{"schema_version":"ocme-site-results-v1","locale":"en","page_type":"derivations","facts":{"questions":36000,"reviewed":36000,"display_candidates":0,"knowledge":302,"guides":299,"paths":59,"batches":360,"families":1441,"atlas":302,"core":80,"evidence":9,"formal_evidence":5,"formal_subjects":4,"lean_files":6,"lean_toolchain":"leanprover/lean4:v4.30.0","question_state":"candidate","english_state":"ai_candidate","question_Lean":"NOT_RUN","canonical_truth_promotion":false},"filters":{"q":"mko-rational-number"},"kind":"guides","total":1,"pages":1,"page":1,"entries":[{"id":"derivation-mko-rational-number-01","title":{"zh-Hant":"有理數：同一個有理數的不同分數表示、交叉相乘與約分","en":"Rational number: different fraction representations of one rational, cross-multiplication and reduction"},"summary":{"zh-Hant":"依 MKO 的定義（存在整數 p、q，q≠0，使 x=p/q），證明 6/(−8)、−3/4、9/(−12) 表示同一個有理數，並把 6/(−8) 精確約成正規形式 −3/4；以交叉相乘證明 2/3≠3/5；說明「5/0」不表示任何數；說明有限小數 −1.25=−5/4 與整數 7=7/1 都是有理數；並在分母為正時用交叉相乘證明 −3/4<−2/3。","en":"Using the MKO's definition (there are integers p, q with q≠0 and x=p/q), prove that 6/(−8), −3/4 and 9/(−12) represent the same rational number, and reduce 6/(−8) exactly to the canonical form −3/4; prove 2/3≠3/5 by cross-multiplication; show that '5/0' denotes no number; show that the finite decimal −1.25=−5/4 and the integer 7=7/1 are rational; and, with positive denominators, prove −3/4<−2/3 by cross-multiplication."},"mko_ids":["mko-rational-number"]}],"title":"Concept derivation guides"}