计算：1+1/2_5/6+7/12_9/20+11/30_13/42+15/56
计算：1+1/2_5/6+7/12_9/20+11/30_13/42+15/56
9/8
解析：
1+1/2-5/6+7/12-9/20+11/30-13/42+15/56
=1+1/2-1/2-1/3+1/3+1/4-1/4-1/5+1/5+1/6-1/6-1/7+1/7+1/8
=1+1/8
=9/8
1又1/2—5/6+7/12—9/20+11/30—13/42+15/56=几
1又1/8
1-1/6+7/12-9/20+11/30-13/42+15/50
=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－(1/2)＋(1/3)＋(1/3)＋(1/8)
=(1/2)＋(2/3)＋(1/8)
=31/24
1+1/2-5/6+7/12-9/20+11/30-13/42
1+1/2-5/6+7/12-9/20+11/30-13/42
=1+1/2-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)
=1-1/7
=6/7
1+1/4-9/20+11/30-13/42+15/56
1+1/4-9/20+11/30-13/42+15/56
=1+1/4-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)+(1/7+1/8)
=1+1/4-1/4-1/5+1/5+1/6-1/6-1/7+1/7+1/8
=1+1/8
=9/8
分数的速算和巧算 1-5/6+7/12--9/20+11/30-13/42+15/56
原体分解
＝1-[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)
=1-1/2-1/3+1/3+1/4-1/4-1/5+1/5+1/6-1/6-1/7+1/7+1/8
＝1/2+1/8
＝5/8
简便计算：1+1/2-5/6+7/12-9/20+11/30
1+1/2-5/6+7/12-9/20+11/30
=1+1/2-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)
=1+1/2-1/2-1/3+1/3+1/4-1/4-1/5+1/5+1/6
=1+1/6
=7/6
1+1/2-5/6+7/15-9/20+11/30-13/60
如果我没算错的话题目第四项应该是7/12
1+1/2-5/6+7/12-9/20+11/30-13/60
=(1+1/2)-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)
=1-1/7
=6/7
1-5/6+7/12-9/20+11/30-13/42+15/56-17/72+19/90+21/110+23/132
个人觉得提问者可能有个+ -号搞错了，应是:
1-5/6+7/12-9/20+11/30-13/42+15/56-17/72+19/90-21/110+23/132
=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+1/10-1/10-1/11+1/11+1/12
=7/12
1-5/6＋7/12-9/20＋11/30-13/42＋15/56-14/72＋90/19等于多少
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
