Question

1又1/12加2又1/20加1又3/30加1又4/42的简便计算

对不起，打错了，应为；1又1/12加2又1/20加3又1/30加4又1/42的简便计算

Answer 1

1又1/12加2又1/20加1又3/30加1又4/42
=1+1/12+2+1/20+3+3/30+4+4/42
=1+2+3+4+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)
=10+1/3-1/7
=10又21分之4；

Answer 2

(1+ 1/12) + (2+ 1/20) + (3+ 1/30) + (4+ 1/42)
= (1 + 2 + 3 + 4) + (1/12 + 1/20 + 1/30 + 1/42)
= 10 + (1/3X4 + 1/4X5 + 1/5X6 + 1/6X7)
= 10 + (1/3 - 1/4) + (1/4 - 1/5) + (1/5 - 1/6) + (1/6 - 1/7)
= 10 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7
= 10 + 1/3 - 1/7
= 10 + 7/21 - 3/21
= 10 + 4/21

Answer 3

整数部分和分数部分分开算，整数部分=10
分数部分=1/3*4+1/4*5+1/5*6+1/6*7
=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1/3-1/7
=4/21
所以，原式=10又4/21