{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260930-r01-fraction-representation-validity-0001","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"48409cfd4f87eb33f0b969fe2ea8b06666f09001141009b117f78c4fcc9e55e1","family_id":"qf-fraction-representation-validity","seed":202609301001,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":0,\"q\":0}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=0 and denominator q=0, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"No","explanation":"A valid denominator must be nonzero. Here q=0, so the representation is invalid even if the numerator is zero."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0002","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b7089e3a4bd5beb9331622c697e6f3ae8ef849b9fdb50890f2deeef964fc3dbd","family_id":"qf-fraction-representation-validity","seed":202609301002,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":0,\"q\":5}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=0 and denominator q=5, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"Yes","explanation":"q=5≠0, so 0/5 is a valid rational-number representation."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0003","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"585539389c6a26515067c485f32d3b3af971f4f1b43fcbf50efe61fe59686872","family_id":"qf-fraction-representation-validity","seed":202609301003,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":-10,\"q\":3}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=-10 and denominator q=3, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"Yes","explanation":"q=3≠0, so -10/3 is a valid rational-number representation."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0004","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a696a3890fb6d610ac3030f9643a7ff2b8237274e7072be585f27d7baebb2fe6","family_id":"qf-fraction-representation-validity","seed":202609301004,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":-9,\"q\":-4}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=-9 and denominator q=-4, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"Yes","explanation":"q=-4≠0, so -9/-4 is a valid rational-number representation."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0005","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"aa6bec76df5ccdb340f88c1ea71b732602cf4f4de66b61d0b60c78bf53b8eab9","family_id":"qf-fraction-representation-validity","seed":202609301005,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":-8,\"q\":5}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=-8 and denominator q=5, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"Yes","explanation":"q=5≠0, so -8/5 is a valid rational-number representation."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0006","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b4e5a4965c443a7b4f466b9fbee0f2af2c8bf9674a2e49674a1464267c1a9ee8","family_id":"qf-fraction-representation-validity","seed":202609301006,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":-7,\"q\":0}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=-7 and denominator q=0, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"No","explanation":"A valid denominator must be nonzero. Here q=0, so the representation is invalid even if the numerator is zero."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0007","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fdf947cfab1ac31e96f4adde77c9d7a7699644c2783d95067bd3548bb05bf972","family_id":"qf-fraction-representation-validity","seed":202609301007,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":-6,\"q\":-7}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=-6 and denominator q=-7, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"Yes","explanation":"q=-7≠0, so -6/-7 is a valid rational-number representation."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0008","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"12e1a0d8495f15b18ba5da1d16ed9abdf9bdd6a44b85e3d2a969626ed1eff1c3","family_id":"qf-fraction-representation-validity","seed":202609301008,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":-5,\"q\":1}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=-5 and denominator q=1, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"Yes","explanation":"q=1≠0, so -5/1 is a valid rational-number representation."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0009","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"62f87974213f68cb0ac0a3d20fb2ee915651631d042356c387db4c504f10160f","family_id":"qf-fraction-representation-validity","seed":202609301009,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":-4,\"q\":2}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=-4 and denominator q=2, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"Yes","explanation":"q=2≠0, so -4/2 is a valid rational-number representation."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0010","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f50dca368ce9bfcc16df00a4030e24f7ffa1d525f25a9ed0af639a104b989648","family_id":"qf-fraction-representation-validity","seed":202609301010,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":-3,\"q\":-3}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=-3 and denominator q=-3, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"Yes","explanation":"q=-3≠0, so -3/-3 is a valid rational-number representation."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0011","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8516bc0a5fbca473127c1d8085b6aea2b7892ea34039f78f7078eb93ba878f3c","family_id":"qf-fraction-representation-validity","seed":202609301011,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":-2,\"q\":0}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=-2 and denominator q=0, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"No","explanation":"A valid denominator must be nonzero. Here q=0, so the representation is invalid even if the numerator is zero."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0012","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5eaf4efd48b26f3da37d23cfd3a92582dcfbf5952783d31f55963a74f295ba08","family_id":"qf-fraction-representation-validity","seed":202609301012,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":-1,\"q\":5}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=-1 and denominator q=5, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"Yes","explanation":"q=5≠0, so -1/5 is a valid rational-number representation."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0013","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"50c3c612e1dcc97242abd52574a43029ae57f07e9e4aae79b602066de87e4d08","family_id":"qf-fraction-representation-validity","seed":202609301013,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":0,\"q\":-6}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=0 and denominator q=-6, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"Yes","explanation":"q=-6≠0, so 0/-6 is a valid rational-number representation."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0014","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5f5b2153f586f756cccd3edde7f342966ecfa7f2940863e5168e327234f15d6f","family_id":"qf-fraction-representation-validity","seed":202609301014,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":1,\"q\":7}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=1 and denominator q=7, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"Yes","explanation":"q=7≠0, so 1/7 is a valid rational-number representation."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0015","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0bd30c973749512b1c16f91a5d02915ab878ea3a8a817ada2299873343ce58d0","family_id":"qf-fraction-representation-validity","seed":202609301015,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":2,\"q\":1}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=2 and denominator q=1, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"Yes","explanation":"q=1≠0, so 2/1 is a valid rational-number representation."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0016","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f0163c5b040c3718b02dbc906a7335bb15dabd77495f6e7b283fb81a1a25420e","family_id":"qf-fraction-representation-validity","seed":202609301016,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":3,\"q\":0}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=3 and denominator q=0, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"No","explanation":"A valid denominator must be nonzero. Here q=0, so the representation is invalid even if the numerator is zero."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0017","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"288c203fa3446b5fab5ab9ab48beaad78d75e77ef862feae12d3f37ae4d1cb2b","family_id":"qf-fraction-representation-validity","seed":202609301017,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":4,\"q\":3}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=4 and denominator q=3, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"Yes","explanation":"q=3≠0, so 4/3 is a valid rational-number representation."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0018","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4d6a5d1ad4d95347dde88d6f6cd1737a7095e34f2cf4268d292fff045d736518","family_id":"qf-fraction-representation-validity","seed":202609301018,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":5,\"q\":4}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=5 and denominator q=4, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"Yes","explanation":"q=4≠0, so 5/4 is a valid rational-number representation."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0019","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"42d0ad110630828648d195a982c6afa5b0ffa0d29be136d447e510a1396ccdf0","family_id":"qf-fraction-representation-validity","seed":202609301019,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":6,\"q\":-5}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=6 and denominator q=-5, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"Yes","explanation":"q=-5≠0, so 6/-5 is a valid rational-number representation."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0020","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6793547c7a8c332f74f8db4b54d99ad9a3d628e6c254620a9bed0a6bee54868f","family_id":"qf-fraction-representation-validity","seed":202609301020,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":7,\"q\":6}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=7 and denominator q=6, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"Yes","explanation":"q=6≠0, so 7/6 is a valid rational-number representation."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0021","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fb21304ef543d2c41f778a9b82eedb93d8c4daa5315a6e80958d2a42d6af0c6e","family_id":"qf-fraction-representation-validity","seed":202609301021,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":8,\"q\":0}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=8 and denominator q=0, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"No","explanation":"A valid denominator must be nonzero. Here q=0, so the representation is invalid even if the numerator is zero."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0022","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"85fe7bb22f1c92ff88dabdaf755115699f171d107da21573bc787c608a5b3a79","family_id":"qf-fraction-representation-validity","seed":202609301022,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":9,\"q\":-1}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=9 and denominator q=-1, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"Yes","explanation":"q=-1≠0, so 9/-1 is a valid rational-number representation."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0023","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"992ce5a578d16337df8cf238500b521ed92b24ffc82489c00e0bcf0680128493","family_id":"qf-fraction-representation-validity","seed":202609301023,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":10,\"q\":2}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=10 and denominator q=2, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"Yes","explanation":"q=2≠0, so 10/2 is a valid rational-number representation."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0024","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dcfb75aeb5e48b0aa9a95c6816915185e216ff91b3319f66096d101424fa4b2c","family_id":"qf-fraction-representation-validity","seed":202609301024,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":11,\"q\":3}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=11 and denominator q=3, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"Yes","explanation":"q=3≠0, so 11/3 is a valid rational-number representation."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-representation-validity-0025","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a1050d97feced156d135639d9670ce0981a3db32d5793df6d8b21177123e9bcf","family_id":"qf-fraction-representation-validity","seed":202609301025,"semantic_template":"qf-fraction-representation-validity/{\"operation\":\"representation_validity\",\"p\":12,\"q\":-4}"},"fields":{"title":"Validity of a Fraction Representation","stem":"For integer numerator p=12 and denominator q=-4, is p/q a valid rational-number representation? Answer Yes or No.","answer":{"kind":"short_text","value":"Yes","explanation":"q=-4≠0, so 12/-4 is a valid rational-number representation."},"skills":["nonzero denominator","integer representation"],"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-r01-fraction-equivalence-0001","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ab61735dd268e6db849ecc472f22b265aeca86f38caad35b80ec2f786b737436","family_id":"qf-fraction-equivalence","seed":202609301101,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-12,\"q\":1,\"r\":24,\"s\":-2}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are -12/(1) and 24/(-2), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"Yes","explanation":"The two cross products are 24 and 24; they are equal, so the answer is Yes."},"skills":["valid denominators","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-r01-fraction-equivalence-0002","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2aefced5a040c61cb16f31d770c759b30060a6008453107e43ab7760875e1046","family_id":"qf-fraction-equivalence","seed":202609301102,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-11,\"q\":-2,\"r\":-32,\"s\":-6}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are -11/(-2) and -32/(-6), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"No","explanation":"The two cross products are 66 and 64; they are different, so the answer is No."},"skills":["valid denominators","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-r01-fraction-equivalence-0003","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"89ead079234c62fec0c10971594ddd5243e3c49dcd3ba3c7aaf364970e54206f","family_id":"qf-fraction-equivalence","seed":202609301103,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-10,\"q\":3,\"r\":-40,\"s\":12}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are -10/(3) and -40/(12), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"Yes","explanation":"The two cross products are -120 and -120; they are equal, so the answer is Yes."},"skills":["valid denominators","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-r01-fraction-equivalence-0004","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e7a07f1647a159c1f0e6df6c8e0aa33829691f3e24b430fccbbd4b090a2b34bf","family_id":"qf-fraction-equivalence","seed":202609301104,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-9,\"q\":-4,\"r\":46,\"s\":20}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are -9/(-4) and 46/(20), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"No","explanation":"The two cross products are -180 and -184; they are different, so the answer is No."},"skills":["valid denominators","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-r01-fraction-equivalence-0005","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1194d77f17cfee38bc75e66b1e378d1a93135445dcc5ea671d6f299f70c19090","family_id":"qf-fraction-equivalence","seed":202609301105,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-8,\"q\":5,\"r\":-16,\"s\":10}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are -8/(5) and -16/(10), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"Yes","explanation":"The two cross products are -80 and -80; they are equal, so the answer is Yes."},"skills":["valid denominators","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-r01-fraction-equivalence-0006","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1e23bf1ab4c7b3c93acf0f29fa40ddd9f7a7b675aeafc7d82df6ca229e249070","family_id":"qf-fraction-equivalence","seed":202609301106,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-7,\"q\":-6,\"r\":-20,\"s\":-18}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are -7/(-6) and -20/(-18), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"No","explanation":"The two cross products are 126 and 120; they are different, so the answer is No."},"skills":["valid denominators","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-r01-fraction-equivalence-0007","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d0181f4d6470b624f906cb52c7b48a83334b0d73acab0ff2623ea510001dce8f","family_id":"qf-fraction-equivalence","seed":202609301107,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-6,\"q\":7,\"r\":24,\"s\":-28}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are -6/(7) and 24/(-28), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"Yes","explanation":"The two cross products are 168 and 168; they are equal, so the answer is Yes."},"skills":["valid denominators","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-r01-fraction-equivalence-0008","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9508309a0f78f2113aa6a7b2cf795c35e09e68b926e6a9cfed49a0aa1862fb78","family_id":"qf-fraction-equivalence","seed":202609301108,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-5,\"q\":-1,\"r\":-24,\"s\":-5}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are -5/(-1) and -24/(-5), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"No","explanation":"The two cross products are 25 and 24; they are different, so the answer is No."},"skills":["valid denominators","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-r01-fraction-equivalence-0009","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d694fb8ed8f030dc81a4ea36254f908f002a6482b427718a27e4bc903761bf67","family_id":"qf-fraction-equivalence","seed":202609301109,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-4,\"q\":2,\"r\":-8,\"s\":4}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are -4/(2) and -8/(4), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"Yes","explanation":"The two cross products are -16 and -16; they are equal, so the answer is Yes."},"skills":["valid denominators","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-r01-fraction-equivalence-0010","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"641b41467fe2c81f916634542e1a56b80bcd333732f9e9ccec78064d10cae191","family_id":"qf-fraction-equivalence","seed":202609301110,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-3,\"q\":-3,\"r\":10,\"s\":9}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are -3/(-3) and 10/(9), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"No","explanation":"The two cross products are -27 and -30; they are different, so the answer is No."},"skills":["valid denominators","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-r01-fraction-equivalence-0011","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"787865eefc0cea16c30ecc013cfa48cc05dcbd5632849f5c7812378db2821f41","family_id":"qf-fraction-equivalence","seed":202609301111,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-2,\"q\":4,\"r\":-8,\"s\":16}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are -2/(4) and -8/(16), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"Yes","explanation":"The two cross products are -32 and -32; they are equal, so the answer is Yes."},"skills":["valid denominators","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-r01-fraction-equivalence-0012","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e8f7f29f3cb29a9e44790f8cf42687c1616a9f43df3b5843ae9875cc301cb734","family_id":"qf-fraction-equivalence","seed":202609301112,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":-1,\"q\":-5,\"r\":-4,\"s\":-25}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are -1/(-5) and -4/(-25), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"No","explanation":"The two cross products are 25 and 20; they are different, so the answer is No."},"skills":["valid denominators","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-r01-fraction-equivalence-0013","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5a2f982b523c812b232b9bb34bc1d232e167a39ed76f87aac9488c7b9df66c41","family_id":"qf-fraction-equivalence","seed":202609301113,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":0,\"q\":6,\"r\":0,\"s\":-12}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are 0/(6) and 0/(-12), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"Yes","explanation":"The two cross products are 0 and 0; they are equal, so the answer is Yes."},"skills":["valid denominators","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-r01-fraction-equivalence-0014","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"78f0efaa12e105c92eaf87b6dd4912f1d2070d279b636a0510a5e0b62684087b","family_id":"qf-fraction-equivalence","seed":202609301114,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":1,\"q\":-7,\"r\":4,\"s\":-21}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are 1/(-7) and 4/(-21), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"No","explanation":"The two cross products are -21 and -28; they are different, so the answer is No."},"skills":["valid denominators","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-r01-fraction-equivalence-0015","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ac295d7c74a339dc48dd80c198a629dd00b859b1a4f8d09eee4ba7a1909aaeac","family_id":"qf-fraction-equivalence","seed":202609301115,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":2,\"q\":1,\"r\":8,\"s\":4}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are 2/(1) and 8/(4), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"Yes","explanation":"The two cross products are 8 and 8; they are equal, so the answer is Yes."},"skills":["valid denominators","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-r01-fraction-equivalence-0016","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a2741f260200ac348f39cb3575704cb312f13986bedc2cc0f7cd3b69c3955532","family_id":"qf-fraction-equivalence","seed":202609301116,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":3,\"q\":-2,\"r\":-14,\"s\":10}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are 3/(-2) and -14/(10), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"No","explanation":"The two cross products are 30 and 28; they are different, so the answer is No."},"skills":["valid denominators","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-r01-fraction-equivalence-0017","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"62d5fbac8b71a3f9b0c1fee5b0acb0f2355db75817bc29570419fc1587621998","family_id":"qf-fraction-equivalence","seed":202609301117,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":4,\"q\":3,\"r\":8,\"s\":6}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are 4/(3) and 8/(6), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"Yes","explanation":"The two cross products are 24 and 24; they are equal, so the answer is Yes."},"skills":["valid denominators","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-r01-fraction-equivalence-0018","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4f0429b57e4090238668211e41f9c1e9a4c6b56ba8dbacd275317191e412f959","family_id":"qf-fraction-equivalence","seed":202609301118,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":5,\"q\":-4,\"r\":16,\"s\":-12}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are 5/(-4) and 16/(-12), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"No","explanation":"The two cross products are -60 and -64; they are different, so the answer is No."},"skills":["valid denominators","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-r01-fraction-equivalence-0019","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"802c4b328a4a729320b98d2f7ff2b69fd2e1157229ca84e16009e22fe5f010f6","family_id":"qf-fraction-equivalence","seed":202609301119,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":6,\"q\":5,\"r\":-24,\"s\":-20}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are 6/(5) and -24/(-20), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"Yes","explanation":"The two cross products are -120 and -120; they are equal, so the answer is Yes."},"skills":["valid denominators","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-r01-fraction-equivalence-0020","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4c5658635067a942c3ac3eed6d3fca1557ec3570f70479b1b50a9a7f80f6fecc","family_id":"qf-fraction-equivalence","seed":202609301120,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":7,\"q\":-6,\"r\":36,\"s\":-30}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are 7/(-6) and 36/(-30), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"No","explanation":"The two cross products are -210 and -216; they are different, so the answer is No."},"skills":["valid denominators","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-r01-fraction-equivalence-0021","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5dd69521ff339e4f86d21221d50f81c9ece38cc4076baa98255d3620d8501030","family_id":"qf-fraction-equivalence","seed":202609301121,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":8,\"q\":7,\"r\":16,\"s\":14}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are 8/(7) and 16/(14), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"Yes","explanation":"The two cross products are 112 and 112; they are equal, so the answer is Yes."},"skills":["valid denominators","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-r01-fraction-equivalence-0022","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5746edcd81f62db6ef698ea4ad667410fca845534739be853ddccbd1ae0aaa55","family_id":"qf-fraction-equivalence","seed":202609301122,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":9,\"q\":-1,\"r\":-26,\"s\":3}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are 9/(-1) and -26/(3), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"No","explanation":"The two cross products are 27 and 26; they are different, so the answer is No."},"skills":["valid denominators","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-r01-fraction-equivalence-0023","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6bfcbb283c055b44245717bba322e558310f86dad3339441452ad9962c6960d7","family_id":"qf-fraction-equivalence","seed":202609301123,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":10,\"q\":2,\"r\":40,\"s\":8}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are 10/(2) and 40/(8), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"Yes","explanation":"The two cross products are 80 and 80; they are equal, so the answer is Yes."},"skills":["valid denominators","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-r01-fraction-equivalence-0024","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"db53d6d4c79c803a908887ed12f20f516d5b7a9d7ad962217863430a310bb103","family_id":"qf-fraction-equivalence","seed":202609301124,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":11,\"q\":-3,\"r\":56,\"s\":-15}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are 11/(-3) and 56/(-15), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"No","explanation":"The two cross products are -165 and -168; they are different, so the answer is No."},"skills":["valid denominators","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-r01-fraction-equivalence-0025","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0086de510472a8f6082c45abe84a031cb09bb404dc043db0f791187475db8908","family_id":"qf-fraction-equivalence","seed":202609301125,"semantic_template":"qf-fraction-equivalence/{\"operation\":\"equivalence\",\"p\":12,\"q\":4,\"r\":-24,\"s\":-8}"},"fields":{"title":"Equivalence of Two Fractions","stem":"The valid fractions are 12/(4) and -24/(-8), with both denominators nonzero. Do they represent the same rational number?","answer":{"kind":"short_text","value":"Yes","explanation":"The two cross products are -96 and -96; they are equal, so the answer is Yes."},"skills":["valid denominators","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-r01-fraction-reduction-0001","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5d2a229f527b21d615f62e3fa831765d520ac5429e29aae44063140050df4eef","family_id":"qf-fraction-reduction","seed":202609301201,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-24,\"q\":2}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction -24/(2) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"-12/1","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is -12/1; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0002","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"022b336260986ab4ce01e0bf7efc40886620f208794ebd41482fea0b49e5a6fa","family_id":"qf-fraction-reduction","seed":202609301202,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-33,\"q\":-6}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction -33/(-6) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"11/2","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is 11/2; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0003","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d4bff931a50da90914c3326ac5a5d0a725535bf66d2eafec4ac7c8dd6d46d4aa","family_id":"qf-fraction-reduction","seed":202609301203,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-40,\"q\":12}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction -40/(12) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"-10/3","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is -10/3; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0004","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ba4f2cf1ee0c120415d031a91d0fd5c6b40681f035215e14e963d8009f5bf21d","family_id":"qf-fraction-reduction","seed":202609301204,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-45,\"q\":-20}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction -45/(-20) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"9/4","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is 9/4; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0005","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"766eae51921ef9500ad5d2f33864a7984c64eb95c4acb7a332fdd2b8723643d6","family_id":"qf-fraction-reduction","seed":202609301205,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-16,\"q\":10}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction -16/(10) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"-8/5","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is -8/5; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0006","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cf410a9253a188e1fd9ab7a3cf015781ade93ee4d03074757e5aaea065d8e571","family_id":"qf-fraction-reduction","seed":202609301206,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-21,\"q\":-18}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction -21/(-18) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"7/6","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is 7/6; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0007","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ab87e2b1b44ae1cf2c1a296b57278e5bb80215075817b35ffa874d16a70ffd85","family_id":"qf-fraction-reduction","seed":202609301207,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-24,\"q\":28}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction -24/(28) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"-6/7","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is -6/7; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0008","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9d0e3c599294d5aece3b6132e7c5ef6463400dff8ad5daa2223df6910317d044","family_id":"qf-fraction-reduction","seed":202609301208,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-25,\"q\":-5}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction -25/(-5) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"5/1","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is 5/1; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0009","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"11311a207630a306b5f55e86ef61268bdbe1f6759b89819a52c80be008c8b61d","family_id":"qf-fraction-reduction","seed":202609301209,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-8,\"q\":4}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction -8/(4) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"-2/1","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is -2/1; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0010","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2539af835396158b31c4bfe2fe373a0281acddbd371bd6c4c65eeaef04dff198","family_id":"qf-fraction-reduction","seed":202609301210,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-9,\"q\":-9}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction -9/(-9) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"1/1","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is 1/1; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0011","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"071c7dff89e3b44e485bacae1808d48b553bca1c18b940c6fd5fb48ad9c5e434","family_id":"qf-fraction-reduction","seed":202609301211,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-8,\"q\":16}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction -8/(16) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"-1/2","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is -1/2; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0012","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"295335cdfd17c0875dadf63b126e94e3f9fabc7a99cf4cb57f4f1b2fc14e8e38","family_id":"qf-fraction-reduction","seed":202609301212,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":-5,\"q\":-25}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction -5/(-25) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"1/5","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is 1/5; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0013","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0ab9923f102efa80ba9885a0073cfd130837bb0989633bf3d801d8f3d3e6510f","family_id":"qf-fraction-reduction","seed":202609301213,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":0,\"q\":12}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction 0/(12) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"0/1","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is 0/1; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0014","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3fc98445d32c83fbdb7a2e0f3f8775a3f16ed9bb3a823b4c114d0591f5b02a38","family_id":"qf-fraction-reduction","seed":202609301214,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":3,\"q\":-21}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction 3/(-21) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"-1/7","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is -1/7; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0015","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f8ced518de568ae8c8a0b089d56e3be9db0fb2f7ed32a26913248eb676b234fc","family_id":"qf-fraction-reduction","seed":202609301215,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":8,\"q\":4}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction 8/(4) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"2/1","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is 2/1; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0016","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"32d2303fd5ed833d6f236b105de2fe83c86dfcaf57b83c311273a4dc33192e14","family_id":"qf-fraction-reduction","seed":202609301216,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":15,\"q\":-10}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction 15/(-10) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"-3/2","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is -3/2; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0017","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f2a53c95abd3e4e77b8a277b514a35251fab91ab400db8fa5d02bdd4d459154f","family_id":"qf-fraction-reduction","seed":202609301217,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":8,\"q\":6}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction 8/(6) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"4/3","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is 4/3; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0018","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8794ddc3384c317801ce537ce67921431486d40f15152c63493e0b9a268853e6","family_id":"qf-fraction-reduction","seed":202609301218,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":15,\"q\":-12}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction 15/(-12) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"-5/4","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is -5/4; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0019","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ad5586a1fee3ddf5f1396f4bcd1f4036897a3095d00d508d9f8c4e36eae4f966","family_id":"qf-fraction-reduction","seed":202609301219,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":24,\"q\":20}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction 24/(20) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"6/5","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is 6/5; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0020","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"52694087dd92d7ebafbc0b6337c4ee499d328a12a4e2dc356cfc76aaf4e3f597","family_id":"qf-fraction-reduction","seed":202609301220,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":35,\"q\":-30}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction 35/(-30) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"-7/6","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is -7/6; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0021","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"89fabefa225c2e3fba6fa9d9cf1a81ab7f8716ce51bde549eebbe9c78aba08c2","family_id":"qf-fraction-reduction","seed":202609301221,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":16,\"q\":14}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction 16/(14) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"8/7","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is 8/7; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0022","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7c89a229041b35432a2701880b376d8bd678b7499717e53f0eb6491b2468f68f","family_id":"qf-fraction-reduction","seed":202609301222,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":27,\"q\":-3}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction 27/(-3) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"-9/1","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is -9/1; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0023","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"48048b4d4edf60e5b579791e35f0f2effd434b2d4d77aac28d6a301d786694aa","family_id":"qf-fraction-reduction","seed":202609301223,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":40,\"q\":8}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction 40/(8) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"5/1","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is 5/1; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0024","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"87184d719b85298994eb10c2947abaa69e10cdf3ddec2c39ca6356c1237e635c","family_id":"qf-fraction-reduction","seed":202609301224,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":55,\"q\":-15}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction 55/(-15) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"-11/3","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is -11/3; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-reduction-0025","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"626f52579885ef305f30b206d4ed6fd5be016d86bb4a45512f3f2c78b683b240","family_id":"qf-fraction-reduction","seed":202609301225,"semantic_template":"qf-fraction-reduction/{\"operation\":\"reduction\",\"p\":24,\"q\":8}"},"fields":{"title":"Fraction Reduction and Normalization","stem":"Reduce the valid integer fraction 24/(8) to lowest terms with a positive denominator. Write the answer as p/q, including integers and zero.","answer":{"kind":"short_text","value":"3/1","explanation":"Normalize the denominator sign and divide numerator and denominator by their greatest common divisor. The canonical result is 3/1; zero is written 0/1."},"skills":["positive denominator","greatest common divisor"],"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-r01-fraction-exact-addition-0001","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"55d40405f6b7b0cc5fa05b2c0f68317ffd10cffa53174ac035fe44e234189c18","family_id":"qf-fraction-exact-addition","seed":202609301301,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":0,\"q\":1,\"r\":0,\"s\":-1}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute 0/(1)+(0)/(-1) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"0/1","explanation":"Use the common-denominator numerator 0×-1+(0)×1 and denominator 1×-1, then normalize and reduce to 0/1."},"skills":["common denominators","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-r01-fraction-exact-addition-0002","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"53e46c77e8760c43427eba96fc30f479fcf69564d66f576167affa59823077a4","family_id":"qf-fraction-exact-addition","seed":202609301302,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":-11,\"q\":-2,\"r\":9,\"s\":2}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute -11/(-2)+(9)/(2) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"10/1","explanation":"Use the common-denominator numerator -11×2+(9)×-2 and denominator -2×2, then normalize and reduce to 10/1."},"skills":["common denominators","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-r01-fraction-exact-addition-0003","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"30b6901cbc20ab1ae7315130d50adc9c913d7cda5f99744299d710b8bf4c2441","family_id":"qf-fraction-exact-addition","seed":202609301303,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":-10,\"q\":3,\"r\":6,\"s\":3}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute -10/(3)+(6)/(3) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"-4/3","explanation":"Use the common-denominator numerator -10×3+(6)×3 and denominator 3×3, then normalize and reduce to -4/3."},"skills":["common denominators","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-r01-fraction-exact-addition-0004","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"90e02ef4fa2f60d5a39d1e08caf161f4cf7cc0002564a241aaa9eff0799c2709","family_id":"qf-fraction-exact-addition","seed":202609301304,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":-9,\"q\":-4,\"r\":3,\"s\":-4}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute -9/(-4)+(3)/(-4) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"3/2","explanation":"Use the common-denominator numerator -9×-4+(3)×-4 and denominator -4×-4, then normalize and reduce to 3/2."},"skills":["common denominators","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-r01-fraction-exact-addition-0005","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"db72556811cfc285944358d5c20975a50ef612a06de79465b24336f58774ec60","family_id":"qf-fraction-exact-addition","seed":202609301305,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":-8,\"q\":5,\"r\":0,\"s\":5}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute -8/(5)+(0)/(5) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"-8/5","explanation":"Use the common-denominator numerator -8×5+(0)×5 and denominator 5×5, then normalize and reduce to -8/5."},"skills":["common denominators","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-r01-fraction-exact-addition-0006","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d65151b2b38ef428d570d2592f02bdb4ffe88d196da5e3d32857b2170ca5e3ae","family_id":"qf-fraction-exact-addition","seed":202609301306,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":-7,\"q\":-6,\"r\":-3,\"s\":1}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute -7/(-6)+(-3)/(1) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"-11/6","explanation":"Use the common-denominator numerator -7×1+(-3)×-6 and denominator -6×1, then normalize and reduce to -11/6."},"skills":["common denominators","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-r01-fraction-exact-addition-0007","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"de54012602846a051df225627b2ae9db2c36f612c19dc477e0f79b2dcd5ca376","family_id":"qf-fraction-exact-addition","seed":202609301307,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":-6,\"q\":7,\"r\":-6,\"s\":-2}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute -6/(7)+(-6)/(-2) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"15/7","explanation":"Use the common-denominator numerator -6×-2+(-6)×7 and denominator 7×-2, then normalize and reduce to 15/7."},"skills":["common denominators","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-r01-fraction-exact-addition-0008","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0d9ca2ac61573a2d5618f9e912cbc54f7ef6a5f8f9135159b855e8e363c2cef4","family_id":"qf-fraction-exact-addition","seed":202609301308,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":-5,\"q\":-1,\"r\":-9,\"s\":3}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute -5/(-1)+(-9)/(3) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"2/1","explanation":"Use the common-denominator numerator -5×3+(-9)×-1 and denominator -1×3, then normalize and reduce to 2/1."},"skills":["common denominators","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-r01-fraction-exact-addition-0009","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b2d442805026408e5bd0f5d7085f964fafe6b5327006c6b7514e30505b85b716","family_id":"qf-fraction-exact-addition","seed":202609301309,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":-4,\"q\":2,\"r\":-12,\"s\":4}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute -4/(2)+(-12)/(4) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"-5/1","explanation":"Use the common-denominator numerator -4×4+(-12)×2 and denominator 2×4, then normalize and reduce to -5/1."},"skills":["common denominators","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-r01-fraction-exact-addition-0010","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fefd43d4396ab5296c1be7143bcf410c665f9820eb9f069944c98d35a67e9aa1","family_id":"qf-fraction-exact-addition","seed":202609301310,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":-3,\"q\":-3,\"r\":10,\"s\":-5}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute -3/(-3)+(10)/(-5) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"-1/1","explanation":"Use the common-denominator numerator -3×-5+(10)×-3 and denominator -3×-5, then normalize and reduce to -1/1."},"skills":["common denominators","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-r01-fraction-exact-addition-0011","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"56de0f3ddb60ed5acfee5bfdbd6f62d2831ba030c8add2106d5f2082ba1b4423","family_id":"qf-fraction-exact-addition","seed":202609301311,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":-2,\"q\":4,\"r\":7,\"s\":1}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute -2/(4)+(7)/(1) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"13/2","explanation":"Use the common-denominator numerator -2×1+(7)×4 and denominator 4×1, then normalize and reduce to 13/2."},"skills":["common denominators","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-r01-fraction-exact-addition-0012","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4f497186b8b80ee165dd78af450be48e0fbbe5484d169ee27856f6852545b43c","family_id":"qf-fraction-exact-addition","seed":202609301312,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":-1,\"q\":-5,\"r\":4,\"s\":2}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute -1/(-5)+(4)/(2) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"11/5","explanation":"Use the common-denominator numerator -1×2+(4)×-5 and denominator -5×2, then normalize and reduce to 11/5."},"skills":["common denominators","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-r01-fraction-exact-addition-0013","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"db45290833d03cfcd4fcaa5ed78eec00f340029a84ad0c25d5fb16c4e1faa847","family_id":"qf-fraction-exact-addition","seed":202609301313,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":0,\"q\":6,\"r\":1,\"s\":-3}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute 0/(6)+(1)/(-3) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"-1/3","explanation":"Use the common-denominator numerator 0×-3+(1)×6 and denominator 6×-3, then normalize and reduce to -1/3."},"skills":["common denominators","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-r01-fraction-exact-addition-0014","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"828aa31ce892e85698c6a5565cc56051801430829c8e65c6d17490bfd10b2bb9","family_id":"qf-fraction-exact-addition","seed":202609301314,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":1,\"q\":-7,\"r\":-2,\"s\":4}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute 1/(-7)+(-2)/(4) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"-9/14","explanation":"Use the common-denominator numerator 1×4+(-2)×-7 and denominator -7×4, then normalize and reduce to -9/14."},"skills":["common denominators","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-r01-fraction-exact-addition-0015","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d3237cee43fd8be3473481678646cffc457dfdf5e259717d60fc85b76d80cbda","family_id":"qf-fraction-exact-addition","seed":202609301315,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":2,\"q\":1,\"r\":-5,\"s\":5}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute 2/(1)+(-5)/(5) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"1/1","explanation":"Use the common-denominator numerator 2×5+(-5)×1 and denominator 1×5, then normalize and reduce to 1/1."},"skills":["common denominators","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-r01-fraction-exact-addition-0016","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f7440d3812606303511acd4624d4747f11a12ebd5f21a9982d053b98993ea298","family_id":"qf-fraction-exact-addition","seed":202609301316,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":3,\"q\":-2,\"r\":-8,\"s\":-1}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute 3/(-2)+(-8)/(-1) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"13/2","explanation":"Use the common-denominator numerator 3×-1+(-8)×-2 and denominator -2×-1, then normalize and reduce to 13/2."},"skills":["common denominators","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-r01-fraction-exact-addition-0017","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4b5b08bfd6b14c82af61fe413bea8bf9ec58438bd3393ed6986d58d022db16c5","family_id":"qf-fraction-exact-addition","seed":202609301317,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":4,\"q\":3,\"r\":-11,\"s\":2}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute 4/(3)+(-11)/(2) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"-25/6","explanation":"Use the common-denominator numerator 4×2+(-11)×3 and denominator 3×2, then normalize and reduce to -25/6."},"skills":["common denominators","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-r01-fraction-exact-addition-0018","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9ca7d4b4d125ab580613589bd9e0a27ee2d7a02abc3a9659ae77a3c229e58d32","family_id":"qf-fraction-exact-addition","seed":202609301318,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":5,\"q\":-4,\"r\":11,\"s\":3}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute 5/(-4)+(11)/(3) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"29/12","explanation":"Use the common-denominator numerator 5×3+(11)×-4 and denominator -4×3, then normalize and reduce to 29/12."},"skills":["common denominators","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-r01-fraction-exact-addition-0019","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9111070b7d8e17f001116e8ca0c085f950d87be4aba3c6b331b63bd25169b641","family_id":"qf-fraction-exact-addition","seed":202609301319,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":6,\"q\":5,\"r\":8,\"s\":-4}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute 6/(5)+(8)/(-4) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"-4/5","explanation":"Use the common-denominator numerator 6×-4+(8)×5 and denominator 5×-4, then normalize and reduce to -4/5."},"skills":["common denominators","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-r01-fraction-exact-addition-0020","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9987d3ab3f493880057401b9df7c3e51092460d8cea22d8fef3d4b60d6fe0b0f","family_id":"qf-fraction-exact-addition","seed":202609301320,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":7,\"q\":-6,\"r\":5,\"s\":5}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute 7/(-6)+(5)/(5) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"-1/6","explanation":"Use the common-denominator numerator 7×5+(5)×-6 and denominator -6×5, then normalize and reduce to -1/6."},"skills":["common denominators","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-r01-fraction-exact-addition-0021","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3fa66aaa20d501df14de794cc9f582db510605452f114da0259f905bf12f660c","family_id":"qf-fraction-exact-addition","seed":202609301321,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":8,\"q\":7,\"r\":2,\"s\":1}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute 8/(7)+(2)/(1) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"22/7","explanation":"Use the common-denominator numerator 8×1+(2)×7 and denominator 7×1, then normalize and reduce to 22/7."},"skills":["common denominators","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-r01-fraction-exact-addition-0022","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b1e778f8324410ff004ca8b7803bad307fac73852a3a425971f9f1d8fd3f5752","family_id":"qf-fraction-exact-addition","seed":202609301322,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":9,\"q\":-1,\"r\":-1,\"s\":-2}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute 9/(-1)+(-1)/(-2) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"-17/2","explanation":"Use the common-denominator numerator 9×-2+(-1)×-1 and denominator -1×-2, then normalize and reduce to -17/2."},"skills":["common denominators","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-r01-fraction-exact-addition-0023","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2f188ffebbb0434db0b2f7f3758cb45f0b8d33b0ae6383ec98ddf98957992d7c","family_id":"qf-fraction-exact-addition","seed":202609301323,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":10,\"q\":2,\"r\":-4,\"s\":3}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute 10/(2)+(-4)/(3) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"11/3","explanation":"Use the common-denominator numerator 10×3+(-4)×2 and denominator 2×3, then normalize and reduce to 11/3."},"skills":["common denominators","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-r01-fraction-exact-addition-0024","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"105abc90d8f014cdb852a757f2fe2c17a65a5940efd773aadb3319333c60e270","family_id":"qf-fraction-exact-addition","seed":202609301324,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":11,\"q\":-3,\"r\":-7,\"s\":4}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute 11/(-3)+(-7)/(4) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"-65/12","explanation":"Use the common-denominator numerator 11×4+(-7)×-3 and denominator -3×4, then normalize and reduce to -65/12."},"skills":["common denominators","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-r01-fraction-exact-addition-0025","batch_id":"batch-20260930-r01-fraction-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"209812bb36475a2fb3d7735f8292aabffe958275fb91bb9e17abd6bfd629176d","family_id":"qf-fraction-exact-addition","seed":202609301325,"semantic_template":"qf-fraction-exact-addition/{\"operation\":\"addition\",\"p\":12,\"q\":4,\"r\":-10,\"s\":-5}"},"fields":{"title":"Exact Fraction Addition","stem":"Compute 12/(4)+(-10)/(-5) exactly and write the result in lowest terms with a positive denominator.","answer":{"kind":"short_text","value":"5/1","explanation":"Use the common-denominator numerator 12×-5+(-10)×4 and denominator 4×-5, then normalize and reduce to 5/1."},"skills":["common denominators","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."}}