6:@0.063510:0.510692:0.072963:0.510692:0.072963:0.494068:0.063510:0.494068:0.000000
Tema:@0.047190:0.135475:0.083321:0.135475:0.083321:0.113749:0.047190:0.113749:0.000000:0.000000:0.000000:0.000000
1:@0.059451:0.122645:0.071060:0.122645:0.071060:0.065614:0.059451:0.065614:0.000000
El conjunto de los números reales :@0.115891:0.142691:0.624946:0.142691:0.624946:0.101955:0.115891:0.101955:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.626453:0.142653:0.662739:0.142653:0.662739:0.107575:0.626453:0.107575:0.000000
M.4.1.28. Reconocer el conjunto de los números reales   e identificar sus elementos. M.4.1.29. Aproximar números reales a números decimales para resolver problemas. :@0.125388:0.064786:0.877702:0.064786:0.877702:0.054357:0.125388:0.054357:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.371120:0.064241:0.379587:0.064241:0.379587:0.056056:0.371120:0.056056:0.000000
M.4.1.30. Establecer relaciones de orden en un conjunto de números reales utilizando la recta numérica y la simbología matemática (=, , ≥). M.4.1.31. Calcular adiciones y :@0.125388:0.075348:0.877629:0.075348:0.877629:0.064918:0.125388:0.064918:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
multiplicaciones con números reales y con términos algebraicos aplicando propiedades en   (propiedad distributiva de la suma con respecto al producto).:@0.125388:0.085909:0.812758:0.085909:0.812758:0.075480:0.125388:0.075480:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.531050:0.085363:0.539516:0.085363:0.539516:0.077178:0.531050:0.077178:0.000000
Los números reales :@0.115209:0.171891:0.312078:0.171891:0.312078:0.150594:0.115209:0.150594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El conjunto de los números reales   está formado por la unión de los números racionales e irracionales.  :@0.115209:0.191116:0.883936:0.191116:0.883936:0.174727:0.115209:0.174727:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.369140:0.190259:0.382445:0.190259:0.382445:0.177396:0.369140:0.177396:0.000000
R:@0.115209:0.206855:0.128514:0.206855:0.128514:0.193993:0.115209:0.193993:0.000000
 = :@0.128329:0.207712:0.147384:0.207712:0.147384:0.191323:0.128329:0.191323:0.000000:0.000000:0.000000
Q  Q  :@0.147384:0.206855:0.208213:0.206855:0.208213:0.193993:0.147384:0.193993:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∪:@0.167156:0.208390:0.181309:0.208390:0.181309:0.192817:0.167156:0.192817:0.000000
  ' contiene a los conjuntos numéricos estudiados anteriormente:  ,  ,   y  '.:@0.181309:0.207712:0.763419:0.207712:0.763419:0.191323:0.181309:0.191323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
N Z Q Q:@0.671611:0.206855:0.759052:0.206855:0.759052:0.193993:0.671611:0.193993:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Aproximación de números reales:@0.115209:0.240101:0.397187:0.240101:0.397187:0.221846:0.115209:0.221846:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para redondear o aproximar un número a una unidad determinada, debemos fijarnos en la cifra inmedia-:@0.115209:0.259751:0.879896:0.259751:0.879896:0.243524:0.115209:0.243524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tamente posterior: si es mayor o igual que 5 se aumenta en uno la cifra anterior.:@0.115209:0.276183:0.691555:0.276183:0.691555:0.259956:0.115209:0.259956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Por ejemplo, si queremos aproximar el número 1,257 1 a las decenas, 7 > 5 entonces 1,2 7 1   1,26 o 3,141 5 :@0.115209:0.296148:0.883861:0.296148:0.883861:0.279921:0.115209:0.279921:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.735217:0.296148:0.744121:0.296148:0.744121:0.279921:0.735217:0.279921:0.000000
≈:@0.769172:0.296819:0.779188:0.296819:0.779188:0.281400:0.769172:0.281400:0.000000
si aproximamos a las decenas, analizamos que 1 < 5 es, entonces 3,1 1 5   3,14:@0.115209:0.312580:0.687906:0.312580:0.687906:0.296353:0.115209:0.296353:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.609305:0.312580:0.618209:0.312580:0.618209:0.296353:0.609305:0.296353:0.000000
≈:@0.644008:0.313251:0.654024:0.313251:0.654024:0.297832:0.644008:0.297832:0.000000
Relaciones de orden en los números reales:@0.115209:0.341399:0.478771:0.341399:0.478771:0.323145:0.115209:0.323145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Un número real   es menor que otro  , si y solo si   se encuentra ubicado a la izquierda de   sobre la recta :@0.115209:0.361049:0.883916:0.361049:0.883916:0.344822:0.115209:0.344822:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.232288:0.361049:0.241466:0.361049:0.241466:0.344849:0.232288:0.344849:0.000000
b:@0.383687:0.361049:0.392864:0.361049:0.392864:0.344849:0.383687:0.344849:0.000000
a:@0.474639:0.361049:0.483817:0.361049:0.483817:0.344849:0.474639:0.344849:0.000000
b:@0.770139:0.361049:0.779316:0.361049:0.779316:0.344849:0.770139:0.344849:0.000000
numérica; por ejemplo:  2:@0.115209:0.377481:0.311780:0.377345:0.311780:0.361118:0.115209:0.361254:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
π:@0.327540:0.378016:0.337556:0.378016:0.342076:0.362597:0.332059:0.362597:0.000000
<:@0.315782:0.378016:0.325798:0.378016:0.325798:0.362597:0.315782:0.362597:0.000000
.:@0.340798:0.377480:0.343973:0.377480:0.343973:0.361254:0.340798:0.361254:0.000000
–1:@0.373097:0.430803:0.391123:0.430803:0.391123:0.414576:0.373097:0.414576:0.000000:0.000000
0:@0.423727:0.430803:0.432631:0.430803:0.432631:0.414576:0.423727:0.414576:0.000000
1:@0.469796:0.430803:0.478700:0.430803:0.478700:0.414576:0.469796:0.414576:0.000000
3:@0.561935:0.430803:0.570838:0.430803:0.570838:0.414576:0.561935:0.414576:0.000000
2:@0.515866:0.430803:0.524769:0.430803:0.524769:0.414576:0.515866:0.414576:0.000000
4:@0.608004:0.430803:0.616908:0.430803:0.616908:0.414576:0.608004:0.414576:0.000000
2:@0.498132:0.402577:0.507035:0.402577:0.507035:0.386351:0.498132:0.386351:0.000000
π:@0.522796:0.403248:0.532812:0.403248:0.537332:0.387830:0.527315:0.387830:0.000000
<:@0.511038:0.403248:0.521054:0.403248:0.521054:0.387830:0.511038:0.387830:0.000000
2:@0.536285:0.402577:0.545189:0.402577:0.545189:0.386351:0.536285:0.386351:0.000000
π:@0.560949:0.403248:0.570966:0.403248:0.575485:0.387830:0.565469:0.387830:0.000000
<:@0.549191:0.403248:0.559208:0.403248:0.559208:0.387830:0.549191:0.387830:0.000000
Propiedades de la adición y multiplicación de los números reales:@0.115209:0.459627:0.667242:0.459627:0.667242:0.441372:0.115209:0.441372:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La adición y multiplicación de números reales cumple con las propiedades: conmutativa, asociativa,  :@0.115209:0.479275:0.883892:0.479275:0.883892:0.463049:0.115209:0.463049:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
existencia del opuesto aditivo, existencia del inverso multiplicativo, existencia del elemento neutro de la :@0.115209:0.495708:0.883865:0.495708:0.883865:0.479481:0.115209:0.479481:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
adición y de la multiplicación, además de la propiedad distributiva.:@0.115209:0.512140:0.598579:0.512140:0.598579:0.495913:0.115209:0.495913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
xy z:@0.130862:0.533529:0.171090:0.533529:0.171090:0.517168:0.130862:0.517168:0.000000:0.000000:0.000000:0.000000
x yz:@0.221010:0.533529:0.269936:0.533529:0.269936:0.517168:0.221010:0.517168:0.000000:0.000000:0.000000:0.000000
xy xz:@0.294352:0.533529:0.340329:0.533529:0.340329:0.517168:0.294352:0.517168:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.191784:0.534401:0.205089:0.534401:0.205089:0.517652:0.191784:0.517652:0.000000
(:@0.230958:0.536661:0.237094:0.536661:0.237094:0.516728:0.230958:0.516728:0.000000
):@0.271425:0.536661:0.277561:0.536661:0.277561:0.516728:0.271425:0.516728:0.000000
∀:@0.117826:0.534207:0.130965:0.534207:0.130965:0.518634:0.117826:0.518634:0.000000
∈:@0.175302:0.534207:0.188441:0.534207:0.188441:0.518634:0.175302:0.518634:0.000000
+:@0.249436:0.534207:0.259553:0.534207:0.259553:0.518634:0.249436:0.518634:0.000000
=:@0.280229:0.534207:0.290346:0.534207:0.290346:0.518634:0.280229:0.518634:0.000000
+:@0.312201:0.534207:0.322318:0.534207:0.322318:0.518634:0.312201:0.518634:0.000000
, ,:@0.140013:0.533529:0.161371:0.533529:0.161371:0.517140:0.140013:0.517140:0.000000:0.000000:0.000000
.:@0.144141:0.533529:0.147347:0.533529:0.147347:0.517140:0.144141:0.517140:0.000000
;:@0.205910:0.533529:0.209117:0.533529:0.209117:0.517140:0.205910:0.517140:0.000000
...:@0.210038:0.533529:0.219326:0.533529:0.219326:0.517140:0.210038:0.517140:0.000000:0.000000:0.000000
a) :@0.115209:0.750181:0.133931:0.750181:0.133931:0.733281:0.115209:0.733281:0.000000:0.000000:0.000000
Encontremos:@0.148452:0.750181:0.250118:0.750181:0.250118:0.733557:0.148452:0.733557:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 una fórmula para calcular el área :@0.250118:0.750181:0.491558:0.750181:0.491558:0.733792:0.250118:0.733792:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
total de los terrenos unidos. :@0.148452:0.766778:0.355557:0.766778:0.355557:0.750389:0.148452:0.750389:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.115209:0.786942:0.119023:0.786942:0.119023:0.770042:0.115209:0.770042:0.000000
El terreno  resultante  tiene  forma  rectangular :@0.148452:0.786942:0.491549:0.786942:0.491549:0.770553:0.148452:0.770553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.160891:0.786942:0.164706:0.786942:0.164706:0.770042:0.160891:0.770042:0.000000
por lo que su área puede calcularse así::@0.148452:0.803539:0.434263:0.803539:0.434263:0.787150:0.148452:0.787150:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.115209:0.823703:0.119023:0.823703:0.119023:0.806803:0.115209:0.806803:0.000000
A:@0.148452:0.823703:0.158348:0.823703:0.158348:0.807342:0.148452:0.807342:0.000000
 :@0.158348:0.823703:0.162163:0.823703:0.162163:0.806803:0.158348:0.806803:0.000000
=      ; donde:   es el largo del terreno; y  , el :@0.162642:0.823703:0.491618:0.823694:0.491618:0.807305:0.162642:0.807314:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
l h:@0.178176:0.823703:0.203484:0.823694:0.203484:0.807333:0.178176:0.807342:0.000000:0.000000:0.000000
∙:@0.186509:0.823380:0.189424:0.823380:0.189424:0.808481:0.186509:0.808481:0.000000
l:@0.267667:0.823694:0.271463:0.823694:0.271463:0.807333:0.267667:0.807333:0.000000
h:@0.457472:0.823694:0.466981:0.823694:0.466981:0.807333:0.457472:0.807333:0.000000
ancho.:@0.148459:0.840291:0.197476:0.840291:0.197476:0.823902:0.148459:0.823902:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.115215:0.860455:0.119030:0.860455:0.119030:0.843555:0.115215:0.843555:0.000000
Luego,   =   +   y   = :@0.148459:0.860455:0.307047:0.860455:0.307047:0.844066:0.148459:0.844066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
l:@0.201862:0.860455:0.205658:0.860455:0.205658:0.844094:0.201862:0.844094:0.000000
a:@0.224712:0.860455:0.233982:0.860455:0.233982:0.844094:0.224712:0.844094:0.000000
b h:@0.253036:0.860455:0.287993:0.860455:0.287993:0.844094:0.253036:0.844094:0.000000:0.000000:0.000000
c:@0.307047:0.860455:0.314713:0.860455:0.314713:0.844094:0.307047:0.844094:0.000000
 :@0.115215:0.880620:0.119030:0.880620:0.119030:0.863719:0.115215:0.863719:0.000000
A:@0.148459:0.880620:0.158355:0.880620:0.158355:0.864259:0.148459:0.864259:0.000000
 :@0.158355:0.880620:0.162169:0.880620:0.162169:0.863719:0.158355:0.863719:0.000000
=     :@0.162169:0.880620:0.191960:0.880611:0.191960:0.864222:0.162169:0.864231:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
l h:@0.177188:0.880620:0.201469:0.880611:0.201469:0.864250:0.177188:0.864259:0.000000:0.000000:0.000000
∙:@0.185009:0.880297:0.187924:0.880297:0.187924:0.865398:0.185009:0.865398:0.000000
 :@0.115209:0.900776:0.118526:0.900776:0.118526:0.884414:0.115209:0.884414:0.000000
A:@0.148452:0.900776:0.158348:0.900776:0.158348:0.884414:0.148452:0.884414:0.000000
 :@0.158348:0.900776:0.162162:0.900776:0.162162:0.883875:0.158348:0.883875:0.000000
= (  +  )   =   + :@0.162162:0.900776:0.291285:0.900776:0.291285:0.884387:0.162162:0.884387:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.182064:0.900776:0.191333:0.900776:0.191333:0.884414:0.182064:0.884414:0.000000
b c:@0.210387:0.900776:0.236241:0.900776:0.236241:0.884414:0.210387:0.884414:0.000000:0.000000:0.000000
ac:@0.255296:0.900776:0.272231:0.900776:0.272231:0.884414:0.255296:0.884414:0.000000:0.000000
bc:@0.291285:0.900776:0.308220:0.900776:0.308220:0.884414:0.291285:0.884414:0.000000:0.000000
b) :@0.532171:0.750191:0.551741:0.750191:0.551741:0.733567:0.532171:0.733567:0.000000:0.000000:0.000000
Determinamos:@0.565414:0.750191:0.679887:0.750191:0.679887:0.733567:0.565414:0.733567:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 el área del terreno cono-:@0.679887:0.750191:0.879900:0.750191:0.879900:0.733802:0.679887:0.733802:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ciendo que tiene 500 m de ancho.:@0.565414:0.766788:0.816395:0.766788:0.816395:0.750399:0.565414:0.750399:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.532171:0.786952:0.535488:0.786952:0.535488:0.770591:0.532171:0.770591:0.000000
A:@0.565414:0.786952:0.575310:0.786952:0.575310:0.770591:0.565414:0.770591:0.000000
 :@0.575310:0.786952:0.579125:0.786952:0.579125:0.770052:0.575310:0.770052:0.000000
= (  +  ) :@0.579125:0.786952:0.645538:0.786952:0.645538:0.770563:0.579125:0.770563:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.599026:0.786952:0.608295:0.786952:0.608295:0.770591:0.599026:0.770591:0.000000
b:@0.627350:0.786952:0.636619:0.786952:0.636619:0.770591:0.627350:0.770591:0.000000
∙ 500 =   ∙ 500 +   ∙ 500:@0.645534:0.786623:0.797696:0.786623:0.797696:0.771724:0.645534:0.771724:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.693966:0.786623:0.702392:0.786623:0.702392:0.771749:0.693966:0.771749:0.000000
b:@0.754492:0.786623:0.762918:0.786623:0.762918:0.771749:0.754492:0.771749:0.000000
 :@0.532173:0.807098:0.535490:0.807098:0.535490:0.790737:0.532173:0.790737:0.000000
A :@0.565416:0.807098:0.578629:0.807098:0.578629:0.790737:0.565416:0.790737:0.000000:0.000000
= 500  + 500:@0.578625:0.806784:0.667919:0.806784:0.667919:0.791885:0.578625:0.791885:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.616804:0.807098:0.626073:0.807098:0.626073:0.790737:0.616804:0.790737:0.000000
b:@0.667919:0.807098:0.677188:0.807098:0.677188:0.790737:0.667919:0.790737:0.000000
 :@0.532181:0.827263:0.535995:0.827263:0.535995:0.810362:0.532181:0.810362:0.000000
Para la solución, hemos aplicado la propie-:@0.565424:0.827263:0.879910:0.827263:0.879910:0.810874:0.565424:0.810874:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.596291:0.827263:0.600105:0.827263:0.600105:0.810362:0.596291:0.810362:0.000000
dad distributiva.:@0.565424:0.843859:0.683138:0.843859:0.683138:0.827470:0.565424:0.827470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.532447:0.718178:0.540813:0.718178:0.540813:0.701789:0.532447:0.701789:0.000000
b:@0.728646:0.718178:0.738818:0.718178:0.738818:0.701789:0.728646:0.701789:0.000000
c:@0.871682:0.666978:0.879900:0.666978:0.879900:0.650589:0.871682:0.650589:0.000000
Actividad resuelta:@0.115354:0.576952:0.270923:0.576952:0.270923:0.558697:0.115354:0.558697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Vamos:@0.115354:0.596801:0.166693:0.596801:0.166693:0.580177:0.115354:0.580177:0.000000:0.000000:0.000000:0.000000:0.000000
 a efectuar una aplicación de los núme-:@0.166693:0.596801:0.457260:0.596801:0.457260:0.580412:0.166693:0.580412:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ros reales y sus propiedades.:@0.115354:0.613397:0.322698:0.613397:0.322698:0.597008:0.115354:0.597008:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El esquema muestra la ubicación y forma de :@0.115354:0.637116:0.461296:0.637116:0.461296:0.620727:0.115354:0.620727:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los terrenos de dos hermanos que han deci-:@0.115354:0.653712:0.457240:0.653712:0.457240:0.637323:0.115354:0.637323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dido unir sus tierras para ser más productivos. :@0.115354:0.670309:0.461333:0.670309:0.461333:0.653920:0.115354:0.653920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.457260:0.670309:0.461296:0.670309:0.461296:0.653920:0.457260:0.653920:0.000000
Las medidas de ambos  terrenos aún no son :@0.115354:0.686905:0.461342:0.686905:0.461342:0.670516:0.115354:0.670516:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
conocidas.:@0.115354:0.703501:0.193395:0.703501:0.193395:0.687112:0.115354:0.687112:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000