Question

1-5/6＋7/12-9/20＋11/30-13/42＋15/56-14/72＋90/19等于多少

Answer 1

这道题要用“分数拆分法”来做，就是说把题中的各个分数拆分成下面的算式，达到正负抵消，从而使计算简便。

题中的“14/72”错啦，应该是“17/72”；还有“90/19”的分子分母写反啦，应该是“19/90”

5/6=1/2＋1/3
7/12=1/3＋1/4
9/20=1/4＋1/5
11/30=1/5＋1/6
13/42=1/6＋1/7
15/56=1/7＋1/8
17/72=1/8＋1/9
19/90=1/9＋1/10

1-5/6＋7/12-9/20＋11/30-13/42＋15/56-14/72＋19/90
=1-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)+(1/7+1/8)-(1/8+1/9)+(1/9+1/10) 去括号
=1-1/2-1/3+1/3+1/4-1/4-1/5+1/5+1/6-1/6-1/7+1/7+1/8-1/8-1/9+1/9+1/10
=1-1/2+1/10
=0.5＋0.1
=0.6

Answer 2

题目有错！最后一个应该是：19/90
1-5/6＋7/12-9/20＋11/30-13/42＋15/56-14/72＋19/90
=1-(1/2 +1/3)-(1/3+1/4)-(1/4+1/5)+(1/5+1/6).........+(1/9+1/10)
=1-1/2-1/3+1/3+1/4-1/4-1/5.........+1/9+1/10
=1-1/2+1/10
=3/5