112:@0.052592:0.966074:0.080768:0.966074:0.080768:0.949450:0.052592:0.949450:0.000000:0.000000:0.000000
Tema 5:@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
Ecuaciones con números racionales:@0.305293:0.083059:0.764688:0.083059:0.764688:0.055403:0.305293:0.055403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ecuaciones de primer grado en   :@0.305303:0.218398:0.653463:0.218398:0.653463:0.196589:0.305303:0.196589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Q Q:@0.630479:0.222429:0.648726:0.222429:0.648726:0.196061:0.630479:0.196061:0.000000:0.000000:0.000000
En matemáticas se encuentran expresiones como: :@0.305303:0.249982:0.676762:0.249982:0.676762:0.234312:0.305303:0.234312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.702412:0.250659:0.712529:0.250659:0.712529:0.235086:0.702412:0.235086:0.000000
= +:@0.738125:0.250659:0.773727:0.250659:0.773727:0.235086:0.738125:0.235086:0.000000:0.000000:0.000000
65:@0.681202:0.241020:0.698985:0.241020:0.698985:0.225350:0.681202:0.225350:0.000000:0.000000
10 10:@0.680058:0.260471:0.733387:0.260471:0.733387:0.244802:0.680058:0.244802:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.720945:0.241023:0.729938:0.241023:0.729938:0.225354:0.720945:0.225354:0.000000
61:@0.751889:0.249974:0.784340:0.249974:0.784340:0.234304:0.751889:0.234304:0.000000:0.000000
Estas expresiones reciben el nombre de igualdad.:@0.305303:0.273706:0.666811:0.273706:0.666811:0.258036:0.305303:0.258036:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Toda igualdad está formada por dos miembros: :@0.305303:0.297425:0.655460:0.297425:0.655460:0.281755:0.305303:0.281755:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.545000:0.327997:0.604189:0.327997:0.604189:0.311249:0.545000:0.311249:0.000000:0.000000:0.000000:0.000000
:@0.582740:0.327997:0.601186:0.327997:0.601186:0.311249:0.582740:0.311249:0.000000
:@0.635096:0.325405:0.663489:0.325405:0.663489:0.308656:0.635096:0.308656:0.000000
6,50,5:@0.544633:0.321154:0.605610:0.321154:0.605610:0.305484:0.544633:0.305484:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
61:@0.634731:0.321154:0.667182:0.321154:0.667182:0.305484:0.634731:0.305484:0.000000:0.000000
+:@0.569658:0.321831:0.579774:0.321831:0.579774:0.306258:0.569658:0.306258:0.000000
=:@0.614529:0.321831:0.624646:0.321831:0.624646:0.306258:0.614529:0.306258:0.000000
+:@0.646464:0.321831:0.656581:0.321831:0.656581:0.306258:0.646464:0.306258:0.000000
     1.  miembro         2.  miembro:@0.498334:0.350851:0.718131:0.350851:0.718131:0.336606:0.498334:0.336606:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
er:@0.527768:0.345354:0.535386:0.345354:0.535386:0.337049:0.527768:0.337049:0.000000:0.000000
o :@0.645146:0.345354:0.652480:0.345354:0.652480:0.337049:0.645146:0.337049:0.000000:0.000000
Observa lo que sucede con una igualdad cuando sumamos, restamos, multiplica-:@0.305303:0.374889:0.903652:0.374889:0.903652:0.359220:0.305303:0.359220:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mos o dividimos el mismo número racional en ambos miembros de ella::@0.305303:0.391486:0.834541:0.391486:0.834541:0.375816:0.305303:0.375816:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Se observa que la igualdad se conserva en cada caso. Esta :@0.305303:0.584045:0.749131:0.584045:0.749131:0.568375:0.305303:0.568375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propiedad:@0.750771:0.584045:0.834119:0.584045:0.834119:0.567145:0.750771:0.567145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 recibe el :@0.834119:0.584045:0.907701:0.584045:0.907701:0.568375:0.834119:0.568375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nombre de :@0.305303:0.600642:0.391452:0.600642:0.391452:0.584972:0.305303:0.584972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propiedad uniforme de la igualdad.:@0.391452:0.600642:0.672673:0.600642:0.672673:0.583741:0.391452:0.583741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si en una igualdad se encuentra un término desconocido, la igualdad se llama :@0.305303:0.683969:0.907590:0.683969:0.907590:0.668299:0.305303:0.668299:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ecuación:@0.305303:0.700566:0.376858:0.700566:0.376858:0.683665:0.305303:0.683665:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.376858:0.700566:0.380064:0.700566:0.380064:0.684896:0.376858:0.684896:0.000000
Ejemplo 1 :@0.305303:0.723980:0.378360:0.723980:0.378360:0.708868:0.305303:0.708868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Resolvemos:@0.305303:0.747767:0.400499:0.747767:0.400499:0.730867:0.305303:0.730867:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la siguiente ecuación: :@0.400499:0.747767:0.566898:0.747767:0.566898:0.732097:0.400499:0.732097:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.570981:0.747767:0.578463:0.747767:0.578463:0.731406:0.570981:0.731406:0.000000
3:@0.597738:0.738017:0.606731:0.738017:0.606731:0.722347:0.597738:0.722347:0.000000
4:@0.597522:0.759162:0.606515:0.759162:0.606515:0.743492:0.597522:0.743492:0.000000
3:@0.640450:0.738023:0.649443:0.738023:0.649443:0.722353:0.640450:0.722353:0.000000
5:@0.640450:0.759162:0.649443:0.759162:0.649443:0.743492:0.640450:0.743492:0.000000
+:@0.582341:0.748445:0.592458:0.748445:0.592458:0.732872:0.582341:0.732872:0.000000
= −:@0.612231:0.748445:0.636647:0.748445:0.636647:0.732872:0.612231:0.732872:0.000000:0.000000:0.000000
Solución:@0.305303:0.769668:0.365964:0.769668:0.365964:0.754555:0.305303:0.754555:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Shutterstock, 499777219.:@0.091447:0.252653:0.091447:0.177374:0.080059:0.177374:0.080059:0.252653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué cantidad hay que añadir a 5,74 para que la suma total sea –11,34?:@0.312004:0.165265:0.832799:0.165265:0.832799:0.149595:0.312004:0.149595:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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
Suma 2,5:@0.421051:0.416769:0.489451:0.416769:0.489451:0.401191:0.421051:0.401191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Resta 2,5:@0.720734:0.416769:0.788112:0.416769:0.788112:0.401191:0.720734:0.401191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(6,5 + 0,5) :@0.358196:0.442242:0.426596:0.442242:0.426596:0.427997:0.358196:0.427997:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+2,5:@0.426596:0.442242:0.455845:0.442242:0.455845:0.427997:0.426596:0.427997:0.000000:0.000000:0.000000:0.000000
 = 6 + (1 + :@0.455845:0.442242:0.528601:0.442242:0.528601:0.427997:0.455845:0.427997:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2,5:@0.528601:0.442242:0.547866:0.442242:0.547866:0.427997:0.528601:0.427997:0.000000:0.000000:0.000000
):@0.547866:0.442242:0.552306:0.442242:0.552306:0.427997:0.547866:0.427997:0.000000
7 + 2,5 = 6 + 3,5:@0.401819:0.460888:0.508666:0.460888:0.508666:0.446642:0.401819:0.446642:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
9,5 = 9,5:@0.427316:0.479533:0.483168:0.479533:0.483168:0.465288:0.427316:0.465288:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(6,5 + 0,5) :@0.657125:0.442229:0.725525:0.442229:0.725525:0.427984:0.657125:0.427984:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
– 2,5:@0.725525:0.442229:0.756836:0.442229:0.756836:0.427984:0.725525:0.427984:0.000000:0.000000:0.000000:0.000000:0.000000
 = 6 + (1 :@0.756836:0.442229:0.815938:0.442229:0.815938:0.427984:0.756836:0.427984:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
– 2,5:@0.815938:0.442229:0.847248:0.442229:0.847248:0.427984:0.815938:0.427984:0.000000:0.000000:0.000000:0.000000:0.000000
):@0.847248:0.442229:0.851688:0.442229:0.851688:0.427984:0.847248:0.427984:0.000000
7 – 2,5 = 6 – 1,5:@0.702591:0.460875:0.806222:0.460875:0.806222:0.446630:0.702591:0.446630:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4,5 = 4,5:@0.726480:0.479521:0.782333:0.479521:0.782333:0.465276:0.726480:0.465276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Multiplicación (– 4,5):@0.377628:0.504994:0.532838:0.504994:0.532838:0.489416:0.377628:0.489416:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
División (– 4,5):@0.699526:0.504994:0.809271:0.504994:0.809271:0.489416:0.699526:0.489416:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(6,5 + 0,5)(:@0.356403:0.530467:0.425574:0.530467:0.425574:0.516221:0.356403:0.516221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–4,5:@0.425574:0.530467:0.453215:0.530467:0.453215:0.516221:0.425574:0.516221:0.000000:0.000000:0.000000:0.000000
) = (6 + 1)(:@0.453215:0.530467:0.521967:0.530467:0.521967:0.516221:0.453215:0.516221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–4,5:@0.521967:0.530467:0.549608:0.530467:0.549608:0.516221:0.521967:0.516221:0.000000:0.000000:0.000000:0.000000
):@0.549608:0.530467:0.554048:0.530467:0.554048:0.516221:0.549608:0.516221:0.000000
–31,5 = –31,5 :@0.410748:0.549112:0.503372:0.549112:0.503372:0.534867:0.410748:0.534867:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(6,5 + 0,5) : (:@0.645315:0.530467:0.724738:0.530467:0.724738:0.516221:0.645315:0.516221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–4,5:@0.724738:0.530467:0.752379:0.530467:0.752379:0.516221:0.724738:0.516221:0.000000:0.000000:0.000000:0.000000
) = (6 + 1) : (:@0.752379:0.530467:0.831384:0.530467:0.831384:0.516221:0.752379:0.516221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–4,5:@0.831384:0.530467:0.859025:0.530467:0.859025:0.516221:0.831384:0.516221:0.000000:0.000000:0.000000:0.000000
):@0.859025:0.530467:0.863465:0.530467:0.863465:0.516221:0.859025:0.516221:0.000000
–1,5 = –1,5:@0.718087:0.549112:0.790692:0.549112:0.790692:0.534867:0.718087:0.534867:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Aplica  la :@0.323456:0.801023:0.396273:0.801023:0.396273:0.785353:0.323456:0.785353:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propiedad uniforme:@0.403450:0.801023:0.570902:0.801023:0.570902:0.784122:0.403450:0.784122:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 y :@0.570902:0.801023:0.594269:0.801023:0.594269:0.785353:0.570902:0.785353:0.000000:0.000000:0.000000
resta :@0.323456:0.827674:0.362596:0.827674:0.362596:0.812004:0.323456:0.812004:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.367674:0.817619:0.375849:0.817619:0.375849:0.803374:0.367674:0.803374:0.000000
4:@0.367517:0.838757:0.375692:0.838757:0.375692:0.824512:0.367517:0.824512:0.000000
.:@0.381024:0.827677:0.384230:0.827677:0.384230:0.812008:0.381024:0.812008:0.000000
Utiliza transposición de términos.:@0.621937:0.799765:0.863486:0.799765:0.863486:0.784401:0.621937:0.784401:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.625968:0.827010:0.632769:0.827010:0.632769:0.812136:0.625968:0.812136:0.000000
3:@0.664230:0.817266:0.672405:0.817266:0.672405:0.803021:0.664230:0.803021:0.000000
5:@0.664237:0.838404:0.672412:0.838404:0.672412:0.824158:0.664237:0.824158:0.000000
3:@0.690568:0.817266:0.698743:0.817266:0.698743:0.803021:0.690568:0.803021:0.000000
4:@0.690412:0.838404:0.698588:0.838404:0.698588:0.824158:0.690412:0.824158:0.000000
=− −:@0.637694:0.827626:0.685321:0.827626:0.685321:0.813469:0.637694:0.813469:0.000000:0.000000:0.000000:0.000000
La  incógnita  se  deja  en  el :@0.704034:0.825753:0.892388:0.825753:0.892388:0.811507:0.704034:0.811507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
primer miembro y el :@0.621947:0.852156:0.766016:0.852156:0.766016:0.837911:0.621947:0.837911:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.772353:0.842412:0.780529:0.842412:0.780529:0.828167:0.772353:0.828167:0.000000
4:@0.772196:0.863550:0.780371:0.863550:0.780371:0.849304:0.772196:0.849304:0.000000
 pasa al segun-:@0.785703:0.852156:0.888697:0.852156:0.888697:0.837911:0.785703:0.837911:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
do término con operación contraria, es :@0.621932:0.874787:0.892398:0.874787:0.892398:0.860542:0.621932:0.860542:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
decir, con resta.:@0.621932:0.889875:0.724775:0.889875:0.724775:0.875630:0.621932:0.875630:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.735267:0.902584:0.742068:0.902584:0.742068:0.887710:0.735267:0.887710:0.000000
27:@0.773529:0.892840:0.789712:0.892840:0.789712:0.878594:0.773529:0.878594:0.000000:0.000000
20:@0.773536:0.913978:0.789719:0.913978:0.789719:0.899733:0.773536:0.899733:0.000000:0.000000
=−:@0.746994:0.903200:0.769643:0.903200:0.769643:0.889043:0.746994:0.889043:0.000000:0.000000
+:@0.402229:0.861895:0.411426:0.861895:0.411426:0.847738:0.402229:0.847738:0.000000
−:@0.429452:0.861895:0.438649:0.861895:0.438649:0.847738:0.429452:0.847738:0.000000
=− −:@0.457730:0.861895:0.505357:0.861895:0.505357:0.847738:0.457730:0.847738:0.000000:0.000000:0.000000:0.000000
=−:@0.420406:0.901890:0.443055:0.901890:0.443055:0.887732:0.420406:0.887732:0.000000:0.000000
=−:@0.484953:0.901890:0.507602:0.901890:0.507602:0.887732:0.484953:0.887732:0.000000:0.000000
y:@0.391558:0.861279:0.398359:0.861279:0.398359:0.846405:0.391558:0.846405:0.000000
y:@0.382807:0.901277:0.389608:0.901277:0.389608:0.886403:0.382807:0.886403:0.000000
y:@0.473219:0.901277:0.480021:0.901277:0.480021:0.886403:0.473219:0.886403:0.000000
3:@0.416678:0.851535:0.424853:0.851535:0.424853:0.837290:0.416678:0.837290:0.000000
4:@0.416527:0.872670:0.424703:0.872670:0.424703:0.858425:0.416527:0.858425:0.000000
3:@0.443901:0.851535:0.452076:0.851535:0.452076:0.837290:0.443901:0.837290:0.000000
4:@0.443750:0.872670:0.451925:0.872670:0.451925:0.858425:0.443750:0.858425:0.000000
3:@0.484274:0.851535:0.492449:0.851535:0.492449:0.837290:0.484274:0.837290:0.000000
5:@0.484274:0.872670:0.492449:0.872670:0.492449:0.858425:0.484274:0.858425:0.000000
3:@0.510609:0.851535:0.518784:0.851535:0.518784:0.837290:0.510609:0.837290:0.000000
4:@0.510458:0.872670:0.518633:0.872670:0.518633:0.858425:0.510458:0.858425:0.000000
+0:@0.395185:0.901274:0.416561:0.901274:0.416561:0.887028:0.395185:0.887028:0.000000:0.000000
27:@0.446967:0.891530:0.463149:0.891530:0.463149:0.877284:0.446967:0.877284:0.000000:0.000000
20:@0.446936:0.912671:0.463119:0.912671:0.463119:0.898426:0.446936:0.898426:0.000000:0.000000
;:@0.466987:0.901277:0.469902:0.901277:0.469902:0.887032:0.466987:0.887032:0.000000
27:@0.511482:0.891533:0.527664:0.891533:0.527664:0.877288:0.511482:0.877288:0.000000:0.000000
20:@0.511487:0.912671:0.527670:0.912671:0.527670:0.898426:0.511487:0.898426:0.000000:0.000000
Si en ambos miembros de una igualdad adicionamos, sustraemos, multiplica-:@0.320179:0.627107:0.888115:0.627107:0.888115:0.611437:0.320179:0.611437:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mos o dividimos por un mismo número, la igualdad se conserva.:@0.316826:0.643703:0.789878:0.643703:0.789878:0.628033:0.316826:0.628033:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En años anteriores :@0.106213:0.414372:0.232139:0.414372:0.232139:0.400127:0.106213:0.400127:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
realizabas ecuaciones :@0.106213:0.429460:0.253886:0.429460:0.253886:0.415215:0.106213:0.415215:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuando los ejercicios :@0.106213:0.444548:0.248607:0.444548:0.248607:0.430302:0.106213:0.430302:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tenían un cajón :@0.106213:0.459635:0.213914:0.459635:0.213914:0.445390:0.106213:0.445390:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para completar las :@0.106213:0.474723:0.232778:0.474723:0.232778:0.460478:0.106213:0.460478:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
igualdades. Ese cajón :@0.106213:0.489811:0.251555:0.489811:0.251555:0.475565:0.106213:0.475565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es ahora reemplazado :@0.106213:0.504898:0.257151:0.504898:0.257151:0.490653:0.106213:0.490653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en las ecuaciones por :@0.106213:0.519986:0.253835:0.519986:0.253835:0.505741:0.106213:0.505741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
letras.:@0.106213:0.535073:0.144593:0.535073:0.144593:0.520828:0.106213:0.520828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Recuerda que...:@0.136265:0.389346:0.258346:0.389346:0.258346:0.372445:0.136265:0.372445:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.142666:0.563954:0.151863:0.563954:0.151863:0.549796:0.142666:0.549796:0.000000
=:@0.177159:0.563954:0.186356:0.563954:0.186356:0.549796:0.177159:0.549796:0.000000
+:@0.227835:0.563954:0.237032:0.563954:0.237032:0.549796:0.227835:0.549796:0.000000
+:@0.140723:0.583555:0.149920:0.583555:0.149920:0.569398:0.140723:0.569398:0.000000
=:@0.175216:0.583555:0.184413:0.583555:0.184413:0.569398:0.175216:0.569398:0.000000
x:@0.125024:0.582944:0.131809:0.582944:0.131809:0.568070:0.125024:0.568070:0.000000
x:@0.206005:0.582944:0.212790:0.582944:0.212790:0.568070:0.206005:0.568070:0.000000
6:@0.160100:0.563337:0.168275:0.563337:0.168275:0.549092:0.160100:0.549092:0.000000
9:@0.195280:0.563337:0.203455:0.563337:0.203455:0.549092:0.195280:0.549092:0.000000
6:@0.245269:0.563337:0.253445:0.563337:0.253445:0.549092:0.245269:0.549092:0.000000
6:@0.158157:0.582939:0.166332:0.582939:0.166332:0.568694:0.158157:0.568694:0.000000
9:@0.193337:0.582939:0.201512:0.582939:0.201512:0.568694:0.193337:0.568694:0.000000
+6:@0.218365:0.582939:0.239741:0.582939:0.239741:0.568694:0.218365:0.568694:0.000000:0.000000
:@0.122982:0.565310:0.050199:0.565310:0.050199:0.545516:0.122982:0.545516:0.000000
:@0.208156:0.565310:0.135374:0.565310:0.135374:0.545516:0.208156:0.545516:0.000000
Los quipus fueron el :@0.106105:0.718755:0.244763:0.718755:0.244763:0.704510:0.106105:0.704510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
principal sistema de :@0.106105:0.733843:0.243037:0.733843:0.243037:0.719597:0.106105:0.719597:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
registro de información :@0.106105:0.748930:0.265586:0.748930:0.265586:0.734685:0.106105:0.734685:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de los incas. Mediante  :@0.106105:0.764018:0.260627:0.764018:0.260627:0.749773:0.106105:0.749773:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cordeles anudados de :@0.106105:0.779105:0.257128:0.779105:0.257128:0.764860:0.106105:0.764860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
distintos colores, se :@0.106105:0.794193:0.238950:0.794193:0.238950:0.779948:0.106105:0.779948:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
registraba información :@0.106105:0.809281:0.260409:0.809281:0.260409:0.795035:0.106105:0.795035:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
contable que se basó :@0.106105:0.824368:0.252336:0.824368:0.252336:0.810123:0.106105:0.810123:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en un ordenamiento :@0.106105:0.839456:0.247895:0.839456:0.247895:0.825211:0.106105:0.825211:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
decimal. Esto permitía :@0.106105:0.854543:0.256908:0.854543:0.256908:0.840298:0.106105:0.840298:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
representar cantidades :@0.106105:0.869631:0.262472:0.869631:0.262472:0.855386:0.106105:0.855386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
desde las unidades :@0.106105:0.884719:0.236824:0.884719:0.236824:0.870473:0.106105:0.870473:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hasta las decenas de :@0.106105:0.899806:0.246708:0.899806:0.246708:0.885561:0.106105:0.885561:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
millares.:@0.106105:0.914894:0.159897:0.914894:0.159897:0.900649:0.106105:0.900649:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interculturalidad:@0.136439:0.691738:0.264659:0.691738:0.264659:0.674837:0.136439:0.674837:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.4.1.20.:@0.096359:0.940989:0.142269:0.940989:0.142269:0.930234:0.096359:0.930234:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Resolver ecuaciones de primer grado con una incógnita en :@0.142269:0.940989:0.422520:0.940989:0.422520:0.931017:0.142269:0.931017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.425242:0.942330:0.436972:0.942330:0.436972:0.928627:0.425242:0.928627:0.000000
 en la solución de problemas sencillos.:@0.440947:0.940989:0.619250:0.940989:0.619250:0.931017:0.440947:0.931017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
? + 5,74 = –11,34;   –11,34 – 5,74 = –17,08.   La cantidad que hay que añadir es –17,08.:@0.317594:0.175697:0.714632:0.175697:0.714632:0.165725:0.317594:0.165725:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000