 與有理點 0/1 均明示。0/1 是否屬於此閉區間？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"0≤0/1≤1 的精確交叉乘積判定為真；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261136,"parameters":{"a":0,"b":1,"point":[0,1],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":0,\"b\":1,\"operation\":\"closed_interval\",\"point\":[0,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0014","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [1, 3] 與有理點 1/1 均明示。1/1 是否屬於此閉區間？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"1≤1/1≤3 的精確交叉乘積判定為真；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261137,"parameters":{"a":1,"b":3,"point":[1,1],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":1,\"b\":3,\"operation\":\"closed_interval\",\"point\":[1,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0015","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [2, 5] 與有理點 4/3 均明示。4/3 是否屬於此閉區間？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"2≤4/3≤5 的精確交叉乘積判定為假；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261138,"parameters":{"a":2,"b":5,"point":[4,3],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":2,\"b\":5,\"operation\":\"closed_interval\",\"point\":[4,3]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0016","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [3, 7] 與有理點 3/4 均明示。3/4 是否屬於此閉區間？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"3≤3/4≤7 的精確交叉乘積判定為假；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261139,"parameters":{"a":3,"b":7,"point":[3,4],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":3,\"b\":7,\"operation\":\"closed_interval\",\"point\":[3,4]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0017","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [4, 9] 與有理點 8/1 均明示。8/1 是否屬於此閉區間？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"4≤8/1≤9 的精確交叉乘積判定為真；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261140,"parameters":{"a":4,"b":9,"point":[8,1],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":4,\"b\":9,\"operation\":\"closed_interval\",\"point\":[8,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0018","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [5, 11] 與有理點 4/1 均明示。4/1 是否屬於此閉區間？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"5≤4/1≤11 的精確交叉乘積判定為假；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261141,"parameters":{"a":5,"b":11,"point":[4,1],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":5,\"b\":11,\"operation\":\"closed_interval\",\"point\":[4,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0019","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [6, 7] 與有理點 2/1 均明示。2/1 是否屬於此閉區間？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"6≤2/1≤7 的精確交叉乘積判定為假；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261142,"parameters":{"a":6,"b":7,"point":[2,1],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":6,\"b\":7,\"operation\":\"closed_interval\",\"point\":[2,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0020","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [7, 9] 與有理點 2/1 均明示。2/1 是否屬於此閉區間？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"7≤2/1≤9 的精確交叉乘積判定為假；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261143,"parameters":{"a":7,"b":9,"point":[2,1],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":7,\"b\":9,\"operation\":\"closed_interval\",\"point\":[2,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0021","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [8, 11] 與有理點 8/1 均明示。8/1 是否屬於此閉區間？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"8≤8/1≤11 的精確交叉乘積判定為真；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261144,"parameters":{"a":8,"b":11,"point":[8,1],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":8,\"b\":11,\"operation\":\"closed_interval\",\"point\":[8,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0022","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [9, 13] 與有理點 5/1 均明示。5/1 是否屬於此閉區間？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"9≤5/1≤13 的精確交叉乘積判定為假；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261145,"parameters":{"a":9,"b":13,"point":[5,1],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":9,\"b\":13,\"operation\":\"closed_interval\",\"point\":[5,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0023","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [10, 15] 與有理點 14/3 均明示。14/3 是否屬於此閉區間？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"10≤14/3≤15 的精確交叉乘積判定為假；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261146,"parameters":{"a":10,"b":15,"point":[14,3],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":10,\"b\":15,\"operation\":\"closed_interval\",\"point\":[14,3]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0024","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [11, 17] 與有理點 13/4 均明示。13/4 是否屬於此閉區間？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"11≤13/4≤17 的精確交叉乘積判定為假；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261147,"parameters":{"a":11,"b":17,"point":[13,4],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":11,\"b\":17,\"operation\":\"closed_interval\",\"point\":[13,4]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-closed-interval-0025","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"閉區間中的有理點","stem_zh":"閉區間 [12, 13] 與有理點 12/1 均明示。12/1 是否屬於此閉區間？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"12≤12/1≤13 的精確交叉乘積判定為真；端點相等時仍屬於閉區間。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["閉區間","有理數比較"]},"variant":{"family_id":"qf-real-rational-closed-interval","seed":20261148,"parameters":{"a":12,"b":13,"point":[12,1],"operation":"closed_interval","semantic_template":"qf-real-rational-closed-interval/{\"a\":12,\"b\":13,\"operation\":\"closed_interval\",\"point\":[12,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0001","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 -10/1 與 12/1。求精確距離 |-10/1−12/1| 的最簡分數。","answer":{"kind":"short_text","value":"22/1","explanation_zh":"|-10/1−12/1|=22/1；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261224,"parameters":{"left":[-10,1],"right":[12,1],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[-10,1],\"operation\":\"exact_rational_distance\",\"right\":[12,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0002","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 -9/2 與 11/2。求精確距離 |-9/2−11/2| 的最簡分數。","answer":{"kind":"short_text","value":"10/1","explanation_zh":"|-9/2−11/2|=10/1；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261225,"parameters":{"left":[-9,2],"right":[11,2],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[-9,2],\"operation\":\"exact_rational_distance\",\"right\":[11,2]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0003","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 -8/3 與 10/3。求精確距離 |-8/3−10/3| 的最簡分數。","answer":{"kind":"short_text","value":"6/1","explanation_zh":"|-8/3−10/3|=6/1；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261226,"parameters":{"left":[-8,3],"right":[10,3],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[-8,3],\"operation\":\"exact_rational_distance\",\"right\":[10,3]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0004","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 -7/4 與 9/4。求精確距離 |-7/4−9/4| 的最簡分數。","answer":{"kind":"short_text","value":"4/1","explanation_zh":"|-7/4−9/4|=4/1；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261227,"parameters":{"left":[-7,4],"right":[9,4],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[-7,4],\"operation\":\"exact_rational_distance\",\"right\":[9,4]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0005","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 -6/5 與 8/5。求精確距離 |-6/5−8/5| 的最簡分數。","answer":{"kind":"short_text","value":"14/5","explanation_zh":"|-6/5−8/5|=14/5；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261228,"parameters":{"left":[-6,5],"right":[8,5],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[-6,5],\"operation\":\"exact_rational_distance\",\"right\":[8,5]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0006","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 -5/1 與 7/6。求精確距離 |-5/1−7/6| 的最簡分數。","answer":{"kind":"short_text","value":"37/6","explanation_zh":"|-5/1−7/6|=37/6；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261229,"parameters":{"left":[-5,1],"right":[7,6],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[-5,1],\"operation\":\"exact_rational_distance\",\"right\":[7,6]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0007","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 -2/1 與 6/7。求精確距離 |-2/1−6/7| 的最簡分數。","answer":{"kind":"short_text","value":"20/7","explanation_zh":"|-2/1−6/7|=20/7；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261230,"parameters":{"left":[-2,1],"right":[6,7],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[-2,1],\"operation\":\"exact_rational_distance\",\"right\":[6,7]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0008","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 -1/1 與 5/1。求精確距離 |-1/1−5/1| 的最簡分數。","answer":{"kind":"short_text","value":"6/1","explanation_zh":"|-1/1−5/1|=6/1；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261231,"parameters":{"left":[-1,1],"right":[5,1],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[-1,1],\"operation\":\"exact_rational_distance\",\"right\":[5,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0009","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 -1/2 與 2/1。求精確距離 |-1/2−2/1| 的最簡分數。","answer":{"kind":"short_text","value":"5/2","explanation_zh":"|-1/2−2/1|=5/2；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261232,"parameters":{"left":[-1,2],"right":[2,1],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[-1,2],\"operation\":\"exact_rational_distance\",\"right\":[2,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0010","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 -1/5 與 1/1。求精確距離 |-1/5−1/1| 的最簡分數。","answer":{"kind":"short_text","value":"6/5","explanation_zh":"|-1/5−1/1|=6/5；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261233,"parameters":{"left":[-1,5],"right":[1,1],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[-1,5],\"operation\":\"exact_rational_distance\",\"right\":[1,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0011","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 0/1 與 1/2。求精確距離 |0/1−1/2| 的最簡分數。","answer":{"kind":"short_text","value":"1/2","explanation_zh":"|0/1−1/2|=1/2；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261234,"parameters":{"left":[0,1],"right":[1,2],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[0,1],\"operation\":\"exact_rational_distance\",\"right\":[1,2]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0012","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 1/2 與 1/5。求精確距離 |1/2−1/5| 的最簡分數。","answer":{"kind":"short_text","value":"3/10","explanation_zh":"|1/2−1/5|=3/10；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261235,"parameters":{"left":[1,2],"right":[1,5],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[1,2],\"operation\":\"exact_rational_distance\",\"right\":[1,5]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0013","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 2/3 與 0/1。求精確距離 |2/3−0/1| 的最簡分數。","answer":{"kind":"short_text","value":"2/3","explanation_zh":"|2/3−0/1|=2/3；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261236,"parameters":{"left":[2,3],"right":[0,1],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[2,3],\"operation\":\"exact_rational_distance\",\"right\":[0,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0014","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 3/4 與 -1/7。求精確距離 |3/4−-1/7| 的最簡分數。","answer":{"kind":"short_text","value":"25/28","explanation_zh":"|3/4−-1/7|=25/28；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261237,"parameters":{"left":[3,4],"right":[-1,7],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[3,4],\"operation\":\"exact_rational_distance\",\"right\":[-1,7]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0015","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 4/5 與 -2/1。求精確距離 |4/5−-2/1| 的最簡分數。","answer":{"kind":"short_text","value":"14/5","explanation_zh":"|4/5−-2/1|=14/5；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261238,"parameters":{"left":[4,5],"right":[-2,1],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[4,5],\"operation\":\"exact_rational_distance\",\"right\":[-2,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0016","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 5/1 與 -3/2。求精確距離 |5/1−-3/2| 的最簡分數。","answer":{"kind":"short_text","value":"13/2","explanation_zh":"|5/1−-3/2|=13/2；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261239,"parameters":{"left":[5,1],"right":[-3,2],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[5,1],\"operation\":\"exact_rational_distance\",\"right\":[-3,2]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0017","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 3/1 與 -4/3。求精確距離 |3/1−-4/3| 的最簡分數。","answer":{"kind":"short_text","value":"13/3","explanation_zh":"|3/1−-4/3|=13/3；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261240,"parameters":{"left":[3,1],"right":[-4,3],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[3,1],\"operation\":\"exact_rational_distance\",\"right\":[-4,3]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0018","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 7/3 與 -5/4。求精確距離 |7/3−-5/4| 的最簡分數。","answer":{"kind":"short_text","value":"43/12","explanation_zh":"|7/3−-5/4|=43/12；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261241,"parameters":{"left":[7,3],"right":[-5,4],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[7,3],\"operation\":\"exact_rational_distance\",\"right\":[-5,4]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0019","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 2/1 與 -6/5。求精確距離 |2/1−-6/5| 的最簡分數。","answer":{"kind":"short_text","value":"16/5","explanation_zh":"|2/1−-6/5|=16/5；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261242,"parameters":{"left":[2,1],"right":[-6,5],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[2,1],\"operation\":\"exact_rational_distance\",\"right\":[-6,5]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0020","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 9/5 與 -7/6。求精確距離 |9/5−-7/6| 的最簡分數。","answer":{"kind":"short_text","value":"89/30","explanation_zh":"|9/5−-7/6|=89/30；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261243,"parameters":{"left":[9,5],"right":[-7,6],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[9,5],\"operation\":\"exact_rational_distance\",\"right\":[-7,6]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0021","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 10/1 與 -8/7。求精確距離 |10/1−-8/7| 的最簡分數。","answer":{"kind":"short_text","value":"78/7","explanation_zh":"|10/1−-8/7|=78/7；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261244,"parameters":{"left":[10,1],"right":[-8,7],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[10,1],\"operation\":\"exact_rational_distance\",\"right\":[-8,7]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0022","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 11/2 與 -9/1。求精確距離 |11/2−-9/1| 的最簡分數。","answer":{"kind":"short_text","value":"29/2","explanation_zh":"|11/2−-9/1|=29/2；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261245,"parameters":{"left":[11,2],"right":[-9,1],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[11,2],\"operation\":\"exact_rational_distance\",\"right\":[-9,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0023","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 4/1 與 -5/1。求精確距離 |4/1−-5/1| 的最簡分數。","answer":{"kind":"short_text","value":"9/1","explanation_zh":"|4/1−-5/1|=9/1；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261246,"parameters":{"left":[4,1],"right":[-5,1],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[4,1],\"operation\":\"exact_rational_distance\",\"right\":[-5,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0024","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 13/4 與 -11/3。求精確距離 |13/4−-11/3| 的最簡分數。","answer":{"kind":"short_text","value":"83/12","explanation_zh":"|13/4−-11/3|=83/12；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261247,"parameters":{"left":[13,4],"right":[-11,3],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[13,4],\"operation\":\"exact_rational_distance\",\"right\":[-11,3]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260923-real-rational-point-distance-0025","batch_id":"batch-20260923-real-number-rational-points","language":"zh-Hant","source_mko_ids":["mko-real-number"],"title_zh":"有理點的精確距離","stem_zh":"兩個有理實數點為 14/5 與 -3/1。求精確距離 |14/5−-3/1| 的最簡分數。","answer":{"kind":"short_text","value":"29/5","explanation_zh":"|14/5−-3/1|=29/5；以整數分子分母精確相減並取絕對值。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","絕對差"]},"variant":{"family_id":"qf-real-rational-point-distance","seed":20261248,"parameters":{"left":[14,5],"right":[-3,1],"operation":"exact_rational_distance","semantic_template":"qf-real-rational-point-distance/{\"left\":[14,5],\"operation\":\"exact_rational_distance\",\"right\":[-3,1]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-23","contract_version":"ocme-question-factory-v0.1"}}