脱式计算（怎么样简便怎样算）9又1/3+99又1/3+999又1/3+2又2/3==0.125×9+0.1×125%==1111----+-----+-----+.+------1×22×33×49×10==

Question

脱式计算（怎么样简便怎样算）
9又1/3+99又1/3+999又1/3+2又2/3
=
=
0.125×9+0.1×125%
=
=
1 1 1 1
---- + ----- + ----- + .+ ------
1×2 2×3 3×4 9×10
=
=

Answer 1

9又1/3+99又1/3+999又1/3+2又2/3
=9+(1/3)+99+(1/3)+999+(1/3)+2+(2/3)
=9+99+999+2+[(1/3)+(1/3)+(1/3)]+(2/3)
=(10-1)+(100-1)+(1000-1)+2+1+(2/3)
=1110又2/3
0.125×9+0.1×125%
=0.125*9+0.1*1.25
=0.125*9+1*0.125
=0.125*（9+1）
=1.25
1 1 1 1
---- + ----- + ----- + .+ ------
1×2 2×3 3×4 9×10
=[（1/1）-（1/2）]+[（1/2）-（1/3）]+……+[（1/9）-（1/10）]
= 1-1/2+1/2-1/3+……+1/9-1/10
=1-1/10
=9/10