题目

(1)1-1/6+1/42+1/56+1/72+1/90
(2)5/4-9/20+11/30-13/42+15/56-17/72+19/90
(3)1/3+3/4+2/5+5/7+7/8+9/20+10/21+11/24+12/35

提问时间：2020-11-22

答案

1)1-1/6+1/42+1/56+1/72+1/90
=5/6+1/42+1/56+1/72+1/90
=6/7+1/56+1/72+1/90
=49/56+1/72+1/90
=7/8+1/72+1/90
=64/72+1/90
=81/90
=9/10
(2)5/4-9/20+11/30-13/42+15/56-17/72+19/90
=25/20-9/20+11/30-13/42+15/56-17/72+19/90
=16/20+11/30-13/42+15/56-17/72+19/90
=24/30+11/30-13/42+15/56-17/72+19/90
=35/30-13/42+15/56-17/72+19/90
=49/42-13/42+15/56-17/72+19/90
=36/42+15/56-17/72+19/90
=48/56+15/56-17/72+19/90
=63/56-17/72+19/90
=81/72-17/72+19/90
=64/72+19/90
=8/9+19/90
=80/90+19/90
=99/90
=11/10
(3)1/3+3/4+2/5+5/7+7/8+9/20+10/21+11/24+12/35
=1/3+3/4+2/5+5/7+7/8+1/5+1/4+1/7+1/3+1/3+1/8+1/7+1/5
=(1/3+1/3+1/3)+(3/4+1/4)+(2/5+1/5+1/5)+(5/7+1/7+1/7)+(7/8+1/8)
=1+1+4/5+1+1
=24/5=4.8
1.前面两题的关键是两个数相加或相减后得到的数值约分后,刚好和后一个数字可以找到公约数
2.后面一题经过观察发现后面的四个数字如:9/20可以分解为1/4+5/1,找到规律后就可以快速解题