(1+1/3+1/5+1/10+1/15+1/30)/(1/2+1/4+1/6+1/12+1/20+1/60)=​?简算

问题描述:

(1+1/3+1/5+1/10+1/15+1/30)/(1/2+1/4+1/6+1/12+1/20+1/60)=​?
简算

答案是13/8

(1+1/3+1/5+1/10+1/15+1/30)/(1/2+1/4+1/6+1/12+1/20+1/60)
=(1+1/3+1/5+1/10+1/10)/(1/2+1/4+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6)
=(1/2+1/3+1/5+1/5)/(1+1/4-1/6)
=(1/2+1/3+2/5)/(13/12)
=37/30÷13/12
=74/65

(1+1/3+1/5+1/10+1/15+1/30)/(1/2+1/4+1/6+1/12+1/20+1/60)=(30/30+10/30+6/30+3/30+2/30+1/30)/(30/60+15/60+10/60+5/60+3/60+1/60)=(52/30)/(64/60)=(26/15)/(16/15)=26/15×15/16=13/8