Question

35/6-49/12+63/20-77/30+91/42-105/56简便运算

回答ok了，告诉你们明星qq哦！

Answer 1

原式=7*（5/6-7/12+9/20-11/30+13/42-15/56）=7*m
m=(2+3)/(2*3)-(3+4)/(3*4)+(4+5)/(4*5)-(5+6)/(5*6)+(6+7)/(6*7)-(7+8)/(7*8)
=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
=3/8
原式=7*m=7*(3/8)=21/8

Answer 2

35/6-49/12+63/20-77/30+91/42-105/56
=7×（5/6-7/12+9/20-11/30+13/42-15/56）
=7×[(2+3)/2*3-(3+4)/3*4+(4+5)/4*5-(5+6)/5*6+(6+7)/6*7-(7+8)/7*8]
=7×（1/2+1/3-1/3-1/4+1/4+1/5-1/5-1/6+1/6+1/7-1/7-1/8）
=7×(1/2-1/8)
=7×3/8
=21/8