请教几道分数简便运算题1/(2×5) +1/(3×5)+1/(8×11)+……1/(20×23)4/3+7/12-9/2

• .1.参考答案-1
  1/(2×5) +1/(3×5)+1/(8×11)+……1/(20×23)?
  1/(2×5)=（1/2-1/5）÷3
  1/(5×8)=（1/5-1/8）÷2
  1/(8×11)=(1/8-1/11)÷3
  ……
  1/(20×23)=（1/20-1/23)÷3
  1/(2×5) +1/(5×8)+1/(8×11)+……1/(20×23)
  =1/3×（1/2-1/5+1/5-1/8+1/8-1/11+...+1/20-1/23）
  =1/3×（1/2-1/23）
  =1/3×21/16
  =7/46
  4/3+7/12-9/20+11/30-13/42
  =1+1/3+1/3+1/4-1/4-1/5+1/5+1/6-1/6-1/7
  =5/3-1/7
  =32/21
  1/12+1/20+1/30+1/42+1/56+1/72+1/90
  =1/3×4+1/4×5+...+1/9×10
  =1/3-1/4+1/4-1/5+...+1/9-1/10
  =1/3-1/10
  =7/30
  1/1×5=(1-1/5)/4
  1/5×9=(1/5-1/9)/4
  1/(1×5) +1/(5×9)+1/(9×13)+……1/(55×59)
  =1/4×（1-1/5+1/5-1/9+1/9-1/13+...+1/55-1/59）
  =1/4×（1-1/59）
  =1/4×58/59
  =29/118
  229又11分之1÷46又44分之1
  =2520/11÷2025/44
  =2520/11×44/2025
  =224/45
  =4又44/45