Question

Вычислите(это дроби) (1/2-1/3): (1/13-1/14)×(1/14-1/15): (1/15-1/16)=? решить резвернуто и второй (1/14-1/15): (1/15-1/16)×(1/16-1/17): (1/17-1/18)=? тоже развернуто решить я в пятом классе

Answer 1

1) (1/2-1/3):(1/13-1/14)×(1/14-1/15):(1/15-1/16)=

(3/(2*3) - 2/(2*3)):(14/(13*14) - 13/(13*14)) * (15/(14*15) - 14/(14*15)):(16/(15*16) - 15/(15*16)) = (1/6):(1/(13*14)) * (1/(14*15)):(1/(15*16)) = ((13*14)/6) * ((15*16)/14*15) =

((13*14)/6) * 16/14 = (13*14*16)/(6*14) = (13*16)/6 = (13*8)/3 = 104/3 = 34 2/3;

2) (1/14-1/15):(1/15-1/16)×(1/16-1/17):(1/17-1/18)=

(15/(14*15) - 14/(14*15)):(16/(15*16) - 15/(15*16)) * (17/(16*17) - 16/(16*17)):(18/(17*18) - 17/(17*18)) =

(1/(14*15)):(1/(15*16)) * (1/(15*16)):(1/(16*17)) = ((15*16)/(14*15)) * ((16*17)/(15*16)) = (16/14) * (17/15) = (16*17)/(14*15) = (8*17)/(7*15) = 136/105 = 1 31/105;