Question

简便计算？71 1/6*6/7+61 1/5*5/6+51 1/4*4/5+41 1/3*3/4+31 1/2*2/3

Answer 1

711/7+611/6+511/5+411/4+311/3=500+11×(1/7+1/6+1/5+1/4+1/3)=500+11×(1/7+1/2+1/5+1/4)=500+11×(1/7+3/4+1/5)=500+11×153/140=1683/140+50
=500+11×(1+13/140)=511+169/140=512+29/140
这就可以了

Answer 2

711/7+611/6+511/5+411/4+311/3=70×6/7+1×6/7+1/6×6/7+60×5/6+1×5/6+1/5×5/6+50×4/5+1×4/5+1/4×4/5+40×3/4+1×3/4+1/3×3/4+30×2/3+1×2/3+1/2×2/3-1=60+1/7+6/7+50+5/6+1/6+40+4/5+1/5+30+3/4+1/4+20+2/3+1/3-1=（60+50+40+30+20）+（1+1+1+1）=200+4=204

Answer 3

711/7+611/6+511/5+411/4+311/3=500+11×(1/7+1/6+1/5+1/4+1/3)=500+11×(1/7+1/2+1/5+1/4)=500+11×(1/7+3/4+1/5)=500+11×153/140=1683/140+50
=500+11×(1+13/140)=511+169/140=512+29/140