25:@0.921538:0.966074:0.940353:0.966074:0.940353:0.949450:0.921538:0.949450:0.000000:0.000000
Propiedad:@0.111474:0.173531:0.189222:0.173531:0.189222:0.157953:0.111474:0.157953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Enunciado:@0.281829:0.173531:0.360817:0.173531:0.360817:0.157953:0.281829:0.157953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Expresión algebraica:@0.459555:0.173531:0.615217:0.173531:0.615217:0.157953:0.459555:0.157953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplos:@0.735819:0.173531:0.804370:0.173531:0.804370:0.157953:0.735819:0.157953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Clausurativa:@0.103416:0.215035:0.189187:0.215035:0.189187:0.199922:0.103416:0.199922:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Al multiplicar dos números :@0.211503:0.199947:0.394603:0.199947:0.394603:0.185702:0.211503:0.185702:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
enteros, se obtiene como :@0.211503:0.215035:0.384588:0.215035:0.384588:0.200790:0.211503:0.200790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
resultado otro número entero.:@0.211503:0.230123:0.412630:0.230123:0.412630:0.215877:0.211503:0.215877:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.455765:0.214127:0.464570:0.214127:0.469441:0.199503:0.460636:0.199503:0.000000
,:@0.465910:0.214127:0.468956:0.214127:0.468956:0.199240:0.465910:0.199240:0.000000
b:@0.468198:0.214127:0.477862:0.214127:0.482820:0.199240:0.473157:0.199240:0.000000
;:@0.510570:0.214127:0.513616:0.214127:0.513616:0.199240:0.510570:0.199240:0.000000
a:@0.513207:0.214127:0.522013:0.214127:0.526884:0.199503:0.518078:0.199503:0.000000
b c:@0.533797:0.214127:0.566173:0.214127:0.571131:0.199240:0.538756:0.199240:0.000000:0.000000:0.000000
=:@0.548270:0.214770:0.557881:0.214770:0.557881:0.199976:0.548270:0.199976:0.000000
;:@0.569953:0.214127:0.572999:0.214127:0.572999:0.199240:0.569953:0.199240:0.000000
c:@0.589151:0.214127:0.596958:0.214127:0.601917:0.199240:0.594109:0.199240:0.000000
(–3) (+4) = –12:@0.643648:0.215030:0.741834:0.215030:0.741834:0.200785:0.643648:0.200785:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Conmutativa:@0.103433:0.261349:0.193744:0.261349:0.193744:0.246236:0.103433:0.246236:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El orden de los factores no altera :@0.211520:0.253805:0.431961:0.253805:0.431961:0.239560:0.211520:0.239560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el producto.:@0.211520:0.268893:0.292047:0.268893:0.292047:0.254647:0.211520:0.254647:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.460209:0.259765:0.472004:0.259765:0.472004:0.245786:0.460209:0.245786:0.000000
∈:@0.495874:0.259765:0.507669:0.259765:0.507669:0.245786:0.495874:0.245786:0.000000
×= ×:@0.534187:0.259765:0.589058:0.259765:0.589058:0.245786:0.534187:0.245786:0.000000:0.000000:0.000000:0.000000
ab:@0.471921:0.259157:0.493211:0.259157:0.493211:0.245339:0.471921:0.245339:0.000000:0.000000
ab ba:@0.523318:0.259157:0.600157:0.259157:0.600157:0.245339:0.523318:0.245339:0.000000:0.000000:0.000000:0.000000:0.000000
,:@0.480788:0.259157:0.483666:0.259157:0.483666:0.245090:0.480788:0.245090:0.000000
;:@0.515576:0.259157:0.518455:0.259157:0.518455:0.245090:0.515576:0.245090:0.000000
(–3) (4)= (4) (–3) = –12:@0.643648:0.261346:0.791655:0.261346:0.791655:0.247101:0.643648:0.247101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Asociativa:@0.103433:0.307665:0.174380:0.307665:0.174380:0.292553:0.103433:0.292553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Al agrupar de diferente forma los :@0.211520:0.292578:0.434424:0.292578:0.434424:0.278332:0.211520:0.278332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
factores en una multiplicación, el :@0.211520:0.307665:0.434829:0.307665:0.434829:0.293420:0.211520:0.293420:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
producto no se altera.:@0.211520:0.322753:0.357180:0.322753:0.357180:0.308508:0.211520:0.308508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.463213:0.294695:0.473531:0.294695:0.473531:0.282465:0.463213:0.282465:0.000000
∈:@0.505891:0.294695:0.516209:0.294695:0.516209:0.282465:0.505891:0.282465:0.000000
×:@0.476701:0.310998:0.484646:0.310998:0.484646:0.298768:0.476701:0.298768:0.000000
× =×:@0.500131:0.310998:0.548134:0.310998:0.548134:0.298768:0.500131:0.298768:0.000000:0.000000:0.000000:0.000000
×:@0.563605:0.310998:0.571550:0.310998:0.571550:0.298768:0.563605:0.298768:0.000000
ab c:@0.473459:0.294163:0.502866:0.294163:0.502866:0.282074:0.473459:0.282074:0.000000:0.000000:0.000000:0.000000
ab:@0.467366:0.310466:0.493922:0.310466:0.493922:0.298377:0.467366:0.298377:0.000000:0.000000
ca:@0.510362:0.310466:0.538119:0.310466:0.538119:0.298377:0.510362:0.298377:0.000000:0.000000
bc:@0.554285:0.310466:0.579871:0.310466:0.579871:0.298377:0.554285:0.298377:0.000000:0.000000
,,:@0.481231:0.294163:0.495297:0.294163:0.495297:0.281857:0.481231:0.281857:0.000000:0.000000
;:@0.520333:0.294163:0.522852:0.294163:0.522852:0.281857:0.520333:0.281857:0.000000
(:@0.462605:0.310466:0.466440:0.310466:0.466440:0.298160:0.462605:0.298160:0.000000
):@0.494718:0.310466:0.498553:0.310466:0.498553:0.298160:0.494718:0.298160:0.000000
(:@0.549798:0.310466:0.553633:0.310466:0.553633:0.298160:0.549798:0.298160:0.000000
):@0.581000:0.310466:0.584835:0.310466:0.584835:0.298160:0.581000:0.298160:0.000000
[:@0.639674:0.309893:0.645504:0.309893:0.645504:0.289477:0.639674:0.289477:0.000000
]:@0.704430:0.309893:0.710260:0.309893:0.710260:0.289477:0.704430:0.289477:0.000000
[:@0.783306:0.309893:0.789136:0.309893:0.789136:0.289477:0.783306:0.289477:0.000000
]:@0.846959:0.309893:0.852788:0.309893:0.852788:0.289477:0.846959:0.289477:0.000000
+:@0.651562:0.307318:0.661173:0.307318:0.661173:0.292523:0.651562:0.292523:0.000000
−:@0.680902:0.307318:0.690513:0.307318:0.690513:0.292523:0.680902:0.292523:0.000000
−= +:@0.715967:0.307318:0.769046:0.307318:0.769046:0.292523:0.715967:0.292523:0.000000:0.000000:0.000000:0.000000
−:@0.795201:0.307318:0.804812:0.307318:0.804812:0.292523:0.795201:0.292523:0.000000
−:@0.823841:0.307318:0.833452:0.307318:0.833452:0.292523:0.823841:0.292523:0.000000
= +:@0.854967:0.307318:0.877673:0.307318:0.877673:0.292523:0.854967:0.292523:0.000000:0.000000:0.000000
(4)( 2) (3)( 4) (2)( 3):@0.645802:0.306674:0.846582:0.306674:0.846582:0.291788:0.645802:0.291788:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
24:@0.877515:0.306674:0.894409:0.306674:0.894409:0.291788:0.877515:0.291788:0.000000:0.000000
Elemento :@0.103426:0.359743:0.173803:0.359743:0.173803:0.344630:0.103426:0.344630:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
neutro:@0.103426:0.378389:0.150400:0.378389:0.150400:0.363276:0.103426:0.363276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La multiplicación de un número :@0.211512:0.346428:0.428553:0.346428:0.428553:0.332183:0.211512:0.332183:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entero con 1 da como producto :@0.211512:0.361516:0.429340:0.361516:0.429340:0.347270:0.211512:0.347270:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el mismo número entero. :@0.211512:0.376603:0.383943:0.376603:0.383943:0.362358:0.211512:0.362358:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1 es el :@0.383943:0.376603:0.431905:0.376603:0.431905:0.361239:0.383943:0.361239:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
elemento neutro.:@0.211512:0.391691:0.336500:0.391691:0.336500:0.376327:0.211512:0.376327:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀∈:@0.485673:0.355861:0.515284:0.355861:0.515284:0.343859:0.485673:0.343859:0.000000:0.000000
∈:@0.534328:0.355861:0.544454:0.355861:0.544454:0.343859:0.534328:0.343859:0.000000
×=× =:@0.494989:0.371839:0.554921:0.371839:0.554921:0.359837:0.494989:0.359837:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.495728:0.355339:0.502871:0.355339:0.502871:0.343476:0.495728:0.343476:0.000000
a:@0.485673:0.371316:0.492816:0.371316:0.492816:0.359453:0.485673:0.359453:0.000000
a a:@0.537396:0.371316:0.564877:0.371316:0.564877:0.359453:0.537396:0.359453:0.000000:0.000000:0.000000
,1:@0.519843:0.355339:0.532241:0.355339:0.532241:0.343263:0.519843:0.343263:0.000000:0.000000
;:@0.554112:0.355339:0.556583:0.355339:0.556583:0.343263:0.554112:0.343263:0.000000
11:@0.504050:0.371316:0.527483:0.371316:0.527483:0.359240:0.504050:0.359240:0.000000:0.000000
(–2) × 1 = 1 × (–2) = –2:@0.643648:0.369068:0.796698:0.369068:0.796698:0.354823:0.643648:0.354823:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Elemento :@0.103433:0.421146:0.173810:0.421146:0.173810:0.406033:0.103433:0.406033:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
absorbente:@0.103433:0.439791:0.183408:0.439791:0.183408:0.424679:0.103433:0.424679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Todo número entero :@0.211520:0.415375:0.353512:0.415375:0.353512:0.401129:0.211520:0.401129:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
multiplicado por 0 da como :@0.211520:0.430462:0.401124:0.430462:0.401124:0.416217:0.211520:0.416217:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
resultado 0.:@0.211520:0.445550:0.288665:0.445550:0.288665:0.431305:0.211520:0.431305:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀ ∈:@0.491690:0.421314:0.528086:0.421314:0.528086:0.404194:0.491690:0.404194:0.000000:0.000000:0.000000
a:@0.504067:0.420749:0.512873:0.420749:0.512873:0.405206:0.504067:0.405206:0.000000
!:@0.527893:0.421577:0.539570:0.421577:0.539570:0.405666:0.527893:0.405666:0.000000
,0:@0.539885:0.420749:0.552560:0.420749:0.552560:0.405179:0.539885:0.405179:0.000000:0.000000
∉:@0.555203:0.421314:0.567685:0.421314:0.567685:0.404194:0.555203:0.404194:0.000000
!:@0.567492:0.421577:0.579169:0.421577:0.579169:0.405666:0.567492:0.405666:0.000000
;:@0.579484:0.420749:0.582530:0.420749:0.582530:0.405179:0.579484:0.405179:0.000000
a:@0.491708:0.440457:0.500514:0.440457:0.500514:0.424914:0.491708:0.424914:0.000000
⋅:@0.502159:0.441022:0.506536:0.441022:0.506536:0.423902:0.502159:0.423902:0.000000
0 0:@0.507533:0.440457:0.540253:0.440457:0.540253:0.424888:0.507533:0.424888:0.000000:0.000000:0.000000
=:@0.519070:0.441022:0.528681:0.441022:0.528681:0.423902:0.519070:0.423902:0.000000
⋅:@0.541811:0.441022:0.546187:0.441022:0.546187:0.423902:0.541811:0.423902:0.000000
a:@0.547535:0.440457:0.556341:0.440457:0.556341:0.424914:0.547535:0.424914:0.000000
=:@0.559422:0.441022:0.569033:0.441022:0.569033:0.423902:0.559422:0.423902:0.000000
0:@0.572062:0.440457:0.580605:0.440457:0.580605:0.424888:0.572062:0.424888:0.000000
(–2) × 0 = 0 × (–2)= 0:@0.643648:0.430473:0.784653:0.430473:0.784653:0.416228:0.643648:0.416228:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La multiplicación se relaciona con la adición y sustracción mediante la propiedad distributiva.:@0.103433:0.469249:0.723498:0.469249:0.723498:0.455003:0.103433:0.455003:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Distributiva:@0.103433:0.523111:0.184446:0.523111:0.184446:0.507999:0.103433:0.507999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Un número entero multiplicado :@0.211520:0.492936:0.427272:0.492936:0.427272:0.478691:0.211520:0.478691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por una adición o sustracción :@0.211520:0.508024:0.411895:0.508024:0.411895:0.493779:0.211520:0.493779:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es igual a la suma o resta de los :@0.211520:0.523111:0.423585:0.523111:0.423585:0.508866:0.211520:0.508866:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
productos del número por cada :@0.211520:0.538199:0.427758:0.538199:0.427758:0.523954:0.211520:0.523954:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
elemento.:@0.211520:0.553287:0.278746:0.553287:0.278746:0.539041:0.211520:0.539041:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.460209:0.513152:0.472956:0.513152:0.472956:0.498044:0.460209:0.498044:0.000000
∈:@0.512018:0.513152:0.524764:0.513152:0.524764:0.498044:0.512018:0.498044:0.000000
±:@0.486668:0.533291:0.496482:0.533291:0.496482:0.518184:0.486668:0.518184:0.000000
= ×±×:@0.515772:0.533291:0.599831:0.533291:0.599831:0.518184:0.515772:0.518184:0.000000:0.000000:0.000000:0.000000:0.000000
ab c:@0.472866:0.512495:0.508675:0.512495:0.508675:0.497561:0.472866:0.497561:0.000000:0.000000:0.000000:0.000000
ab c:@0.460209:0.532634:0.506959:0.532634:0.506959:0.517700:0.460209:0.517700:0.000000:0.000000:0.000000:0.000000
a ba:@0.529126:0.532634:0.587281:0.532634:0.587281:0.517700:0.529126:0.517700:0.000000:0.000000:0.000000:0.000000
,,:@0.482431:0.512495:0.499557:0.512495:0.499557:0.497293:0.482431:0.497293:0.000000:0.000000
;:@0.529663:0.512495:0.532773:0.512495:0.532773:0.497293:0.529663:0.497293:0.000000
(:@0.469041:0.532634:0.473778:0.532634:0.473778:0.517432:0.469041:0.517432:0.000000
):@0.508353:0.532634:0.513090:0.532634:0.513090:0.517432:0.508353:0.517432:0.000000
c:@0.602513:0.532634:0.610486:0.532634:0.610486:0.517432:0.602513:0.517432:0.000000
–2 (3 + 4) = –6 + (–8) =:@0.643648:0.513782:0.796698:0.513782:0.796698:0.499537:0.643648:0.499537:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 – 6 – 8 = –14:@0.643648:0.532428:0.733474:0.532428:0.733474:0.518183:0.643648:0.518183:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Propiedades de la multiplicación de números enteros  :@0.096359:0.121431:0.658482:0.121431:0.658482:0.099622:0.096359:0.099622:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La multiplicación de números enteros cumple con las siguientes propiedades::@0.096359:0.144212:0.667061:0.144212:0.667061:0.128543:0.096359:0.128543:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 2:@0.096359:0.590982:0.165865:0.590982:0.165865:0.575869:0.096359:0.575869:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Completamos la siguiente expresión y escribimos la propiedad que cumple.:@0.096359:0.611456:0.652443:0.611456:0.652443:0.595786:0.096359:0.595786:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
×− +:@0.125257:0.639629:0.174790:0.639629:0.174790:0.624056:0.125257:0.624056:0.000000:0.000000:0.000000:0.000000
×:@0.203832:0.639629:0.213949:0.639629:0.213949:0.624056:0.203832:0.624056:0.000000
=× −+:@0.233464:0.639629:0.308501:0.639629:0.308501:0.624056:0.233464:0.624056:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.338059:0.639629:0.348176:0.639629:0.348176:0.624056:0.338059:0.624056:0.000000
(:@0.098555:0.638952:0.103439:0.638952:0.103439:0.623282:0.098555:0.623282:0.000000
3)(:@0.148439:0.638952:0.182032:0.638952:0.182032:0.623282:0.148439:0.623282:0.000000:0.000000:0.000000
5) 6( 3:@0.216713:0.638952:0.296431:0.638952:0.296431:0.623282:0.216713:0.623282:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
) 12:@0.330412:0.638952:0.368096:0.638952:0.368096:0.623282:0.330412:0.623282:0.000000:0.000000:0.000000:0.000000
Solución:@0.096359:0.664833:0.157020:0.664833:0.157020:0.649720:0.096359:0.649720:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
×− +:@0.116357:0.685734:0.165891:0.685734:0.165891:0.670162:0.116357:0.670162:0.000000:0.000000:0.000000:0.000000
×:@0.186032:0.685734:0.196149:0.685734:0.196149:0.670162:0.186032:0.670162:0.000000
=× −+:@0.215664:0.685734:0.290701:0.685734:0.290701:0.670162:0.215664:0.670162:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.310198:0.685734:0.320314:0.685734:0.320314:0.670162:0.310198:0.670162:0.000000
(6:@0.098558:0.685057:0.113632:0.685057:0.113632:0.669387:0.098558:0.669387:0.000000:0.000000
3) (6 5) 6( 35)12   Se está aplicando la propiedad distributiva.:@0.139541:0.685057:0.662964:0.685052:0.662964:0.669382:0.139541:0.669387:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   :@0.344294:0.690086:0.356401:0.690086:0.356401:0.674416:0.344294:0.674416:0.000000:0.000000:0.000000
Ejemplo 3:@0.096359:0.712304:0.165865:0.712304:0.165865:0.697191:0.096359:0.697191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Aplicamos la propiedad asociativa de dos maneras diferentes.:@0.096359:0.732779:0.546668:0.732779:0.546668:0.717109:0.096359:0.717109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−× ×− ×− =:@0.099343:0.760953:0.245622:0.760953:0.245622:0.745380:0.099343:0.745380:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
37 (5)( 4):@0.109290:0.760275:0.232755:0.760275:0.232755:0.744605:0.109290:0.744605:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Solución:@0.096359:0.785740:0.157020:0.785740:0.157020:0.770627:0.096359:0.770627:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.160683:0.810930:0.166206:0.810930:0.166206:0.791589:0.160683:0.791589:0.000000
]:@0.235133:0.810930:0.240655:0.810930:0.240655:0.791589:0.235133:0.791589:0.000000
−×:@0.104474:0.808491:0.132386:0.808491:0.132386:0.794476:0.104474:0.794476:0.000000:0.000000
×− ×−:@0.149800:0.808491:0.221297:0.808491:0.221297:0.794476:0.149800:0.794476:0.000000:0.000000:0.000000:0.000000:0.000000
=− ×:@0.242725:0.808491:0.288864:0.808491:0.288864:0.794476:0.242725:0.794476:0.000000:0.000000:0.000000:0.000000
= −:@0.310292:0.808491:0.331786:0.808491:0.331786:0.794476:0.310292:0.794476:0.000000:0.000000:0.000000
(3 7):@0.099017:0.807881:0.147793:0.807881:0.147793:0.793778:0.099017:0.793778:0.000000:0.000000:0.000000:0.000000:0.000000
(5)( 4):@0.166484:0.807881:0.234781:0.807881:0.234781:0.793778:0.166484:0.793778:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
21 20:@0.264070:0.807881:0.307356:0.807881:0.307356:0.793778:0.264070:0.793778:0.000000:0.000000:0.000000:0.000000:0.000000
420:@0.331637:0.807881:0.355552:0.807881:0.355552:0.793778:0.331637:0.793778:0.000000:0.000000:0.000000
;:@0.368224:0.807473:0.371430:0.807473:0.371430:0.791803:0.368224:0.791803:0.000000
 :@0.371430:0.815010:0.375466:0.815010:0.375466:0.799340:0.371430:0.799340:0.000000
[:@0.420441:0.810138:0.425964:0.810138:0.425964:0.790796:0.420441:0.790796:0.000000
]:@0.475386:0.810138:0.480909:0.810138:0.480909:0.790796:0.475386:0.790796:0.000000
−×:@0.390757:0.807699:0.418670:0.807699:0.418670:0.793683:0.390757:0.793683:0.000000:0.000000
×−:@0.436797:0.807699:0.462586:0.807699:0.462586:0.793683:0.436797:0.793683:0.000000:0.000000
×− =− ×−:@0.482505:0.807699:0.581234:0.807699:0.581234:0.793683:0.482505:0.793683:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
×− =−:@0.603591:0.807699:0.666829:0.807699:0.666829:0.793683:0.603591:0.793683:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.399713:0.807089:0.407806:0.807089:0.407806:0.792986:0.399713:0.792986:0.000000
7 (5):@0.426232:0.807089:0.475025:0.807089:0.475025:0.792986:0.426232:0.792986:0.000000:0.000000:0.000000:0.000000:0.000000
( 4):@0.493716:0.807089:0.521761:0.807089:0.521761:0.792986:0.493716:0.792986:0.000000:0.000000:0.000000:0.000000
3( 35)( 4):@0.545594:0.807089:0.642864:0.807089:0.642864:0.792986:0.545594:0.792986:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
420:@0.666696:0.807089:0.690612:0.807089:0.690612:0.792986:0.666696:0.792986:0.000000:0.000000:0.000000
Ejemplo 4:@0.096359:0.840481:0.165865:0.840481:0.165865:0.825368:0.096359:0.825368:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Resolvemos la operación aplicando dos propiedades.  57 (2):@0.096359:0.864728:0.580755:0.863470:0.580755:0.847801:0.096359:0.849058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−× ×− =:@0.492804:0.864148:0.593640:0.864148:0.593640:0.848575:0.492804:0.848575:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Solución:@0.096359:0.890193:0.157020:0.890193:0.157020:0.875080:0.096359:0.875080:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Asociativa (5 7) (2):@0.096359:0.910876:0.275068:0.910613:0.275068:0.894943:0.096359:0.895206:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−×:@0.182285:0.911291:0.213244:0.911291:0.213244:0.895718:0.182285:0.895718:0.000000:0.000000
×− =−:@0.232538:0.911291:0.300664:0.911291:0.300664:0.895718:0.232538:0.895718:0.000000:0.000000:0.000000:0.000000:0.000000
×− =:@0.320179:0.911291:0.375425:0.911291:0.375425:0.895718:0.320179:0.895718:0.000000:0.000000:0.000000:0.000000
35( 2) 70   5:@0.300499:0.910613:0.425771:0.910918:0.425771:0.895249:0.300499:0.894943:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.440542:0.914050:0.446678:0.914050:0.446678:0.894117:0.440542:0.894117:0.000000
):@0.500800:0.914050:0.506937:0.914050:0.506937:0.894117:0.500800:0.894117:0.000000
−×:@0.406828:0.911596:0.437786:0.911596:0.437786:0.896023:0.406828:0.896023:0.000000:0.000000
×−:@0.458241:0.911596:0.486527:0.911596:0.486527:0.896023:0.458241:0.896023:0.000000:0.000000
=− ×−:@0.509801:0.911596:0.571810:0.911596:0.571810:0.896023:0.509801:0.896023:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.598180:0.911596:0.608297:0.911596:0.608297:0.896023:0.598180:0.896023:0.000000
7 (2):@0.446576:0.910918:0.500753:0.910918:0.500753:0.895249:0.446576:0.895249:0.000000:0.000000:0.000000:0.000000:0.000000
5 (14) 70:@0.532615:0.910918:0.628402:0.910918:0.628402:0.895249:0.532615:0.895249:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Conmutativa    (2)( 5) 770:@0.096359:0.935026:0.350503:0.934164:0.350503:0.918494:0.096359:0.919356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−× −× =:@0.224882:0.934842:0.330380:0.934842:0.330380:0.919269:0.224882:0.919269:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−× ×− =:@0.409843:0.933802:0.515341:0.933802:0.515341:0.918229:0.409843:0.918229:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(2)7 (5)70  :@0.404131:0.933125:0.549071:0.935026:0.549071:0.919356:0.404131:0.917455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  :@0.578831:0.935026:0.586903:0.935026:0.586903:0.919356:0.578831:0.919356:0.000000:0.000000
Cuando hay dificultades :@0.733044:0.636463:0.897753:0.636463:0.897753:0.622218:0.733044:0.622218:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en la expresión oral, :@0.733044:0.651551:0.868804:0.651551:0.868804:0.637306:0.733044:0.637306:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es importante buscar :@0.733044:0.666639:0.878553:0.666639:0.878553:0.652393:0.733044:0.652393:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
métodos alternativos :@0.733044:0.681726:0.877783:0.681726:0.877783:0.667481:0.733044:0.667481:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de comunicación.:@0.733044:0.696814:0.852287:0.696814:0.852287:0.682569:0.733044:0.682569:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DFA:@0.765616:0.611952:0.797974:0.611952:0.797974:0.595052:0.765616:0.595052:0.000000:0.000000:0.000000
En economía y finanzas, :@0.732126:0.779874:0.895192:0.779874:0.895192:0.765628:0.732126:0.765628:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los números negativos :@0.732126:0.794961:0.886598:0.794961:0.886598:0.780716:0.732126:0.780716:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
expresan pérdidas :@0.732126:0.810049:0.857449:0.810049:0.857449:0.795804:0.732126:0.795804:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o saldos en contra. :@0.732126:0.825136:0.860499:0.825136:0.860499:0.810891:0.732126:0.810891:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Mantener el control de :@0.732126:0.840224:0.888474:0.840224:0.888474:0.825979:0.732126:0.825979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los gastos ayuda a tener :@0.732126:0.855312:0.895726:0.855312:0.895726:0.841066:0.732126:0.841066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una economía sana.:@0.732126:0.870399:0.865525:0.870399:0.865525:0.856154:0.732126:0.856154:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué opinas? :@0.732126:0.892616:0.824984:0.892616:0.824984:0.878371:0.732126:0.878371:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Debate:@0.824984:0.892616:0.875979:0.892616:0.875979:0.877503:0.824984:0.877503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.875979:0.892616:0.879647:0.892616:0.879647:0.878371:0.875979:0.878371:0.000000
con tus compañeros de :@0.732126:0.907703:0.893701:0.907703:0.893701:0.893458:0.732126:0.893458:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
clase.:@0.732126:0.922791:0.767875:0.922791:0.767875:0.908546:0.732126:0.908546:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia  :@0.762461:0.742889:0.873488:0.742889:0.873488:0.725988:0.762461:0.725988:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
socioemocional:@0.762461:0.756719:0.885079:0.756719:0.885079:0.739819:0.762461:0.739819:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ©:@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