Question

(1+1/2+1/3+1/4+1/5+1/6)x(1/2+1/3+1/4+1/5)-(1/2*1/3+1/4+1/5+1/6)x(1/2+1/3+1/4+1/5) 用简便算法

(1+1/2+1/3+1/4+1/5+1/6)x(1/2+1/3+1/4+1/5)-(1/2*1/3+1/4+1/5+1/6)x(1/2+1/3+1/4+1/5) 用简便算法
要具体算式，不要什么a=(1+1/2+1/3+1/4+1/5+1/6)

Answer 1

a=1/2+1/3+1/4+1/5+1/6

b=1/2+1/3+1/4+1/5

(1+1/2+1/3+1/4+1/5+1/6)x(1/2+1/3+1/4+1/5)-(1/2*1/3+1/4+1/5+1/6)x(1/2+1/3+1/4+1/5)
=(1+a)b-ab

=b+ab-ab

=b=1/2+1/3+1/4+1/5
也可用分配律

Answer 2

(1+1/2+1/3+1/4+1/5+1/6)x(1/2+1/3+1/4+1/5)-(1/2*1/3+1/4+1/5+1/6)x(1/2+1/3+1/4+1/5)
=（1/2+1/3+1/4+1/5）×[(1+1/2+1/3+1/4+1/5+1/6)-(1/2*1/3+1/4+1/5+1/6)]
=(1/2+1/3+1/4+1/5)×1
=1/2+1/3+1/4+1/5
=30/60+20/60+15/60+12/60
=(30+20+15+12)/60
=77/60

Answer 3

(1+1/2+1/3+1/4+1/5+1/6)x(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4+1/5+1/6)x(1/2+1/3+1/4+1/5)
=[(1+1/2+1/3+1/4+1/5+1/6)-(1/2+1/3+1/4+1/5+1/6)]×(1/2+1/3+1/4+1/5)
=(1+1/2+1/3+1/4+1/5+1/6-1/2-1/3-1/4-1/5-1/6)(1/2+1/3+1/4+1/5)
=1×(1/2+1/3+1/4+1/5)
=1/2+1/3+1/4+1/5
=77/60

Answer 4

(1+1/2+1/3+1/4+1/5+1/6)x(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4+1/5+1/6)x(1/2+1/3+1/4+1/5)
= (1/2+1/3+1/4+1/5)（1+1/2+1/3+1/4+1/5+1/6 - 1/2+1/3+1/4+1/5+1/6）
= (1/2+1/3+1/4+1/5)*1
= 1/2+1/3+1/4+1/5
= 77/60

Answer 5

(1+1/2+1/3+1/4+1/5+1/6)x(1/2+1/3+1/4+1/5)-(1/2*1/3+1/4+1/5+1/6)x(1/2+1/3+1/4+1/5)
=[(1+1/2+1/3+1/4+1/5+1/6)-(1/2*1/3+1/4+1/5+1/6)]*(1/2+1/3+1/4+1/5)
=5/3*(1/2+1/3+1/4+1/5)
=5/3*(30+20+15+12)/60
=77/24