巧算31X1/2X1/3+41X1/3X1/4+51X1/4X1/5=?

来源：百度知道 编辑：UC知道 时间：2024/04/29 11:00:25

31*1/2*1/3 + 41*1/3*1/4 + 51*1/4*1/5

=(30+1)*1/2*1/3 + (40+1)*1/3*1/4 + (50+1)*1/4*1/5

=5+1/6 + 10/3+1/12 + 5/2+1/20

=300/60 + 10/60 + 200/60 + 5/60 + 150/60 + 3/60

=668/60

=167/15

31X1/2X1/3+41X1/3X1/4+51X1/4X1/5
=(41X1/2X1/3+41X1/3X1/4+41X1/4X1/5)+(10X1/4X1/5-10X1/2X1/3)
=41X(1/2X1/3+1/3X1/4+1/4X1/5)+10X(1/4X1/5-1/2X1/3)
=41X(1/2-1/3+1/3-1/4+1/4-1/5)+10X(1/20-1/6)
=41X(1/2-1/5)-10X7/60
=41X3/10-7/6
=40X3/10+3/10-7/6
=12-13/15
=11又2/15

前面肯定还有个推导模式啊。。在哪里呢？
小学课本和寒暑假作业上蛮多这种。。
给出推导模式就很简单，凭空这样算，难。