先来看一个规律
(1/2)×(1/3)=1/6 (1/2)-(1/3)=(3/6)-(2/6)=1/6
所以 (1/2)×(1/3)=(1/2)-(1/3)
同样 (1/3)×(1/4)=1/12 (1/3)-(1/4)=(4/12)-(3/12)=1/12
所以 (1/3)×(1/4)=(1/3)-(1/4)
依此类推……………………
根据这个规律,原来的式了就可以变成 :
(1/2)×(1/3)+(1/3)×(1/4)+(1/4)×(1/5)…………+(1/8)×(1/9)+(1/9)×(1/10)
=(1/2)-(1/3)+(1/3)-(1/4)+(1/4)-(1/5)…………+(1/8)-(1/9)+(1/9)-(1/10)
=(1/2)-(1/10)
=4/10=2/5
(最后一个式子第二行中,-1/3+1/3=0, -1/4+1/4=0 ………… )
——————————————————————————————————————————-做作业就只需这样写:(1/2)×(1/3)+(1/3)×(1/4)…………+(1/9)×(1/10)
=(1/2)-(1/3)+(1/3)-(1/4)…………+(1/9)-(1/10)
=(1/2)-(1/10)
=2/5
分数上的括号都不要写