小学6年级数学简便计算题 高手进

来源：百度知道 编辑：UC知道 时间：2024/04/28 01:56:08
1/12+1/20+1/30+1/42+1/56+1/72+1/90
1-1/4+1/20+1/30+1/42+1/56
(1+1/3+1/5+1/7)*(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/9)+(1/3+1/5+1/7)

1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1/3*4+1/4*5+...+1/9*10
=1/3-1/4+1/4-1/5+...+1/9-1/10
=1/3-1/10
=7/30

1-1/4+1/20+1/30+1/42+1/56
=1-1/4+1/4*5+1/5*6+1/6*7+1/7*8
=1-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1-1/8
=7/8

(1+1/3+1/5+1/7)*(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/9)*(1/3+1/5+1/7)

设A=1/3+1/5+1/7，则：

1+1/3+1/5+1/7=1+A
1/3+1/5+1/7+1/9=A+1/9
1+1/3+1/5+1/7+1/9=1+A+1/9

原式=（1+A）（A+1/9）-（1+A+1/9）*A

=A+1/9+AA+A*1/9-A-AA-A*1/9

=1/9

即原式=1/9

1.7/30
2.33/40