96:@0.057273:0.966074:0.076087:0.966074:0.076087:0.949450:0.057273:0.949450:0.000000:0.000000
Tema 1:@0.124729:0.083964:0.219414:0.083964:0.219414:0.055923:0.124729:0.055923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Números racionales :@0.305303:0.083049:0.569000:0.083049:0.569000:0.055393:0.305303:0.055393:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tema 1:@0.124739:0.083954:0.219424:0.083954:0.219424:0.055913:0.124739:0.055913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Luis organiza las actividades en su tiempo libre de un día normal así::@0.305303:0.208692:0.803950:0.208692:0.803950:0.193022:0.305303:0.193022:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Considera el hecho de que Luis comienza a nadar con un punto inicial en 0.:@0.305303:0.322308:0.858774:0.322308:0.858774:0.306638:0.305303:0.306638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si Luis está llegando a la piscina, hace :@0.305303:0.352071:0.597805:0.352071:0.597805:0.336401:0.305303:0.336401:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.604283:0.338170:0.612377:0.338170:0.612377:0.324067:0.604283:0.324067:0.000000
2:@0.603578:0.357195:0.611671:0.357195:0.611671:0.343093:0.603578:0.343093:0.000000
 hora que salió de casa. Se representa :@0.616394:0.352063:0.907698:0.352063:0.907698:0.336393:0.616394:0.336393:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
con: :@0.305298:0.382241:0.340440:0.382241:0.340440:0.366571:0.305298:0.366571:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.343649:0.380527:0.353766:0.380527:0.353766:0.364954:0.343649:0.364954:0.000000
1:@0.358355:0.370099:0.367347:0.370099:0.367347:0.354429:0.358355:0.354429:0.000000
2:@0.357576:0.391244:0.366568:0.391244:0.366568:0.375575:0.357576:0.375575:0.000000
. Si él sale de la piscina, llegará a su casa dentro de   hora. Se representa :@0.369902:0.382238:0.907674:0.382238:0.907674:0.366569:0.369902:0.366569:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.746230:0.369602:0.754323:0.369602:0.754323:0.355500:0.746230:0.355500:0.000000
2:@0.745523:0.388628:0.753616:0.388628:0.753616:0.374525:0.745523:0.374525:0.000000
con: :@0.305295:0.414933:0.340436:0.414933:0.340436:0.399263:0.305295:0.399263:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.343428:0.416989:0.353545:0.416989:0.353545:0.401416:0.343428:0.401416:0.000000
1:@0.358134:0.406561:0.367126:0.406561:0.367126:0.390891:0.358134:0.390891:0.000000
2:@0.357353:0.427706:0.366346:0.427706:0.366346:0.412036:0.357353:0.412036:0.000000
Representación de fracciones en la recta numérica:@0.305303:0.601666:0.775181:0.601666:0.775181:0.581693:0.305303:0.581693:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para representar fracciones en la recta numérica, se divide la parte entera en tantas :@0.305303:0.624762:0.907609:0.624762:0.907609:0.609092:0.305303:0.609092:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
veces como indica el denominador y luego se cuentan sobre la recta, las partes :@0.305303:0.641358:0.907738:0.641358:0.907738:0.625688:0.305303:0.625688:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que indica el numerador de la fracción hacia la derecha si la fracción es positiva, :@0.305303:0.657954:0.907758:0.657954:0.907758:0.642285:0.305303:0.642285:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o a la izquierda si es negativa.:@0.305303:0.674551:0.520462:0.674551:0.520462:0.658881:0.305303:0.658881:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 1:@0.305303:0.698846:0.374809:0.698846:0.374809:0.684431:0.305303:0.684431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ubicamos:@0.305303:0.729525:0.384413:0.729525:0.384413:0.712624:0.305303:0.712624:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 en la recta numérica las fracciones :@0.384413:0.729525:0.643651:0.729525:0.643651:0.713855:0.384413:0.713855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.643651:0.729525:0.662890:0.729525:0.662890:0.712389:0.643651:0.712389:0.000000:0.000000:0.000000
7 1 7 1:@0.680946:0.719702:0.751326:0.719702:0.751326:0.704032:0.680946:0.704032:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4 3 4 3:@0.681312:0.739229:0.750749:0.739229:0.750749:0.723559:0.681312:0.723559:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.667768:0.728939:0.677885:0.728939:0.677885:0.713366:0.667768:0.713366:0.000000
     b):@0.692679:0.729525:0.727433:0.729525:0.727433:0.712389:0.692679:0.712389:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
;:@0.696401:0.729525:0.699608:0.729525:0.699608:0.713855:0.696401:0.713855:0.000000
  :@0.727433:0.729525:0.735505:0.729525:0.735505:0.713855:0.727433:0.713855:0.000000:0.000000
−:@0.707629:0.728939:0.717746:0.728939:0.717746:0.713366:0.707629:0.713366:0.000000
Solución:@0.305303:0.754516:0.365964:0.754516:0.365964:0.740100:0.305303:0.740100:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.305303:0.775136:0.324542:0.775136:0.324542:0.758000:0.305303:0.758000:0.000000:0.000000:0.000000
Convertimos:@0.333792:0.775136:0.435476:0.775136:0.435476:0.758235:0.333792:0.758235:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la fracción en fracción mixta. Ubicamos en la recta la parte en-:@0.435476:0.775136:0.903698:0.775136:0.903698:0.759466:0.435476:0.759466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tera, dividimos entre –1 y –2 en cuatro partes y contamos tres de estas hacia la :@0.333792:0.791732:0.907646:0.791732:0.907646:0.776063:0.333792:0.776063:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
izquierda de –1. :@0.333792:0.808329:0.453590:0.808329:0.453590:0.792659:0.333792:0.792659:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b):@0.305303:0.832048:0.321962:0.832048:0.321962:0.814912:0.305303:0.814912:0.000000:0.000000
 :@0.321962:0.832048:0.325684:0.832048:0.325684:0.814912:0.321962:0.814912:0.000000
Dividimos:@0.333792:0.832048:0.414358:0.832048:0.414358:0.815147:0.333792:0.815147:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 entre 0 y 1 en tres partes y contamos una de estas hacia la derecha :@0.414358:0.832048:0.907625:0.832048:0.907625:0.816378:0.414358:0.816378:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de 0.:@0.333792:0.848644:0.368989:0.848644:0.368989:0.832974:0.333792:0.832974:0.000000:0.000000:0.000000:0.000000:0.000000
Termina clases :@0.332018:0.236080:0.432281:0.236080:0.432281:0.221834:0.332018:0.221834:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
13h00:@0.359475:0.251167:0.401155:0.251167:0.401155:0.236922:0.359475:0.236922:0.000000:0.000000:0.000000:0.000000:0.000000
Llega a casa :@0.489575:0.236080:0.573018:0.236080:0.573018:0.221834:0.489575:0.221834:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
13h45:@0.508622:0.251167:0.550302:0.251167:0.550302:0.236922:0.508622:0.236922:0.000000:0.000000:0.000000:0.000000:0.000000
Almuerza :@0.647097:0.236080:0.714323:0.236080:0.714323:0.221834:0.647097:0.221834:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
14h00:@0.658037:0.251167:0.699717:0.251167:0.699717:0.236922:0.658037:0.236922:0.000000:0.000000:0.000000:0.000000:0.000000
Sale hacia la piscina :@0.763426:0.236080:0.898032:0.236080:0.898032:0.221834:0.763426:0.221834:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
14h30:@0.808054:0.251167:0.849734:0.251167:0.849734:0.236922:0.808054:0.236922:0.000000:0.000000:0.000000:0.000000:0.000000
Llega a la piscina :@0.397721:0.277382:0.513614:0.277382:0.513614:0.263137:0.397721:0.263137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
15h00:@0.432985:0.292470:0.474665:0.292470:0.474665:0.278224:0.432985:0.278224:0.000000:0.000000:0.000000:0.000000:0.000000
Sale de la piscina :@0.547940:0.277382:0.664620:0.277382:0.664620:0.263137:0.547940:0.263137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
16h00:@0.583606:0.292470:0.625286:0.292470:0.625286:0.278224:0.583606:0.278224:0.000000:0.000000:0.000000:0.000000:0.000000
Llega a la casa :@0.707775:0.277382:0.806044:0.277382:0.806044:0.263137:0.707775:0.263137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
16h30:@0.734227:0.292470:0.775907:0.292470:0.775907:0.278224:0.734227:0.278224:0.000000:0.000000:0.000000:0.000000:0.000000
En la fracción     es :@0.106213:0.479797:0.248826:0.479797:0.248826:0.465552:0.106213:0.465552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.202438:0.472183:0.210781:0.472183:0.210781:0.457458:0.202438:0.457458:0.000000
b:@0.202251:0.489758:0.210593:0.489758:0.210593:0.475033:0.202251:0.475033:0.000000
a:@0.218688:0.479797:0.227115:0.479797:0.227115:0.464924:0.218688:0.464924:0.000000
el numerador e indica :@0.106213:0.501171:0.256096:0.501171:0.256096:0.486926:0.106213:0.486926:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
las partes que se toma :@0.106213:0.516259:0.259427:0.516259:0.259427:0.502014:0.106213:0.502014:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la unidad; y,   es el :@0.106213:0.531347:0.254604:0.531347:0.254604:0.517101:0.106213:0.517101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.209121:0.531347:0.217547:0.531347:0.217547:0.516473:0.209121:0.516473:0.000000
denominador e indica :@0.106213:0.546434:0.257420:0.546434:0.257420:0.532189:0.106213:0.532189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
las partes en las que :@0.106213:0.561522:0.244251:0.561522:0.244251:0.547277:0.106213:0.547277:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se divide la unidad. Si :@0.106213:0.576610:0.252225:0.576610:0.252225:0.562364:0.106213:0.562364:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
| | <| |, la fracción se :@0.106213:0.591697:0.247318:0.591697:0.247318:0.577452:0.106213:0.577452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.109764:0.591697:0.118191:0.591697:0.118191:0.576823:0.109764:0.576823:0.000000
b:@0.138947:0.591697:0.147373:0.591697:0.147373:0.576823:0.138947:0.576823:0.000000
denomina propia; caso :@0.106213:0.606785:0.262578:0.606785:0.262578:0.592540:0.106213:0.592540:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
contrario, es impropia. :@0.106213:0.621872:0.258172:0.621872:0.258172:0.607627:0.106213:0.607627:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Recuerda que...:@0.136265:0.443958:0.258346:0.443958:0.258346:0.427057:0.136265:0.427057:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Figura 3.1 Diagrama de Venn:@0.096359:0.891189:0.268132:0.891189:0.268132:0.878368:0.096359:0.878368:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Shutterstock, 344304677.:@0.091447:0.218856:0.091447:0.143577:0.080059:0.143577:0.080059:0.218856:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Con qué número representarías la mitad, un tercio y un cuarto?:@0.312004:0.165265:0.781865:0.165265:0.781865:0.149595:0.312004:0.149595:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.345697:0.138636:0.471205:0.138636:0.471205:0.121736:0.345697:0.121736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–2:@0.363240:0.910701:0.375677:0.910701:0.375677:0.899305:0.363240:0.899305:0.000000:0.000000
–1 :@0.471782:0.909192:0.487154:0.909192:0.487154:0.897796:0.471782:0.897796:0.000000:0.000000:0.000000
1:@0.690769:0.909192:0.697309:0.909192:0.697309:0.897796:0.690769:0.897796:0.000000
2:@0.800960:0.909192:0.807500:0.909192:0.807500:0.897796:0.800960:0.897796:0.000000
0:@0.582736:0.909192:0.590174:0.909192:0.590174:0.896730:0.582736:0.896730:0.000000
1:@0.619365:0.862110:0.626233:0.862110:0.626233:0.850144:0.619365:0.850144:0.000000
3:@0.618929:0.876959:0.625796:0.876959:0.625796:0.864993:0.618929:0.864993:0.000000
−:@0.529422:0.913481:0.537147:0.913481:0.537147:0.901589:0.529422:0.901589:0.000000
2:@0.539568:0.906120:0.546435:0.906120:0.546435:0.894154:0.539568:0.894154:0.000000
5:@0.539708:0.920969:0.546576:0.920969:0.546576:0.909003:0.539708:0.909003:0.000000
−:@0.428284:0.869476:0.436010:0.869476:0.436010:0.857584:0.428284:0.857584:0.000000
1:@0.435911:0.868958:0.442778:0.868958:0.442778:0.856992:0.435911:0.856992:0.000000
1:@0.442989:0.862115:0.449857:0.862115:0.449857:0.850149:0.442989:0.850149:0.000000
3:@0.442553:0.876964:0.449420:0.876964:0.449420:0.864998:0.442553:0.864998:0.000000
El conjunto de los números racionales   está definido como el cociente entre :@0.320102:0.459996:0.892044:0.459996:0.892044:0.444326:0.320102:0.444326:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.601467:0.457702:0.614370:0.457702:0.614370:0.442629:0.601467:0.442629:0.000000
dos números enteros de la siguiente manera::@0.316755:0.476593:0.646754:0.476593:0.646754:0.460923:0.316755:0.460923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
!:@0.496002:0.514112:0.511642:0.514112:0.511642:0.495841:0.496002:0.495841:0.000000
=:@0.514316:0.513900:0.525353:0.513900:0.525353:0.496912:0.514316:0.496912:0.000000
a:@0.539967:0.503927:0.550079:0.503927:0.550079:0.487135:0.539967:0.487135:0.000000
b:@0.539766:0.525020:0.549878:0.525020:0.549878:0.508227:0.539766:0.508227:0.000000
/ ,:@0.555264:0.513161:0.579910:0.513161:0.579910:0.496067:0.555264:0.496067:0.000000:0.000000:0.000000
a b:@0.565637:0.513161:0.591288:0.513161:0.591288:0.496369:0.565637:0.496369:0.000000:0.000000:0.000000
∈:@0.594887:0.513900:0.609220:0.513900:0.609220:0.496912:0.594887:0.496912:0.000000
\:@0.612798:0.514112:0.626207:0.514112:0.626207:0.495841:0.612798:0.495841:0.000000
 con :@0.626931:0.513161:0.665247:0.513161:0.665247:0.496067:0.626931:0.496067:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.665026:0.513161:0.675138:0.513161:0.675138:0.496369:0.665026:0.496369:0.000000
≠ ⎬:@0.678314:0.513900:0.712308:0.514217:0.712308:0.497229:0.678314:0.496912:0.000000:0.000000:0.000000
0:@0.692024:0.513161:0.701834:0.513161:0.701834:0.496067:0.692024:0.496067:0.000000
⎧:@0.528005:0.503490:0.537935:0.503490:0.537935:0.486501:0.528005:0.486501:0.000000
⎨:@0.528005:0.514217:0.537935:0.514217:0.537935:0.497229:0.528005:0.497229:0.000000
⎩:@0.528005:0.525261:0.537935:0.525261:0.537935:0.508273:0.528005:0.508273:0.000000
⎫:@0.702377:0.503490:0.712308:0.503490:0.712308:0.486501:0.702377:0.486501:0.000000
⎭:@0.702377:0.525261:0.712308:0.525261:0.712308:0.508273:0.702377:0.508273:0.000000
Los números racionales se pueden expresar como una fracción o como un :@0.316752:0.548095:0.895359:0.548095:0.895359:0.532425:0.316752:0.532425:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
número decimal.:@0.316752:0.564692:0.440915:0.564692:0.440915:0.549022:0.316752:0.549022:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.118640:0.832171:0.130735:0.832171:0.130735:0.816945:0.118640:0.816945:0.000000
: Números naturales:@0.134032:0.831065:0.253487:0.831065:0.253487:0.818244:0.134032:0.818244:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.118640:0.850446:0.129814:0.850446:0.129814:0.835220:0.118640:0.835220:0.000000
: Números enteros:@0.134032:0.849340:0.243671:0.849340:0.243671:0.836519:0.134032:0.836519:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.118274:0.868721:0.131307:0.868721:0.131307:0.853495:0.118274:0.853495:0.000000
: Números racionales:@0.134032:0.867614:0.258718:0.867614:0.258718:0.854794:0.134032:0.854794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.134124:0.775471:0.141482:0.775471:0.141482:0.762650:0.134124:0.762650:0.000000
−3:@0.119047:0.755351:0.135390:0.755351:0.135390:0.742531:0.119047:0.742531:0.000000:0.000000
−1:@0.149201:0.737744:0.165545:0.737744:0.165545:0.724923:0.149201:0.724923:0.000000:0.000000
−4:@0.182702:0.744036:0.199046:0.744036:0.199046:0.731215:0.182702:0.731215:0.000000:0.000000
0:@0.196106:0.788042:0.203464:0.788042:0.203464:0.775222:0.196106:0.775222:0.000000
0,1:@0.235050:0.786153:0.252389:0.786153:0.252389:0.773332:0.235050:0.773332:0.000000:0.000000:0.000000
−3,11:@0.227647:0.740403:0.261330:0.740403:0.261330:0.727582:0.227647:0.727582:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.150000:0.769190:0.157358:0.769190:0.157358:0.756370:0.150000:0.756370:0.000000
3:@0.146653:0.788054:0.154011:0.788054:0.154011:0.775233:0.146653:0.775233:0.000000
1:@0.178841:0.703054:0.185463:0.703054:0.185463:0.691515:0.178841:0.691515:0.000000
3:@0.178416:0.720558:0.185037:0.720558:0.185037:0.709019:0.178416:0.709019:0.000000
1:@0.221188:0.710090:0.228545:0.710090:0.228545:0.697269:0.221188:0.697269:0.000000
3:@0.220715:0.729539:0.228073:0.729539:0.228073:0.716718:0.220715:0.716718:0.000000
:@0.162757:0.779723:0.174852:0.779723:0.174852:0.764497:0.162757:0.764497:0.000000
:@0.201328:0.766046:0.212502:0.766046:0.212502:0.750820:0.201328:0.750820:0.000000
:@0.247347:0.761645:0.260380:0.761645:0.260380:0.746419:0.247347:0.746419:0.000000
−:@0.207953:0.718387:0.216939:0.718387:0.216939:0.705566:0.207953:0.705566:0.000000
0,5:@0.125612:0.723230:0.142480:0.723230:0.142480:0.710757:0.125612:0.710757:0.000000:0.000000:0.000000
:@0.135650:0.714945:0.141664:0.714945:0.141664:0.701613:0.135650:0.701613:0.000000
M.4.1.13:@0.096359:0.934702:0.139502:0.934702:0.139502:0.923947:0.096359:0.923947:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Reconocer el conjunto de los números racionales :@0.139502:0.934702:0.376635:0.934702:0.376635:0.924730:0.139502:0.924730:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.379357:0.936044:0.391087:0.936044:0.391087:0.922340:0.379357:0.922340:0.000000
 e identificar sus elementos.:@0.395063:0.934702:0.524077:0.934702:0.524077:0.924730:0.395063:0.924730:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.4.1.15.:@0.096361:0.944762:0.142271:0.944762:0.142271:0.934007:0.096361:0.934007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Establecer relaciones de orden en un conjunto de números racionales uilizando la recta numérica y la simbología matemática (=, <, ≤, >, ≥).:@0.142271:0.944762:0.793987:0.944762:0.793987:0.934790:0.142271:0.934790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.824487:0.166434:0.831832:0.166434:0.831832:0.150370:0.824487:0.150370:0.000000
1 1 1:@0.794797:0.157662:0.846225:0.157664:0.846225:0.142279:0.794797:0.142277:0.000000:0.000000:0.000000:0.000000:0.000000
2 3 4:@0.794049:0.176689:0.845472:0.176689:0.845472:0.161304:0.794049:0.161304:0.000000:0.000000:0.000000:0.000000:0.000000
,:@0.805828:0.166434:0.808976:0.166434:0.808976:0.151049:0.805828:0.151049:0.000000