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{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-denominator-sign-normalization-0011","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-denominator-sign-normalization","stem_zh":"將 -2/-2 正規化為分母為正的精確表示。","answer":{"kind":"short_text","value":"2/2","explanation_zh":"q=-2 為負，只將負號移到分子，得到 2/2；比值未改變，未做 gcd 約分或最簡化。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["分母符號正規化"]},"variant":{"family_id":"qf-rational-denominator-sign-normalization","seed":20261031,"parameters":{"p":-2,"q":-2,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":-2,\"q\":-2}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-denominator-sign-normalization-0012","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-denominator-sign-normalization","stem_zh":"將 -1/-3 正規化為分母為正的精確表示。","answer":{"kind":"short_text","value":"1/3","explanation_zh":"q=-3 為負，只將負號移到分子，得到 1/3；比值未改變，未做 gcd 約分或最簡化。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["分母符號正規化"]},"variant":{"family_id":"qf-rational-denominator-sign-normalization","seed":20261032,"parameters":{"p":-1,"q":-3,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":-1,\"q\":-3}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-denominator-sign-normalization-0013","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-denominator-sign-normalization","stem_zh":"將 0/-4 正規化為分母為正的精確表示。","answer":{"kind":"short_text","value":"0/4","explanation_zh":"q=-4 為負，只將負號移到分子，得到 0/4；比值未改變，未做 gcd 約分或最簡化。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["分母符號正規化"]},"variant":{"family_id":"qf-rational-denominator-sign-normalization","seed":20261033,"parameters":{"p":0,"q":-4,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":0,\"q\":-4}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-denominator-sign-normalization-0014","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-denominator-sign-normalization","stem_zh":"將 1/-5 正規化為分母為正的精確表示。","answer":{"kind":"short_text","value":"-1/5","explanation_zh":"q=-5 為負，只將負號移到分子，得到 -1/5；比值未改變，未做 gcd 約分或最簡化。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["分母符號正規化"]},"variant":{"family_id":"qf-rational-denominator-sign-normalization","seed":20261034,"parameters":{"p":1,"q":-5,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":1,\"q\":-5}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-denominator-sign-normalization-0015","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-denominator-sign-normalization","stem_zh":"將 2/-6 正規化為分母為正的精確表示。","answer":{"kind":"short_text","value":"-2/6","explanation_zh":"q=-6 為負，只將負號移到分子，得到 -2/6；比值未改變，未做 gcd 約分或最簡化。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["分母符號正規化"]},"variant":{"family_id":"qf-rational-denominator-sign-normalization","seed":20261035,"parameters":{"p":2,"q":-6,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":2,\"q\":-6}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-denominator-sign-normalization-0016","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-denominator-sign-normalization","stem_zh":"將 3/-7 正規化為分母為正的精確表示。","answer":{"kind":"short_text","value":"-3/7","explanation_zh":"q=-7 為負，只將負號移到分子，得到 -3/7；比值未改變，未做 gcd 約分或最簡化。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["分母符號正規化"]},"variant":{"family_id":"qf-rational-denominator-sign-normalization","seed":20261036,"parameters":{"p":3,"q":-7,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":3,\"q\":-7}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-denominator-sign-normalization-0017","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-denominator-sign-normalization","stem_zh":"將 4/-8 正規化為分母為正的精確表示。","answer":{"kind":"short_text","value":"-4/8","explanation_zh":"q=-8 為負，只將負號移到分子，得到 -4/8；比值未改變，未做 gcd 約分或最簡化。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["分母符號正規化"]},"variant":{"family_id":"qf-rational-denominator-sign-normalization","seed":20261037,"parameters":{"p":4,"q":-8,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":4,\"q\":-8}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-denominator-sign-normalization-0018","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-denominator-sign-normalization","stem_zh":"將 5/-9 正規化為分母為正的精確表示。","answer":{"kind":"short_text","value":"-5/9","explanation_zh":"q=-9 為負，只將負號移到分子，得到 -5/9；比值未改變，未做 gcd 約分或最簡化。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["分母符號正規化"]},"variant":{"family_id":"qf-rational-denominator-sign-normalization","seed":20261038,"parameters":{"p":5,"q":-9,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":5,\"q\":-9}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-denominator-sign-normalization-0019","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-denominator-sign-normalization","stem_zh":"將 6/-1 正規化為分母為正的精確表示。","answer":{"kind":"short_text","value":"-6/1","explanation_zh":"q=-1 為負，只將負號移到分子，得到 -6/1；比值未改變，未做 gcd 約分或最簡化。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["分母符號正規化"]},"variant":{"family_id":"qf-rational-denominator-sign-normalization","seed":20261039,"parameters":{"p":6,"q":-1,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":6,\"q\":-1}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-denominator-sign-normalization-0020","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-denominator-sign-normalization","stem_zh":"將 7/-2 正規化為分母為正的精確表示。","answer":{"kind":"short_text","value":"-7/2","explanation_zh":"q=-2 為負，只將負號移到分子，得到 -7/2；比值未改變，未做 gcd 約分或最簡化。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["分母符號正規化"]},"variant":{"family_id":"qf-rational-denominator-sign-normalization","seed":20261040,"parameters":{"p":7,"q":-2,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":7,\"q\":-2}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-denominator-sign-normalization-0021","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-denominator-sign-normalization","stem_zh":"將 8/-3 正規化為分母為正的精確表示。","answer":{"kind":"short_text","value":"-8/3","explanation_zh":"q=-3 為負，只將負號移到分子，得到 -8/3；比值未改變，未做 gcd 約分或最簡化。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["分母符號正規化"]},"variant":{"family_id":"qf-rational-denominator-sign-normalization","seed":20261041,"parameters":{"p":8,"q":-3,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":8,\"q\":-3}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-denominator-sign-normalization-0022","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-denominator-sign-normalization","stem_zh":"將 9/-4 正規化為分母為正的精確表示。","answer":{"kind":"short_text","value":"-9/4","explanation_zh":"q=-4 為負，只將負號移到分子，得到 -9/4；比值未改變，未做 gcd 約分或最簡化。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["分母符號正規化"]},"variant":{"family_id":"qf-rational-denominator-sign-normalization","seed":20261042,"parameters":{"p":9,"q":-4,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":9,\"q\":-4}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-denominator-sign-normalization-0023","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-denominator-sign-normalization","stem_zh":"將 10/-5 正規化為分母為正的精確表示。","answer":{"kind":"short_text","value":"-10/5","explanation_zh":"q=-5 為負，只將負號移到分子，得到 -10/5；比值未改變，未做 gcd 約分或最簡化。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["分母符號正規化"]},"variant":{"family_id":"qf-rational-denominator-sign-normalization","seed":20261043,"parameters":{"p":10,"q":-5,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":10,\"q\":-5}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-denominator-sign-normalization-0024","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-denominator-sign-normalization","stem_zh":"將 11/-6 正規化為分母為正的精確表示。","answer":{"kind":"short_text","value":"-11/6","explanation_zh":"q=-6 為負，只將負號移到分子，得到 -11/6；比值未改變，未做 gcd 約分或最簡化。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["分母符號正規化"]},"variant":{"family_id":"qf-rational-denominator-sign-normalization","seed":20261044,"parameters":{"p":11,"q":-6,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":11,\"q\":-6}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-denominator-sign-normalization-0025","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-denominator-sign-normalization","stem_zh":"將 12/-7 正規化為分母為正的精確表示。","answer":{"kind":"short_text","value":"-12/7","explanation_zh":"q=-7 為負，只將負號移到分子，得到 -12/7；比值未改變，未做 gcd 約分或最簡化。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["分母符號正規化"]},"variant":{"family_id":"qf-rational-denominator-sign-normalization","seed":20261045,"parameters":{"p":12,"q":-7,"semantic_template":"qf-rational-denominator-sign-normalization/{\"p\":12,\"q\":-7}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0001","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=1、s=2 均非零。-11/1 與 -22/2 是否等值？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"-11×2=-22×1，故兩分數等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261121,"parameters":{"p":-11,"q":1,"r":-22,"s":2,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":-11,\"q\":1,\"r\":-22,\"s\":2}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0002","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=2、s=4 均非零。-10/2 與 -19/4 是否等值？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"-10×4≠-19×2，故兩分數不等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261122,"parameters":{"p":-10,"q":2,"r":-19,"s":4,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":-10,\"q\":2,\"r\":-19,\"s\":4}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0003","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=3、s=6 均非零。-9/3 與 -18/6 是否等值？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"-9×6=-18×3，故兩分數等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261123,"parameters":{"p":-9,"q":3,"r":-18,"s":6,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":-9,\"q\":3,\"r\":-18,\"s\":6}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0004","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=4、s=8 均非零。-8/4 與 -15/8 是否等值？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"-8×8≠-15×4，故兩分數不等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261124,"parameters":{"p":-8,"q":4,"r":-15,"s":8,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":-8,\"q\":4,\"r\":-15,\"s\":8}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0005","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=5、s=10 均非零。-7/5 與 -14/10 是否等值？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"-7×10=-14×5，故兩分數等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261125,"parameters":{"p":-7,"q":5,"r":-14,"s":10,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":-7,\"q\":5,\"r\":-14,\"s\":10}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0006","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=6、s=12 均非零。-6/6 與 -11/12 是否等值？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"-6×12≠-11×6，故兩分數不等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261126,"parameters":{"p":-6,"q":6,"r":-11,"s":12,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":-6,\"q\":6,\"r\":-11,\"s\":12}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0007","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=7、s=14 均非零。-5/7 與 -10/14 是否等值？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"-5×14=-10×7，故兩分數等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261127,"parameters":{"p":-5,"q":7,"r":-10,"s":14,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":-5,\"q\":7,\"r\":-10,\"s\":14}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0008","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=1、s=2 均非零。-4/1 與 -7/2 是否等值？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"-4×2≠-7×1，故兩分數不等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261128,"parameters":{"p":-4,"q":1,"r":-7,"s":2,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":-4,\"q\":1,\"r\":-7,\"s\":2}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0009","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=2、s=4 均非零。-3/2 與 -6/4 是否等值？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"-3×4=-6×2，故兩分數等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261129,"parameters":{"p":-3,"q":2,"r":-6,"s":4,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":-3,\"q\":2,\"r\":-6,\"s\":4}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0010","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=3、s=6 均非零。-2/3 與 -3/6 是否等值？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"-2×6≠-3×3，故兩分數不等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261130,"parameters":{"p":-2,"q":3,"r":-3,"s":6,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":-2,\"q\":3,\"r\":-3,\"s\":6}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0011","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=4、s=8 均非零。-1/4 與 -2/8 是否等值？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"-1×8=-2×4，故兩分數等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261131,"parameters":{"p":-1,"q":4,"r":-2,"s":8,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":-1,\"q\":4,\"r\":-2,\"s\":8}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0012","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=5、s=10 均非零。0/5 與 1/10 是否等值？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"0×10≠1×5，故兩分數不等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261132,"parameters":{"p":0,"q":5,"r":1,"s":10,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":0,\"q\":5,\"r\":1,\"s\":10}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0013","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=6、s=12 均非零。1/6 與 2/12 是否等值？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"1×12=2×6，故兩分數等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261133,"parameters":{"p":1,"q":6,"r":2,"s":12,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":1,\"q\":6,\"r\":2,\"s\":12}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0014","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=7、s=14 均非零。2/7 與 5/14 是否等值？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"2×14≠5×7，故兩分數不等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261134,"parameters":{"p":2,"q":7,"r":5,"s":14,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":2,\"q\":7,\"r\":5,\"s\":14}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0015","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=1、s=2 均非零。3/1 與 6/2 是否等值？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"3×2=6×1，故兩分數等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261135,"parameters":{"p":3,"q":1,"r":6,"s":2,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":3,\"q\":1,\"r\":6,\"s\":2}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0016","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=2、s=4 均非零。4/2 與 9/4 是否等值？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"4×4≠9×2，故兩分數不等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261136,"parameters":{"p":4,"q":2,"r":9,"s":4,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":4,\"q\":2,\"r\":9,\"s\":4}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0017","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=3、s=6 均非零。5/3 與 10/6 是否等值？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"5×6=10×3，故兩分數等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261137,"parameters":{"p":5,"q":3,"r":10,"s":6,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":5,\"q\":3,\"r\":10,\"s\":6}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0018","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=4、s=8 均非零。6/4 與 13/8 是否等值？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"6×8≠13×4，故兩分數不等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261138,"parameters":{"p":6,"q":4,"r":13,"s":8,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":6,\"q\":4,\"r\":13,\"s\":8}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0019","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=5、s=10 均非零。7/5 與 14/10 是否等值？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"7×10=14×5，故兩分數等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261139,"parameters":{"p":7,"q":5,"r":14,"s":10,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":7,\"q\":5,\"r\":14,\"s\":10}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0020","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=6、s=12 均非零。8/6 與 17/12 是否等值？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"8×12≠17×6，故兩分數不等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261140,"parameters":{"p":8,"q":6,"r":17,"s":12,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":8,\"q\":6,\"r\":17,\"s\":12}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0021","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=7、s=14 均非零。9/7 與 18/14 是否等值？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"9×14=18×7，故兩分數等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261141,"parameters":{"p":9,"q":7,"r":18,"s":14,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":9,\"q\":7,\"r\":18,\"s\":14}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0022","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=1、s=2 均非零。10/1 與 21/2 是否等值？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"10×2≠21×1，故兩分數不等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261142,"parameters":{"p":10,"q":1,"r":21,"s":2,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":10,\"q\":1,\"r\":21,\"s\":2}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0023","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=2、s=4 均非零。11/2 與 22/4 是否等值？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"11×4=22×2，故兩分數等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261143,"parameters":{"p":11,"q":2,"r":22,"s":4,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":11,\"q\":2,\"r\":22,\"s\":4}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0024","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=3、s=6 均非零。12/3 與 25/6 是否等值？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"12×6≠25×3，故兩分數不等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261144,"parameters":{"p":12,"q":3,"r":25,"s":6,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":12,\"q\":3,\"r\":25,\"s\":6}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-equivalent-fractions-0025","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-equivalent-fractions","stem_zh":"分母 q=4、s=8 均非零。13/4 與 26/8 是否等值？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"13×8=26×4，故兩分數等值；不以字面外觀或小數近似判定。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["交叉乘積","等值分數"]},"variant":{"family_id":"qf-rational-equivalent-fractions","seed":20261145,"parameters":{"p":13,"q":4,"r":26,"s":8,"semantic_template":"qf-rational-equivalent-fractions/{\"p\":13,\"q\":4,\"r\":26,\"s\":8}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0001","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 0/12 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"0/1","explanation_zh":"p=0 的 canonical reduced form 為 0/1。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261221,"parameters":{"p":0,"q":12,"semantic_template":"qf-rational-reduced-form/{\"p\":0,\"q\":12}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0002","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 -12/8 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"-3/2","explanation_zh":"gcd(|-12|,|8|)=4，約分後為 -3/2。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261222,"parameters":{"p":-12,"q":8,"semantic_template":"qf-rational-reduced-form/{\"p\":-12,\"q\":8}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0003","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 27/12 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"9/4","explanation_zh":"gcd(|27|,|12|)=3，約分後為 9/4。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261223,"parameters":{"p":27,"q":12,"semantic_template":"qf-rational-reduced-form/{\"p\":27,\"q\":12}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0004","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 -24/8 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"-3/1","explanation_zh":"gcd(|-24|,|8|)=8，約分後為 -3/1。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261224,"parameters":{"p":-24,"q":8,"semantic_template":"qf-rational-reduced-form/{\"p\":-24,\"q\":8}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0005","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 45/12 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"15/4","explanation_zh":"gcd(|45|,|12|)=3，約分後為 15/4。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261225,"parameters":{"p":45,"q":12,"semantic_template":"qf-rational-reduced-form/{\"p\":45,\"q\":12}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0006","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 -36/8 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"-9/2","explanation_zh":"gcd(|-36|,|8|)=4，約分後為 -9/2。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261226,"parameters":{"p":-36,"q":8,"semantic_template":"qf-rational-reduced-form/{\"p\":-36,\"q\":8}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0007","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 63/12 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"21/4","explanation_zh":"gcd(|63|,|12|)=3，約分後為 21/4。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261227,"parameters":{"p":63,"q":12,"semantic_template":"qf-rational-reduced-form/{\"p\":63,\"q\":12}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0008","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 -48/8 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"-6/1","explanation_zh":"gcd(|-48|,|8|)=8，約分後為 -6/1。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261228,"parameters":{"p":-48,"q":8,"semantic_template":"qf-rational-reduced-form/{\"p\":-48,\"q\":8}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0009","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 81/12 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"27/4","explanation_zh":"gcd(|81|,|12|)=3，約分後為 27/4。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261229,"parameters":{"p":81,"q":12,"semantic_template":"qf-rational-reduced-form/{\"p\":81,\"q\":12}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0010","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 -60/8 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"-15/2","explanation_zh":"gcd(|-60|,|8|)=4，約分後為 -15/2。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261230,"parameters":{"p":-60,"q":8,"semantic_template":"qf-rational-reduced-form/{\"p\":-60,\"q\":8}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0011","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 99/12 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"33/4","explanation_zh":"gcd(|99|,|12|)=3，約分後為 33/4。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261231,"parameters":{"p":99,"q":12,"semantic_template":"qf-rational-reduced-form/{\"p\":99,\"q\":12}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0012","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 -72/8 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"-9/1","explanation_zh":"gcd(|-72|,|8|)=8，約分後為 -9/1。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261232,"parameters":{"p":-72,"q":8,"semantic_template":"qf-rational-reduced-form/{\"p\":-72,\"q\":8}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0013","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 117/12 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"39/4","explanation_zh":"gcd(|117|,|12|)=3，約分後為 39/4。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261233,"parameters":{"p":117,"q":12,"semantic_template":"qf-rational-reduced-form/{\"p\":117,\"q\":12}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0014","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 -84/8 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"-21/2","explanation_zh":"gcd(|-84|,|8|)=4，約分後為 -21/2。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261234,"parameters":{"p":-84,"q":8,"semantic_template":"qf-rational-reduced-form/{\"p\":-84,\"q\":8}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0015","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 135/12 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"45/4","explanation_zh":"gcd(|135|,|12|)=3，約分後為 45/4。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261235,"parameters":{"p":135,"q":12,"semantic_template":"qf-rational-reduced-form/{\"p\":135,\"q\":12}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0016","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 -96/8 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"-12/1","explanation_zh":"gcd(|-96|,|8|)=8，約分後為 -12/1。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261236,"parameters":{"p":-96,"q":8,"semantic_template":"qf-rational-reduced-form/{\"p\":-96,\"q\":8}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0017","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 153/12 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"51/4","explanation_zh":"gcd(|153|,|12|)=3，約分後為 51/4。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261237,"parameters":{"p":153,"q":12,"semantic_template":"qf-rational-reduced-form/{\"p\":153,\"q\":12}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0018","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 -108/8 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"-27/2","explanation_zh":"gcd(|-108|,|8|)=4，約分後為 -27/2。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261238,"parameters":{"p":-108,"q":8,"semantic_template":"qf-rational-reduced-form/{\"p\":-108,\"q\":8}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0019","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 171/12 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"57/4","explanation_zh":"gcd(|171|,|12|)=3，約分後為 57/4。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261239,"parameters":{"p":171,"q":12,"semantic_template":"qf-rational-reduced-form/{\"p\":171,\"q\":12}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0020","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 -120/8 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"-15/1","explanation_zh":"gcd(|-120|,|8|)=8，約分後為 -15/1。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261240,"parameters":{"p":-120,"q":8,"semantic_template":"qf-rational-reduced-form/{\"p\":-120,\"q\":8}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0021","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 189/12 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"63/4","explanation_zh":"gcd(|189|,|12|)=3，約分後為 63/4。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261241,"parameters":{"p":189,"q":12,"semantic_template":"qf-rational-reduced-form/{\"p\":189,\"q\":12}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0022","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 -132/8 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"-33/2","explanation_zh":"gcd(|-132|,|8|)=4，約分後為 -33/2。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261242,"parameters":{"p":-132,"q":8,"semantic_template":"qf-rational-reduced-form/{\"p\":-132,\"q\":8}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0023","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 207/12 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"69/4","explanation_zh":"gcd(|207|,|12|)=3，約分後為 69/4。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261243,"parameters":{"p":207,"q":12,"semantic_template":"qf-rational-reduced-form/{\"p\":207,\"q\":12}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0024","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 -144/8 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"-18/1","explanation_zh":"gcd(|-144|,|8|)=8，約分後為 -18/1。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261244,"parameters":{"p":-144,"q":8,"semantic_template":"qf-rational-reduced-form/{\"p\":-144,\"q\":8}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260920-rational-reduced-form-0025","batch_id":"batch-20260920-rational-number-foundations","language":"zh-Hant","source_mko_ids":["mko-rational-number"],"title_zh":"qf-rational-reduced-form","stem_zh":"將 225/12 約為分母為正的最簡精確形式。","answer":{"kind":"short_text","value":"75/4","explanation_zh":"gcd(|225|,|12|)=3，約分後為 75/4。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["gcd 約分","最簡形式"]},"variant":{"family_id":"qf-rational-reduced-form","seed":20261245,"parameters":{"p":225,"q":12,"semantic_template":"qf-rational-reduced-form/{\"p\":225,\"q\":12}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-20","contract_version":"ocme-question-factory-v0.1"}}