85:@0.942817:0.964671:0.965053:0.964671:0.965053:0.945025:0.942817:0.945025:0.000000:0.000000
M.3.1.44. Reconocer las magnitudes directa o inversamente proporcionales en situaciones cotidianas; plantear proporciones.:@0.105857:0.092104:0.710443:0.092104:0.710443:0.081525:0.105857:0.081525:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
extremos:@0.467155:0.510594:0.542118:0.510594:0.542118:0.493499:0.467155:0.493499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
medios:@0.471698:0.552401:0.531243:0.552401:0.531243:0.535307:0.471698:0.535307:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Proporción:@0.096834:0.135018:0.201260:0.135018:0.201260:0.115044:0.096834:0.115044:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Susana y sus amigos necesitan hacer un pastel. La razón entre la cantidad :@0.096834:0.159936:0.699647:0.159936:0.699647:0.142842:0.096834:0.142842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de harina y azúcar es de 8 a 4. Si se colocan 24 porciones de harina, ¿cuántas :@0.096834:0.178041:0.699699:0.178041:0.699699:0.160947:0.096834:0.160947:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
porciones de azúcar se deben colocar?:@0.096834:0.196146:0.406700:0.196146:0.406700:0.179052:0.096834:0.179052:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para conocer cuántas porciones de azúcar deben ser colocadas, se analiza :@0.096834:0.359093:0.699536:0.359093:0.699536:0.341998:0.096834:0.341998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la siguiente tabla.:@0.096834:0.377198:0.236225:0.377198:0.236225:0.360104:0.096834:0.360104:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Analicemos si existe una proporción entre la cantidad de harina y la :@0.096834:0.449618:0.699558:0.449618:0.699558:0.432524:0.096834:0.432524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cantidad de azúcar.:@0.096834:0.467724:0.251122:0.467724:0.251122:0.450629:0.096834:0.450629:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
8:@0.101546:0.505505:0.111356:0.505505:0.111356:0.488411:0.101546:0.488411:0.000000
4:@0.101747:0.526643:0.111557:0.526643:0.111557:0.509549:0.101747:0.509549:0.000000
24:@0.133570:0.505505:0.153009:0.505505:0.153009:0.488411:0.133570:0.488411:0.000000:0.000000
12:@0.133369:0.526643:0.152808:0.526643:0.152808:0.509549:0.133369:0.509549:0.000000:0.000000
=:@0.117251:0.515989:0.128288:0.515989:0.128288:0.499000:0.117251:0.499000:0.000000
          ó                :@0.158824:0.515249:0.283984:0.515249:0.283984:0.498155:0.158824:0.498155:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
8: 4::24:12:@0.286489:0.512735:0.377756:0.512735:0.377756:0.495641:0.286489:0.495641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   :@0.381140:0.515249:0.402780:0.515249:0.402780:0.498155:0.381140:0.498155:0.000000:0.000000:0.000000
8: 4::24:12:@0.461199:0.527822:0.552466:0.527822:0.552466:0.510728:0.461199:0.510728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Constante de proporcionalidad:@0.096834:0.553283:0.389682:0.553283:0.389682:0.533309:0.096834:0.533309:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
8:@0.101546:0.577260:0.111356:0.577260:0.111356:0.560165:0.101546:0.560165:0.000000
4:@0.101747:0.598397:0.111557:0.598397:0.111557:0.581303:0.101747:0.581303:0.000000
12 16:@0.132323:0.577260:0.191124:0.577260:0.191124:0.560165:0.132323:0.560165:0.000000:0.000000:0.000000:0.000000:0.000000
6:@0.137771:0.598397:0.147581:0.598397:0.147581:0.581303:0.137771:0.581303:0.000000
8:@0.177132:0.598397:0.186943:0.598397:0.186943:0.581303:0.177132:0.581303:0.000000
20:@0.212735:0.577260:0.232174:0.577260:0.232174:0.560165:0.212735:0.560165:0.000000:0.000000
10:@0.212111:0.598397:0.231551:0.598397:0.231551:0.581303:0.212111:0.581303:0.000000:0.000000
24:@0.253785:0.577260:0.273224:0.577260:0.273224:0.560165:0.253785:0.560165:0.000000:0.000000
12:@0.253584:0.598397:0.273023:0.598397:0.273023:0.581303:0.253584:0.581303:0.000000:0.000000
2     k = 2:@0.293675:0.587004:0.367352:0.587004:0.367352:0.569909:0.293675:0.569909:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.117253:0.587743:0.088928:0.587743:0.088928:0.570754:0.117253:0.570754:0.000000
=:@0.156614:0.587743:0.128289:0.587743:0.128289:0.570754:0.156614:0.570754:0.000000
=:@0.196418:0.587743:0.166404:0.587743:0.166404:0.570754:0.196418:0.570754:0.000000
=:@0.237468:0.587743:0.207454:0.587743:0.207454:0.570754:0.237468:0.570754:0.000000
=:@0.278920:0.587743:0.289956:0.587743:0.289956:0.570754:0.278920:0.570754:0.000000
Propiedad fundamental de una proporción:@0.096834:0.730650:0.499461:0.730650:0.499461:0.710677:0.096834:0.710677:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En  toda proporción,  el  producto  de los  extremos  siempre es  igual  al :@0.096834:0.755569:0.699597:0.755569:0.699597:0.738474:0.096834:0.738474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
producto de sus medios.:@0.096834:0.773674:0.294301:0.773674:0.294301:0.756580:0.096834:0.756580:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
8:@0.101546:0.796368:0.111356:0.796368:0.111356:0.779274:0.101546:0.779274:0.000000
4:@0.101755:0.817506:0.111565:0.817506:0.111565:0.800412:0.101755:0.800412:0.000000
24:@0.133584:0.796368:0.153024:0.796368:0.153024:0.779274:0.133584:0.779274:0.000000:0.000000
12:@0.133375:0.817506:0.152815:0.817506:0.152815:0.800412:0.133375:0.800412:0.000000:0.000000
=:@0.117251:0.806852:0.128288:0.806852:0.128288:0.789863:0.117251:0.789863:0.000000
  extremos:  8 × 12 = 96 ;      medios: 4 × 24 = 96. Entonces: 96 = 96.:@0.158824:0.804860:0.691140:0.804860:0.691140:0.787766:0.158824:0.787766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2 = 2.  El valor de la razón es igual.:@0.096847:0.835533:0.366963:0.835528:0.366963:0.818434:0.096847:0.818439:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cuarto desconocido:@0.096834:0.863508:0.285169:0.863508:0.285169:0.843535:0.096834:0.843535:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Es cualquiera de los términos de una proporción. Se representa con :@0.096834:0.888426:0.699518:0.888426:0.699518:0.871332:0.096834:0.871332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cualquier letra minúscula del alfabeto.:@0.096834:0.906532:0.400341:0.906532:0.400341:0.889437:0.096834:0.889437:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.101336:0.923694:0.111448:0.923694:0.111448:0.906902:0.101336:0.906902:0.000000
8:@0.101336:0.944832:0.111146:0.944832:0.111146:0.927738:0.101336:0.927738:0.000000
6:@0.138401:0.923694:0.148211:0.923694:0.148211:0.906600:0.138401:0.906600:0.000000
24:@0.133166:0.944832:0.152605:0.944832:0.152605:0.927738:0.133166:0.927738:0.000000:0.000000
=:@0.116832:0.934177:0.127869:0.934177:0.127869:0.917189:0.116832:0.917189:0.000000
       :@0.158827:0.948526:0.189645:0.948526:0.189645:0.931431:0.158827:0.931431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.192566:0.933438:0.202678:0.933438:0.202678:0.916646:0.192566:0.916646:0.000000
68:@0.223243:0.923692:0.259227:0.923692:0.259227:0.906597:0.223243:0.906597:0.000000:0.000000
24:@0.231097:0.944832:0.250536:0.944832:0.250536:0.927738:0.231097:0.927738:0.000000:0.000000
48:@0.281669:0.923694:0.301108:0.923694:0.301108:0.906600:0.281669:0.906600:0.000000:0.000000
24:@0.281041:0.944832:0.300480:0.944832:0.300480:0.927738:0.281041:0.927738:0.000000:0.000000
2 .:@0.321141:0.933438:0.337203:0.934695:0.337203:0.917601:0.321141:0.916344:0.000000:0.000000:0.000000
=:@0.206494:0.934177:0.217531:0.934177:0.217531:0.917189:0.206494:0.917189:0.000000
×:@0.235704:0.924431:0.246740:0.924431:0.246740:0.907442:0.235704:0.907442:0.000000
=:@0.264498:0.934177:0.275534:0.934177:0.275534:0.917189:0.264498:0.917189:0.000000
=:@0.306372:0.934177:0.317409:0.934177:0.317409:0.917189:0.306372:0.917189:0.000000
Harina:@0.133402:0.400828:0.181037:0.400828:0.181037:0.385158:0.133402:0.385158:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
8:@0.258065:0.400828:0.267058:0.400828:0.267058:0.385158:0.258065:0.385158:0.000000
12:@0.348545:0.400828:0.366530:0.400828:0.366530:0.385158:0.348545:0.385158:0.000000:0.000000
16:@0.443521:0.400828:0.461506:0.400828:0.461506:0.385158:0.443521:0.385158:0.000000:0.000000
20:@0.538497:0.400828:0.556482:0.400828:0.556482:0.385158:0.538497:0.385158:0.000000:0.000000
24:@0.635537:0.400828:0.653522:0.400828:0.653522:0.385158:0.635537:0.385158:0.000000:0.000000
Azúcar:@0.132020:0.421255:0.182419:0.421255:0.182419:0.405585:0.132020:0.405585:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.258065:0.421255:0.267058:0.421255:0.267058:0.405585:0.258065:0.405585:0.000000
6:@0.353041:0.421255:0.362034:0.421255:0.362034:0.405585:0.353041:0.405585:0.000000
8:@0.448017:0.421255:0.457010:0.421255:0.457010:0.405585:0.448017:0.405585:0.000000
10:@0.538497:0.421255:0.556482:0.421255:0.556482:0.405585:0.538497:0.405585:0.000000:0.000000
12:@0.635537:0.421255:0.653522:0.421255:0.653522:0.405585:0.635537:0.405585:0.000000:0.000000
A&A Matemática, (2020).:@0.677206:0.325063:0.677206:0.251760:0.665818:0.251760:0.665818:0.325063:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.113010:0.663422:0.123122:0.663422:0.123122:0.645574:0.113010:0.645574:0.000000
b:@0.112809:0.684560:0.122921:0.684560:0.122921:0.666712:0.112809:0.666712:0.000000
c:@0.146321:0.663422:0.154683:0.663422:0.154683:0.645574:0.146321:0.645574:0.000000
d:@0.145275:0.684560:0.155387:0.684560:0.155387:0.666712:0.145275:0.666712:0.000000
=:@0.128507:0.673906:0.139543:0.673906:0.139543:0.656917:0.128507:0.656917:0.000000
a:b::c:d:@0.188216:0.673166:0.260124:0.673166:0.260124:0.655288:0.188216:0.655288:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
No son lo mismo una :@0.731513:0.279754:0.877644:0.279754:0.877644:0.265509:0.731513:0.265509:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fracción y una razón.:@0.731513:0.294842:0.868613:0.294842:0.868613:0.280597:0.731513:0.280597:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si :@0.731513:0.318655:0.746456:0.318655:0.746456:0.304410:0.731513:0.304410:0.000000:0.000000:0.000000
a:@0.750959:0.312130:0.761071:0.312130:0.761071:0.295337:0.750959:0.295337:0.000000
b:@0.750749:0.333268:0.760861:0.333268:0.760861:0.316475:0.750749:0.316475:0.000000
 es una fracción, :@0.766559:0.318660:0.877275:0.318660:0.877275:0.304415:0.766559:0.304415:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entonces   y   son :@0.731513:0.348836:0.860138:0.348836:0.860138:0.334590:0.731513:0.334590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.797098:0.348836:0.828660:0.348836:0.828660:0.334842:0.797098:0.334842:0.000000:0.000000:0.000000
números enteros, en :@0.731513:0.363923:0.872214:0.363923:0.872214:0.349678:0.731513:0.349678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
donde   ≠ 0; mientras :@0.731513:0.379011:0.881899:0.379011:0.881899:0.364766:0.731513:0.364766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.779425:0.379011:0.787851:0.379011:0.787851:0.365017:0.779425:0.365017:0.000000
que en la razón :@0.731513:0.399794:0.837604:0.399794:0.837604:0.385549:0.731513:0.385549:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.840088:0.390709:0.850200:0.390709:0.850200:0.373916:0.840088:0.373916:0.000000
b:@0.839879:0.411848:0.849991:0.411848:0.849991:0.395055:0.839879:0.395055:0.000000
,    :@0.857707:0.399797:0.880055:0.399797:0.880055:0.385551:0.857707:0.385551:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.864291:0.399797:0.872717:0.399797:0.872717:0.385803:0.864291:0.385803:0.000000
y   pueden ser números :@0.731511:0.422428:0.897088:0.422428:0.897088:0.408183:0.731511:0.408183:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.742551:0.422428:0.750977:0.422428:0.750977:0.408434:0.742551:0.408434:0.000000
decimales.:@0.731511:0.437516:0.801702:0.437516:0.801702:0.423270:0.731511:0.423270:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Escribe:@0.731511:0.456161:0.781282:0.456161:0.781282:0.441049:0.731511:0.441049:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 con tus palabras :@0.781282:0.456161:0.897695:0.456161:0.897695:0.441916:0.781282:0.441916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la diferencia que hay :@0.731511:0.471249:0.872615:0.471249:0.872615:0.457004:0.731511:0.457004:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entre una razón y una :@0.731511:0.486337:0.880405:0.486337:0.880405:0.472091:0.731511:0.472091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fracción.:@0.731511:0.501424:0.787699:0.501424:0.787699:0.487179:0.731511:0.487179:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.781490:0.242610:0.882601:0.242610:0.882601:0.225834:0.781490:0.225834:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.781490:0.256440:0.869519:0.256440:0.869519:0.239664:0.781490:0.239664:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática  :@0.732687:0.621636:0.825194:0.621636:0.825194:0.606272:0.732687:0.606272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y química:@0.732687:0.636724:0.802612:0.636724:0.802612:0.621359:0.732687:0.621359:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los químicos son :@0.732687:0.651811:0.851545:0.651811:0.851545:0.637566:0.732687:0.637566:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
profesionales :@0.732687:0.666899:0.824708:0.666899:0.824708:0.652654:0.732687:0.652654:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que manejan :@0.732687:0.681986:0.824725:0.681986:0.824725:0.667741:0.732687:0.667741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
proporcionalidad para :@0.732687:0.697074:0.884615:0.697074:0.884615:0.682829:0.732687:0.682829:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
crear sus compuestos.:@0.732687:0.712162:0.879905:0.712162:0.879905:0.697916:0.732687:0.697916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad:@0.758804:0.596232:0.905119:0.596232:0.905119:0.579456:0.758804:0.579456:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Shutterstock, 196776020:@0.931545:0.857963:0.931545:0.783997:0.920156:0.783997:0.920156:0.857963:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000
maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000
®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000