Question

一减六分之一加四十二分之一加七十二分之一加九十分之一等于几分之几？

Answer 1

根据题意列式：1 - (1/6+1/42+1/72+1/90）
解：1-（1/6+1/42+1/72+1/90）
=1-（7/42+1/42）+（1.25/90+1/90）
=1- （8/42）+（2.25/90）
=1-（8×22.5/945）+(2.25×10.5/945)
=1-(180+23.65)/945
=1-(203.65/945)
=741.35/945
最终得数是九百四十五分之七百四十一点三五。

Answer 2

1-1/6+1/42+1/72+1/90
= 1-1/6 + 1/(6×7) + 1/(8×9) +1/(9×10)
= 1 -1/6 + 1/6-1/7 + 1/8-1/9 +1/9-1/10
= 1-1/7 + 1/8-1/10

= 1 - 1/7 + (5-4)/40
= 1-1/7+1/40
= 280/280-40/280+7/280
= 247/280

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另外：
1-1/6+1/42+(1/56)+1/72+1/90
= 1-1/6 + 1/(6×7) + 1/(7×8) + 1/(8×9) +1/(9×10)
= 1 -1/6 + 1/6-1/7 + 1/7-1/8 + 1/8-1/9 +1/9-1/10
= 1-1/10

= 9/10

Answer 3

1-1/6+1/42+1/72+1/90
=1-1/6+1/6×1/7+1/6×1/12+1/6×1/15
=5×1/6+1/6×1/7+1/6×1/12+1/6×1/15
=1/6×(5+1/7+1/12+1/15)
=1/6×［5+(12×15)/(7×12×15)+(7×15)/(7×12×15)+(7×12)/(7×12×15)］
=1/6×［5+(12×15+7×15+7×12)/(12×7×15)］
=1/6×［5+(180+105+84)/1260］
=1/6×(5+369/1260)
=1/6×(5×1260+369)/1260
=1/6×(6300+369)/1260
=1/6×6669/1260
=6669/(1260×6)
=2223/(1260×2)
=2223/2520