{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0001","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0b2a58fb64ddfd20ab68f84f334ddd4db3864d467f45bdded0b76ca67d56341f","family_id":"qf-ratio-exact-value","seed":202609302001,"semantic_template":"qf-ratio-exact-value/{\"a\":-12,\"b\":1,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of -12:(1). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-12/1","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to -12/1."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0002","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"61e84b0cdeb0f960d838dd2090e302dec6c6796a4f84984a1fefae421288c9fc","family_id":"qf-ratio-exact-value","seed":202609302002,"semantic_template":"qf-ratio-exact-value/{\"a\":-11,\"b\":-2,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of -11:(-2). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"11/2","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to 11/2."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0003","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eca6a062dd1acf3ac4daf803f3134b4156306c643b8e8f1cbbe3e7a2a264acdb","family_id":"qf-ratio-exact-value","seed":202609302003,"semantic_template":"qf-ratio-exact-value/{\"a\":-10,\"b\":3,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of -10:(3). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-10/3","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to -10/3."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0004","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"da7c02058409c091b1210e74170a90db4ec5f4be33906646550c5c413acf2a28","family_id":"qf-ratio-exact-value","seed":202609302004,"semantic_template":"qf-ratio-exact-value/{\"a\":-9,\"b\":-4,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of -9:(-4). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"9/4","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to 9/4."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0005","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9290e2727583af036a33175b92f0e4b06a5c77419d525fa39ae20cc174fadcd9","family_id":"qf-ratio-exact-value","seed":202609302005,"semantic_template":"qf-ratio-exact-value/{\"a\":-8,\"b\":5,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of -8:(5). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-8/5","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to -8/5."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0006","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"74cb8ec276233f8b60bc2c9061076f887890e47c4c3f80fd52d20e320b34bc8a","family_id":"qf-ratio-exact-value","seed":202609302006,"semantic_template":"qf-ratio-exact-value/{\"a\":-7,\"b\":-6,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of -7:(-6). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"7/6","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to 7/6."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0007","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5dc6bbb0cf58aa97589c4564a49f7f2092ec334ba5604308fd8f1a7a573461f3","family_id":"qf-ratio-exact-value","seed":202609302007,"semantic_template":"qf-ratio-exact-value/{\"a\":-6,\"b\":7,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of -6:(7). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-6/7","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to -6/7."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0008","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8a8471949dcd8be747de3d8226c58ba1cd358c07602d11e099bdee2011743f62","family_id":"qf-ratio-exact-value","seed":202609302008,"semantic_template":"qf-ratio-exact-value/{\"a\":-5,\"b\":-8,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of -5:(-8). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"5/8","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to 5/8."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0009","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5b4686e1e5ddf3e8acd258880ea31f79df91fc8b891d8d47510c4d8f43ea3f9a","family_id":"qf-ratio-exact-value","seed":202609302009,"semantic_template":"qf-ratio-exact-value/{\"a\":-4,\"b\":1,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of -4:(1). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-4/1","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to -4/1."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0010","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f55aa36dadd5fb825bbba140b97886ee73c5cf33c9ae68c3efe5528de286d6f1","family_id":"qf-ratio-exact-value","seed":202609302010,"semantic_template":"qf-ratio-exact-value/{\"a\":-3,\"b\":-2,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of -3:(-2). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"3/2","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to 3/2."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0011","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"28b1b51b901ae34894cf5a7b41c9d8ec6d9792b11bb974ef5872aa357bba6b84","family_id":"qf-ratio-exact-value","seed":202609302011,"semantic_template":"qf-ratio-exact-value/{\"a\":-2,\"b\":3,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of -2:(3). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-2/3","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to -2/3."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0012","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4ac325972787e5e029a16ef4d1cc4dcf4260cde8abf33f9263f99004c231076b","family_id":"qf-ratio-exact-value","seed":202609302012,"semantic_template":"qf-ratio-exact-value/{\"a\":-1,\"b\":-4,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of -1:(-4). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"1/4","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to 1/4."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0013","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f79b4a458ab87128cf076fd319a203ded2be5fb8b66b27566fe498f5531905be","family_id":"qf-ratio-exact-value","seed":202609302013,"semantic_template":"qf-ratio-exact-value/{\"a\":0,\"b\":5,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of 0:(5). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"0/1","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to 0/1."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0014","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e753d42ae7c4248cf3274d3c91ebe04b75ada9726889a3641f16a0b57d5070a2","family_id":"qf-ratio-exact-value","seed":202609302014,"semantic_template":"qf-ratio-exact-value/{\"a\":1,\"b\":-6,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of 1:(-6). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-1/6","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to -1/6."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0015","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4382571bf3f3a6bcfbc507145a07b8a85c52eca49fc934978b703fdf4e590a82","family_id":"qf-ratio-exact-value","seed":202609302015,"semantic_template":"qf-ratio-exact-value/{\"a\":2,\"b\":7,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of 2:(7). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"2/7","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to 2/7."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0016","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"baa598bf875980d6643f6643d90cdc35fb460bf3c4e25bd0cb42d50378f3c27c","family_id":"qf-ratio-exact-value","seed":202609302016,"semantic_template":"qf-ratio-exact-value/{\"a\":3,\"b\":-8,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of 3:(-8). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-3/8","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to -3/8."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0017","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dd39142107cfd449fd1b0970fa153eb7976c62963a9813ec94b2c3d8e91ce91f","family_id":"qf-ratio-exact-value","seed":202609302017,"semantic_template":"qf-ratio-exact-value/{\"a\":4,\"b\":1,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of 4:(1). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"4/1","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to 4/1."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0018","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8921e5ae3e6f69f062ac71621ec04ab406f062c03502a0377530e6beafe36f94","family_id":"qf-ratio-exact-value","seed":202609302018,"semantic_template":"qf-ratio-exact-value/{\"a\":5,\"b\":-2,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of 5:(-2). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-5/2","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to -5/2."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0019","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8cff61c0889fb55d6ff217f657ef893e7ed8a8fab4e19df0bebd8a9cd02d71a5","family_id":"qf-ratio-exact-value","seed":202609302019,"semantic_template":"qf-ratio-exact-value/{\"a\":6,\"b\":3,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of 6:(3). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"2/1","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to 2/1."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0020","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7c5c6a0c2fa18794a9587e396bf712ac640fd85d615131cc8692583ec8131578","family_id":"qf-ratio-exact-value","seed":202609302020,"semantic_template":"qf-ratio-exact-value/{\"a\":7,\"b\":-4,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of 7:(-4). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-7/4","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to -7/4."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0021","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"102e374c784b1fb60b9d2511118dac21c0e47825a3e5d8f5e54a237171e3f7a6","family_id":"qf-ratio-exact-value","seed":202609302021,"semantic_template":"qf-ratio-exact-value/{\"a\":8,\"b\":5,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of 8:(5). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"8/5","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to 8/5."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0022","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9c4674906bdeaae745666013d25681591a246c354cd9b4d7a2f0e9aee0cc3850","family_id":"qf-ratio-exact-value","seed":202609302022,"semantic_template":"qf-ratio-exact-value/{\"a\":9,\"b\":-6,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of 9:(-6). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-3/2","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to -3/2."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0023","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c36244f16baca78cbc1e83f2d828c435ab40156f38a6ab486f74e05cf42f2b85","family_id":"qf-ratio-exact-value","seed":202609302023,"semantic_template":"qf-ratio-exact-value/{\"a\":10,\"b\":7,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of 10:(7). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"10/7","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to 10/7."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0024","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fc2865d607309eadff8b6299925e6a7d5f7584519be6a536d75564cb7fee290e","family_id":"qf-ratio-exact-value","seed":202609302024,"semantic_template":"qf-ratio-exact-value/{\"a\":11,\"b\":-8,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of 11:(-8). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-11/8","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to -11/8."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-ratio-exact-value-0025","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5c548c5073e9a5eb364d0c062a26ba42e0ced70242b37c2b672fcfcc51471e7b","family_id":"qf-ratio-exact-value","seed":202609302025,"semantic_template":"qf-ratio-exact-value/{\"a\":12,\"b\":1,\"operation\":\"ratio_value\"}"},"fields":{"title":"Exact Value of a Numerical Ratio","stem":"In the rational numerical-ratio setting, find the exact value of 12:(1). The consequent is nonzero; answer as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"12/1","explanation":"Divide the antecedent by the consequent in the stated order and normalize the result to 12/1."},"skills":["ratio order","nonzero consequent"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0001","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9dd9aab7e6de16ef5624456c6965d024feaf2679470de750b21624d8265344c5","family_id":"qf-proportion-verification","seed":202609302101,"semantic_template":"qf-proportion-verification/{\"a\":-12,\"b\":-1,\"c\":-24,\"d\":-2,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is -12:(-1)=-24:(-2) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"Yes","explanation":"The exact cross products are 24 and 24; they are equal, so the answer is Yes."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0002","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d8bbc547ce09fd68defb55d6ccd0c3f77c61341e7ed1ef004f6c2b753b2be3f7","family_id":"qf-proportion-verification","seed":202609302102,"semantic_template":"qf-proportion-verification/{\"a\":-11,\"b\":2,\"c\":34,\"d\":-6,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is -11:(2)=34:(-6) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"No","explanation":"The exact cross products are 66 and 68; they are different, so the answer is No."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0003","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1667750673fe96cea9d25d76b102dbaa684beadba01fc9bfd005bfb508059c1c","family_id":"qf-proportion-verification","seed":202609302103,"semantic_template":"qf-proportion-verification/{\"a\":-10,\"b\":3,\"c\":-40,\"d\":12,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is -10:(3)=-40:(12) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"Yes","explanation":"The exact cross products are -120 and -120; they are equal, so the answer is Yes."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0004","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"974d8ba89d23c973bf18ebb42803b48a5df9c627fc27e030130fe66f5d2a0a61","family_id":"qf-proportion-verification","seed":202609302104,"semantic_template":"qf-proportion-verification/{\"a\":-9,\"b\":-4,\"c\":46,\"d\":20,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is -9:(-4)=46:(20) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"No","explanation":"The exact cross products are -180 and -184; they are different, so the answer is No."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0005","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"386bf04f68f9d3d613870c41b711edf3a36765bc0349bf7c30aee8b1fb0c1c9a","family_id":"qf-proportion-verification","seed":202609302105,"semantic_template":"qf-proportion-verification/{\"a\":-8,\"b\":5,\"c\":-48,\"d\":30,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is -8:(5)=-48:(30) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"Yes","explanation":"The exact cross products are -240 and -240; they are equal, so the answer is Yes."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0006","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d34484e7a9c2988b9943793e41e33797ebd7af871b4986b21d77a4c2df809f1f","family_id":"qf-proportion-verification","seed":202609302106,"semantic_template":"qf-proportion-verification/{\"a\":-7,\"b\":6,\"c\":15,\"d\":-12,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is -7:(6)=15:(-12) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"No","explanation":"The exact cross products are 84 and 90; they are different, so the answer is No."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0007","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3e29aa57c01927e241f113778aa1643beb89252324c8d59ffb475519372a1e19","family_id":"qf-proportion-verification","seed":202609302107,"semantic_template":"qf-proportion-verification/{\"a\":-6,\"b\":-7,\"c\":-18,\"d\":-21,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is -6:(-7)=-18:(-21) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"Yes","explanation":"The exact cross products are 126 and 126; they are equal, so the answer is Yes."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0008","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ac250a1b1af5a28e092904d9973908605217944d2e54f322bdb7b8eebc1d79a4","family_id":"qf-proportion-verification","seed":202609302108,"semantic_template":"qf-proportion-verification/{\"a\":-5,\"b\":8,\"c\":21,\"d\":-32,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is -5:(8)=21:(-32) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"No","explanation":"The exact cross products are 160 and 168; they are different, so the answer is No."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0009","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"df1384ddd445aa6fc0a9470acdfe0166675e13f60189f969da32d7077f398665","family_id":"qf-proportion-verification","seed":202609302109,"semantic_template":"qf-proportion-verification/{\"a\":-4,\"b\":1,\"c\":-20,\"d\":5,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is -4:(1)=-20:(5) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"Yes","explanation":"The exact cross products are -20 and -20; they are equal, so the answer is Yes."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0010","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0b68cd87a99f62ed1bf7259f056f42fc35cb9e98702b809c3bd38bd1dab854db","family_id":"qf-proportion-verification","seed":202609302110,"semantic_template":"qf-proportion-verification/{\"a\":-3,\"b\":-2,\"c\":19,\"d\":12,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is -3:(-2)=19:(12) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"No","explanation":"The exact cross products are -36 and -38; they are different, so the answer is No."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0011","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2373293230f1c1cc44b565e0f3ffdbb6da2a3f67a045bcd0a3e3017a527a909d","family_id":"qf-proportion-verification","seed":202609302111,"semantic_template":"qf-proportion-verification/{\"a\":-2,\"b\":3,\"c\":-4,\"d\":6,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is -2:(3)=-4:(6) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"Yes","explanation":"The exact cross products are -12 and -12; they are equal, so the answer is Yes."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0012","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f810b80c10c035a4a665429449adb4863fe2df8d535abbeb65fa53fd7187c284","family_id":"qf-proportion-verification","seed":202609302112,"semantic_template":"qf-proportion-verification/{\"a\":-1,\"b\":4,\"c\":4,\"d\":-12,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is -1:(4)=4:(-12) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"No","explanation":"The exact cross products are 12 and 16; they are different, so the answer is No."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0013","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"32751e97285ccbb133cd1bd7c75f758c308cc260ad3100cbf61c1c156ebbb047","family_id":"qf-proportion-verification","seed":202609302113,"semantic_template":"qf-proportion-verification/{\"a\":0,\"b\":-5,\"c\":0,\"d\":-20,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is 0:(-5)=0:(-20) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"Yes","explanation":"The exact cross products are 0 and 0; they are equal, so the answer is Yes."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0014","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e69cb5f1cc7673b528d60127df0d0c21449e8998d8eaa47e2cda716a4ddd1460","family_id":"qf-proportion-verification","seed":202609302114,"semantic_template":"qf-proportion-verification/{\"a\":1,\"b\":6,\"c\":-4,\"d\":-30,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is 1:(6)=-4:(-30) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"No","explanation":"The exact cross products are -30 and -24; they are different, so the answer is No."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0015","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d8c40d5aad5462a6050f1ea6d7a2a739546336a9009d744598c50868bad6fad4","family_id":"qf-proportion-verification","seed":202609302115,"semantic_template":"qf-proportion-verification/{\"a\":2,\"b\":7,\"c\":12,\"d\":42,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is 2:(7)=12:(42) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"Yes","explanation":"The exact cross products are 84 and 84; they are equal, so the answer is Yes."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0016","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"52287eb1b037846c10e77325da7332752dda152c9235f41d4633b70e7f266a28","family_id":"qf-proportion-verification","seed":202609302116,"semantic_template":"qf-proportion-verification/{\"a\":3,\"b\":-8,\"c\":-5,\"d\":16,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is 3:(-8)=-5:(16) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"No","explanation":"The exact cross products are 48 and 40; they are different, so the answer is No."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0017","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"baf15a6d1b4b58eb17f8603f95ec974aa06a135a56ea3e1f403e9d4871eeb92b","family_id":"qf-proportion-verification","seed":202609302117,"semantic_template":"qf-proportion-verification/{\"a\":4,\"b\":1,\"c\":12,\"d\":3,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is 4:(1)=12:(3) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"Yes","explanation":"The exact cross products are 12 and 12; they are equal, so the answer is Yes."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0018","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"57e239cac6b2e46bd29062f29e56878a9aa77ed77d20115bbf15ab127fca6a43","family_id":"qf-proportion-verification","seed":202609302118,"semantic_template":"qf-proportion-verification/{\"a\":5,\"b\":2,\"c\":-19,\"d\":-8,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is 5:(2)=-19:(-8) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"No","explanation":"The exact cross products are -40 and -38; they are different, so the answer is No."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0019","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"13d84b1514bc518105f8821b9fb4b8ebcbb3339f3003f2a071a1846c12c688d0","family_id":"qf-proportion-verification","seed":202609302119,"semantic_template":"qf-proportion-verification/{\"a\":6,\"b\":-3,\"c\":30,\"d\":-15,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is 6:(-3)=30:(-15) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"Yes","explanation":"The exact cross products are -90 and -90; they are equal, so the answer is Yes."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0020","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8ed19541e989233fc1aa18a94889a04332594a96588b293f501b9a9fc41938b8","family_id":"qf-proportion-verification","seed":202609302120,"semantic_template":"qf-proportion-verification/{\"a\":7,\"b\":4,\"c\":-41,\"d\":-24,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is 7:(4)=-41:(-24) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"No","explanation":"The exact cross products are -168 and -164; they are different, so the answer is No."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0021","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d3b77145c8582b4d27da9c7370e110a952e687a1350766d3468c058424cbf11e","family_id":"qf-proportion-verification","seed":202609302121,"semantic_template":"qf-proportion-verification/{\"a\":8,\"b\":5,\"c\":16,\"d\":10,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is 8:(5)=16:(10) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"Yes","explanation":"The exact cross products are 80 and 80; they are equal, so the answer is Yes."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0022","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ad4abba9ab555b9c932151f2c024e74e02b88a54614c17b89fc6c285014df0bf","family_id":"qf-proportion-verification","seed":202609302122,"semantic_template":"qf-proportion-verification/{\"a\":9,\"b\":-6,\"c\":-26,\"d\":18,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is 9:(-6)=-26:(18) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"No","explanation":"The exact cross products are 162 and 156; they are different, so the answer is No."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0023","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"698d0305503f671ffb6b8652c1aac36be6c2b875751765c6e960a74f40f0f0b7","family_id":"qf-proportion-verification","seed":202609302123,"semantic_template":"qf-proportion-verification/{\"a\":10,\"b\":7,\"c\":40,\"d\":28,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is 10:(7)=40:(28) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"Yes","explanation":"The exact cross products are 280 and 280; they are equal, so the answer is Yes."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0024","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3aadb33d6968af4262749c6742703fbb0d6d2d9a7a0989e06718e3a7845057d7","family_id":"qf-proportion-verification","seed":202609302124,"semantic_template":"qf-proportion-verification/{\"a\":11,\"b\":8,\"c\":-54,\"d\":-40,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is 11:(8)=-54:(-40) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"No","explanation":"The exact cross products are -440 and -432; they are different, so the answer is No."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-verification-0025","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"60c878d8edd2a720d55fa2bcf107f7f5220538e63d8be92a2022e5f87eacc12b","family_id":"qf-proportion-verification","seed":202609302125,"semantic_template":"qf-proportion-verification/{\"a\":12,\"b\":-1,\"c\":72,\"d\":-6,\"operation\":\"proportion_verification\"}"},"fields":{"title":"Exact Proportion Check","stem":"In the rational numerical-ratio setting, is 12:(-1)=72:(-6) a valid proportion? Both consequents are nonzero.","answer":{"kind":"short_text","value":"Yes","explanation":"The exact cross products are -72 and -72; they are equal, so the answer is Yes."},"skills":["nonzero consequent","cross multiplication"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0001","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7061e2480ab0ce0bdb541379b8af222bb175df62e9afe69354089a4526ab53c1","family_id":"qf-proportion-missing-term","seed":202609302201,"semantic_template":"qf-proportion-missing-term/{\"a\":-12,\"b\":1,\"d\":-2,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion -12/(1)=x/(-2). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"24/1","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=24/1, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0002","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"30262caf6b10eac1648706a86b26422fcebf80f30ebc9b0802ff72cd90ba31d5","family_id":"qf-proportion-missing-term","seed":202609302202,"semantic_template":"qf-proportion-missing-term/{\"a\":-11,\"b\":-2,\"d\":3,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion -11/(-2)=x/(3). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"33/2","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=33/2, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0003","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9ec4f4c8589ec45cc56abbf2c48a676fd1cc80daf5c6290b5529518afae80c79","family_id":"qf-proportion-missing-term","seed":202609302203,"semantic_template":"qf-proportion-missing-term/{\"a\":-10,\"b\":3,\"d\":4,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion -10/(3)=x/(4). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-40/3","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=-40/3, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0004","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e6dca894b4d4a0e3d2bc6b75ac21beef3a04164db8f42ece40761f98d38a18d1","family_id":"qf-proportion-missing-term","seed":202609302204,"semantic_template":"qf-proportion-missing-term/{\"a\":-9,\"b\":-4,\"d\":-5,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion -9/(-4)=x/(-5). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-45/4","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=-45/4, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0005","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8159d353f4fb61ce524cd22e255fb279dce9e2ae0fe4e02cc328a399fa1f632e","family_id":"qf-proportion-missing-term","seed":202609302205,"semantic_template":"qf-proportion-missing-term/{\"a\":-8,\"b\":5,\"d\":6,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion -8/(5)=x/(6). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-48/5","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=-48/5, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0006","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"faf360a42a2417949cce9e974b2f50f1294c2ae1da43824281b5a648aa38ca8f","family_id":"qf-proportion-missing-term","seed":202609302206,"semantic_template":"qf-proportion-missing-term/{\"a\":-7,\"b\":-6,\"d\":2,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion -7/(-6)=x/(2). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"7/3","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=7/3, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0007","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3d28858c0dd86d7de2c604b7bf74477ab3124d5e95adad0a1b7df0e74045273c","family_id":"qf-proportion-missing-term","seed":202609302207,"semantic_template":"qf-proportion-missing-term/{\"a\":-6,\"b\":7,\"d\":-3,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion -6/(7)=x/(-3). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"18/7","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=18/7, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0008","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"70113127112e00714cd74b51cbc48bada0173b5a035687585e66761169568530","family_id":"qf-proportion-missing-term","seed":202609302208,"semantic_template":"qf-proportion-missing-term/{\"a\":-5,\"b\":-1,\"d\":4,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion -5/(-1)=x/(4). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"20/1","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=20/1, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0009","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dd26421c7aa405198a905670fbcf79278cef3bd25ea6614629da0935b8714f5d","family_id":"qf-proportion-missing-term","seed":202609302209,"semantic_template":"qf-proportion-missing-term/{\"a\":-4,\"b\":2,\"d\":5,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion -4/(2)=x/(5). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-10/1","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=-10/1, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0010","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7901ab79cb441e07863f69401e62d38e8c3a9868273e13bf84037bcc53ef03ed","family_id":"qf-proportion-missing-term","seed":202609302210,"semantic_template":"qf-proportion-missing-term/{\"a\":-3,\"b\":-3,\"d\":-6,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion -3/(-3)=x/(-6). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-6/1","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=-6/1, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0011","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d95e17f3e77a67cec441edaeac09d3a12443ab070ba59513f66e520be81fafb9","family_id":"qf-proportion-missing-term","seed":202609302211,"semantic_template":"qf-proportion-missing-term/{\"a\":-2,\"b\":4,\"d\":2,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion -2/(4)=x/(2). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-1/1","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=-1/1, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0012","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ff0bbac8b83807be8aaaa2f6df42dff339c11860d6c553f357e07185ad5bef62","family_id":"qf-proportion-missing-term","seed":202609302212,"semantic_template":"qf-proportion-missing-term/{\"a\":-1,\"b\":-5,\"d\":3,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion -1/(-5)=x/(3). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"3/5","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=3/5, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0013","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6316fd47ca1aff4f9c52614737298d6fa8315aab39b081ad1b1a6f504764355b","family_id":"qf-proportion-missing-term","seed":202609302213,"semantic_template":"qf-proportion-missing-term/{\"a\":0,\"b\":6,\"d\":-4,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion 0/(6)=x/(-4). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"0/1","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=0/1, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0014","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"08bb51dfea072fe6aafc8680998f51f9fcbc6f49103c459cc1a0f7517fabb9ef","family_id":"qf-proportion-missing-term","seed":202609302214,"semantic_template":"qf-proportion-missing-term/{\"a\":1,\"b\":-7,\"d\":5,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion 1/(-7)=x/(5). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-5/7","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=-5/7, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0015","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"27d33c3b9110ec2b974eb106286ac9d243f3dffcb736cd96f0538fe54d761eb3","family_id":"qf-proportion-missing-term","seed":202609302215,"semantic_template":"qf-proportion-missing-term/{\"a\":2,\"b\":1,\"d\":6,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion 2/(1)=x/(6). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"12/1","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=12/1, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0016","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"776e44c843f7315ad0708ef62d17a328dcd933aeb2d423f7c55a743b75393376","family_id":"qf-proportion-missing-term","seed":202609302216,"semantic_template":"qf-proportion-missing-term/{\"a\":3,\"b\":-2,\"d\":-2,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion 3/(-2)=x/(-2). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"3/1","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=3/1, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0017","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0c926ce1e966677dea819a64d816adfedf50cb81ca58905874e243f0419a3487","family_id":"qf-proportion-missing-term","seed":202609302217,"semantic_template":"qf-proportion-missing-term/{\"a\":4,\"b\":3,\"d\":3,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion 4/(3)=x/(3). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"4/1","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=4/1, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0018","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7b0d67d006b5c54396aa77da198798828dc424366da8da3bfd62f26871e6b955","family_id":"qf-proportion-missing-term","seed":202609302218,"semantic_template":"qf-proportion-missing-term/{\"a\":5,\"b\":-4,\"d\":4,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion 5/(-4)=x/(4). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-5/1","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=-5/1, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0019","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d6d4f764878c636c43dfca566694fcd546ad0e2dd25ea1f77e4a002433fcb5b0","family_id":"qf-proportion-missing-term","seed":202609302219,"semantic_template":"qf-proportion-missing-term/{\"a\":6,\"b\":5,\"d\":-5,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion 6/(5)=x/(-5). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-6/1","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=-6/1, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0020","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"525d605df3cde646eabc838b3edb721ebde7d14126297d54305337469a49e438","family_id":"qf-proportion-missing-term","seed":202609302220,"semantic_template":"qf-proportion-missing-term/{\"a\":7,\"b\":-6,\"d\":6,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion 7/(-6)=x/(6). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-7/1","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=-7/1, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0021","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ad7bb092716592ada4fdc25646f3749658d59ec494e787695c171f8f347d7fcc","family_id":"qf-proportion-missing-term","seed":202609302221,"semantic_template":"qf-proportion-missing-term/{\"a\":8,\"b\":7,\"d\":2,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion 8/(7)=x/(2). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"16/7","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=16/7, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0022","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fece3200ee8f119eb37c5ec8632307185ebc0b52bffb7f98cb3ca9db0d796628","family_id":"qf-proportion-missing-term","seed":202609302222,"semantic_template":"qf-proportion-missing-term/{\"a\":9,\"b\":-1,\"d\":-3,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion 9/(-1)=x/(-3). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"27/1","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=27/1, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0023","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d15eac272ddf246bb66eb6d3031efe1e7d0b296bae65ea1bba2c72a9a982471c","family_id":"qf-proportion-missing-term","seed":202609302223,"semantic_template":"qf-proportion-missing-term/{\"a\":10,\"b\":2,\"d\":4,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion 10/(2)=x/(4). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"20/1","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=20/1, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0024","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8e0f536d9a2e7a0fbc3f1fdc662d47ba62929da310330fa3df5ae9441fa3d475","family_id":"qf-proportion-missing-term","seed":202609302224,"semantic_template":"qf-proportion-missing-term/{\"a\":11,\"b\":-3,\"d\":5,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion 11/(-3)=x/(5). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-55/3","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=-55/3, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-missing-term-0025","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"aab990d2d79cd48483ccd201a5dab5594a5d33e64f9e6da5690f44279701e44c","family_id":"qf-proportion-missing-term","seed":202609302225,"semantic_template":"qf-proportion-missing-term/{\"a\":12,\"b\":4,\"d\":-6,\"operation\":\"missing_term\"}"},"fields":{"title":"Missing Term in a Proportion","stem":"Solve the rational proportion 12/(4)=x/(-6). Both denominators are nonzero; give x as a reduced p/q with a positive denominator.","answer":{"kind":"short_text","value":"-18/1","explanation":"From bx=ad, x=ad/b. Exact substitution and reduction give x=-18/1, uniquely because b≠0."},"skills":["solving proportions","exact rational arithmetic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0001","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"df6320ae1b37e573c3783ac1b3d893099a35c1568a7d457720bdf1dc136139d0","family_id":"qf-proportion-fixed-factor","seed":202609302301,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-12,\"operation\":\"fixed_factor\",\"x\":-3,\"y\":36}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=-12. Does the explicit point (x,y)=(-3,36) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"Yes","explanation":"kx=36 and the stated y is 36; comparison gives Yes and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0002","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"89ae69eac527d6aad3fb3b50830d34c5325b077587597ce5c2f6eac046f4704b","family_id":"qf-proportion-fixed-factor","seed":202609302302,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-11,\"operation\":\"fixed_factor\",\"x\":-2,\"y\":23}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=-11. Does the explicit point (x,y)=(-2,23) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"No","explanation":"kx=22 and the stated y is 23; comparison gives No and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0003","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d663ca059d7dd520661def4120fdb163a6e8390798b99cd7a9914da4e95282a4","family_id":"qf-proportion-fixed-factor","seed":202609302303,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-10,\"operation\":\"fixed_factor\",\"x\":-1,\"y\":10}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=-10. Does the explicit point (x,y)=(-1,10) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"Yes","explanation":"kx=10 and the stated y is 10; comparison gives Yes and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0004","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dd146f7915988b716b7d4740f4edcc2a411e4977862aee076c7cd0557d98f99b","family_id":"qf-proportion-fixed-factor","seed":202609302304,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-9,\"operation\":\"fixed_factor\",\"x\":0,\"y\":1}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=-9. Does the explicit point (x,y)=(0,1) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"No","explanation":"kx=0 and the stated y is 1; comparison gives No and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0005","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d93e82ee5adcbbffd97ea3b647f75b75fabc28edadcf10ecd1ec56c8df7017bb","family_id":"qf-proportion-fixed-factor","seed":202609302305,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-8,\"operation\":\"fixed_factor\",\"x\":1,\"y\":-8}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=-8. Does the explicit point (x,y)=(1,-8) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"Yes","explanation":"kx=-8 and the stated y is -8; comparison gives Yes and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0006","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8563b847bac11e7dc4493cea696caa1e7c081cdeaa1be3d6f6c56d26f302fd16","family_id":"qf-proportion-fixed-factor","seed":202609302306,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-7,\"operation\":\"fixed_factor\",\"x\":2,\"y\":-13}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=-7. Does the explicit point (x,y)=(2,-13) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"No","explanation":"kx=-14 and the stated y is -13; comparison gives No and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0007","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d68b9c07e8425b9a261633fe6521c97a75144373630ddd9b47e1579e79e08046","family_id":"qf-proportion-fixed-factor","seed":202609302307,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-6,\"operation\":\"fixed_factor\",\"x\":3,\"y\":-18}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=-6. Does the explicit point (x,y)=(3,-18) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"Yes","explanation":"kx=-18 and the stated y is -18; comparison gives Yes and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0008","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"43fac4238b2035a132bc50ad53d3c5d1f6051fda3a4b0b26de32f74dddd8b909","family_id":"qf-proportion-fixed-factor","seed":202609302308,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-5,\"operation\":\"fixed_factor\",\"x\":-3,\"y\":16}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=-5. Does the explicit point (x,y)=(-3,16) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"No","explanation":"kx=15 and the stated y is 16; comparison gives No and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0009","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ec4416181b74150ff7062c1d29011edb3031063e99b4d03ba1590b6ba2b2b9f1","family_id":"qf-proportion-fixed-factor","seed":202609302309,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-4,\"operation\":\"fixed_factor\",\"x\":-2,\"y\":8}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=-4. Does the explicit point (x,y)=(-2,8) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"Yes","explanation":"kx=8 and the stated y is 8; comparison gives Yes and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0010","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"75c4d673b6b442f98083310be173459a649eba0593dca37cecaec81a5ce63443","family_id":"qf-proportion-fixed-factor","seed":202609302310,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-3,\"operation\":\"fixed_factor\",\"x\":-1,\"y\":4}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=-3. Does the explicit point (x,y)=(-1,4) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"No","explanation":"kx=3 and the stated y is 4; comparison gives No and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0011","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e0ec6ff40a19e06c5be13f80e9b0beea8cb19a8ba6abecb5212fcb54697097f1","family_id":"qf-proportion-fixed-factor","seed":202609302311,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-2,\"operation\":\"fixed_factor\",\"x\":0,\"y\":0}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=-2. Does the explicit point (x,y)=(0,0) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"Yes","explanation":"kx=0 and the stated y is 0; comparison gives Yes and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0012","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6aa0b96e6780fab1a78795172c60a83378adf91e26bf4eaac0778cd1dee32fcd","family_id":"qf-proportion-fixed-factor","seed":202609302312,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-1,\"operation\":\"fixed_factor\",\"x\":1,\"y\":0}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=-1. Does the explicit point (x,y)=(1,0) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"No","explanation":"kx=-1 and the stated y is 0; comparison gives No and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0013","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8727c921eedb150a534d98ebf6ad9cf4bac739e3babe94f00fc8f5143d2fc51a","family_id":"qf-proportion-fixed-factor","seed":202609302313,"semantic_template":"qf-proportion-fixed-factor/{\"k\":0,\"operation\":\"fixed_factor\",\"x\":2,\"y\":0}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=0. Does the explicit point (x,y)=(2,0) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"Yes","explanation":"kx=0 and the stated y is 0; comparison gives Yes and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0014","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f335bff03b98015c772160987430a0ef9bea093508992436a714708c05c157d6","family_id":"qf-proportion-fixed-factor","seed":202609302314,"semantic_template":"qf-proportion-fixed-factor/{\"k\":1,\"operation\":\"fixed_factor\",\"x\":3,\"y\":4}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=1. Does the explicit point (x,y)=(3,4) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"No","explanation":"kx=3 and the stated y is 4; comparison gives No and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0015","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6f63c62438d5b3113f1b9d8b7f4f7c1caa30292f34413f84b53b413abd430810","family_id":"qf-proportion-fixed-factor","seed":202609302315,"semantic_template":"qf-proportion-fixed-factor/{\"k\":2,\"operation\":\"fixed_factor\",\"x\":-3,\"y\":-6}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=2. Does the explicit point (x,y)=(-3,-6) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"Yes","explanation":"kx=-6 and the stated y is -6; comparison gives Yes and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0016","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"52fbd223e8c854e7443ece4b86dd88e9f1c35af817c5041a173557f9f8412f80","family_id":"qf-proportion-fixed-factor","seed":202609302316,"semantic_template":"qf-proportion-fixed-factor/{\"k\":3,\"operation\":\"fixed_factor\",\"x\":-2,\"y\":-5}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=3. Does the explicit point (x,y)=(-2,-5) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"No","explanation":"kx=-6 and the stated y is -5; comparison gives No and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0017","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f3c7ed254f24b64f0e604eff8d867abd0a364619e599ed738d34ac64c1f7ca98","family_id":"qf-proportion-fixed-factor","seed":202609302317,"semantic_template":"qf-proportion-fixed-factor/{\"k\":4,\"operation\":\"fixed_factor\",\"x\":-1,\"y\":-4}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=4. Does the explicit point (x,y)=(-1,-4) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"Yes","explanation":"kx=-4 and the stated y is -4; comparison gives Yes and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0018","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c6480562bcae108cb91845ed83d131aad672e7f72b53957d588ab469dab3b4c3","family_id":"qf-proportion-fixed-factor","seed":202609302318,"semantic_template":"qf-proportion-fixed-factor/{\"k\":5,\"operation\":\"fixed_factor\",\"x\":0,\"y\":1}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=5. Does the explicit point (x,y)=(0,1) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"No","explanation":"kx=0 and the stated y is 1; comparison gives No and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0019","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d24950a6afdfd305d09854e3f568ebf96c541e5a732761a59d7d204268eb3a6f","family_id":"qf-proportion-fixed-factor","seed":202609302319,"semantic_template":"qf-proportion-fixed-factor/{\"k\":6,\"operation\":\"fixed_factor\",\"x\":1,\"y\":6}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=6. Does the explicit point (x,y)=(1,6) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"Yes","explanation":"kx=6 and the stated y is 6; comparison gives Yes and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0020","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"12aea67d793ac94228a92bbbfaa4d8d1d77d5f05eebcdc40e35acc2f6dcb9333","family_id":"qf-proportion-fixed-factor","seed":202609302320,"semantic_template":"qf-proportion-fixed-factor/{\"k\":7,\"operation\":\"fixed_factor\",\"x\":2,\"y\":15}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=7. Does the explicit point (x,y)=(2,15) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"No","explanation":"kx=14 and the stated y is 15; comparison gives No and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0021","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1b771393fcf5b131ebe8cf73210a85cdd4bc6de13d3fc559e0ff7721b66afaa5","family_id":"qf-proportion-fixed-factor","seed":202609302321,"semantic_template":"qf-proportion-fixed-factor/{\"k\":8,\"operation\":\"fixed_factor\",\"x\":3,\"y\":24}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=8. Does the explicit point (x,y)=(3,24) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"Yes","explanation":"kx=24 and the stated y is 24; comparison gives Yes and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0022","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e65a72c64f9ab35e837645ffeb6de6ff096d5ebdbdd3cc9a2f1999abd8900522","family_id":"qf-proportion-fixed-factor","seed":202609302322,"semantic_template":"qf-proportion-fixed-factor/{\"k\":9,\"operation\":\"fixed_factor\",\"x\":-3,\"y\":-26}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=9. Does the explicit point (x,y)=(-3,-26) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"No","explanation":"kx=-27 and the stated y is -26; comparison gives No and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0023","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f41ebf0496f1bd629f5dd7406046f52fa7808a11577d8e54d10ce5ebb54e6624","family_id":"qf-proportion-fixed-factor","seed":202609302323,"semantic_template":"qf-proportion-fixed-factor/{\"k\":10,\"operation\":\"fixed_factor\",\"x\":-2,\"y\":-20}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=10. Does the explicit point (x,y)=(-2,-20) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"Yes","explanation":"kx=-20 and the stated y is -20; comparison gives Yes and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0024","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6f77ed7bba7e6801cbe5ba0b8ee61f70f80c99fa64e00a3dd50df9775bd1c3b2","family_id":"qf-proportion-fixed-factor","seed":202609302324,"semantic_template":"qf-proportion-fixed-factor/{\"k\":11,\"operation\":\"fixed_factor\",\"x\":-1,\"y\":-10}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=11. Does the explicit point (x,y)=(-1,-10) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"No","explanation":"kx=-11 and the stated y is -10; comparison gives No and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r02-proportion-fixed-factor-0025","batch_id":"batch-20260930-r02-ratio-proportion-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7954f90a2f1ffab6f95184276f65813299fc3c42f7cad44dce79dd4b01e17c6f","family_id":"qf-proportion-fixed-factor","seed":202609302325,"semantic_template":"qf-proportion-fixed-factor/{\"k\":12,\"operation\":\"fixed_factor\",\"x\":0,\"y\":0}"},"fields":{"title":"Fixed-Factor Proportion Check","stem":"In the rational setting, the fixed factor is k=12. Does the explicit point (x,y)=(0,0) satisfy y=kx? Check only this point.","answer":{"kind":"short_text","value":"Yes","explanation":"kx=0 and the stated y is 0; comparison gives Yes and does not justify any claim about other inputs."},"skills":["fixed proportionality factor","pointwise verification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}