Question

（1+1/2+1/3+1/4）X（1/2+1/3+1/4+1/5）—（1+1/2+1/3+1/4+1/5）X（1/2+1/3+1/4）=

41.2X8.1+11X9.25+537X0.19= （请附计算过程。）

Answer 1

（1+1/2+1/3+1/4）X（1/2+1/3+1/4+1/5）—（1+1/2+1/3+1/4+1/5）X（1/2+1/3+1/4） (加1减1)
=（1+1/2+1/3+1/4）X（1-1+1/2+1/3+1/4+1/5）—（1+1/2+1/3+1/4+1/5）X（1/2+1/3+1/4）
=(1+1/2+1/3+1/4)*(1+1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4)-(1+1/2+1/3+1/4+1/5）X（1/2+1/3+1/4） (第一项与第三项合并)
=(1+1/2+1/2+1/4+1/5)*1-(1+1/2+1/3+1/4)
=1/5

41.2X8.1+11X9.25+537X0.19
=412*0.81+11*9.25+537*0.19
=412*0.81+11*9.25+(412+125)*0.19
=412*(0.81+0.19)+11*9.25+125*0.19
=412+11*9.25+125*0.19
=412+11*(8+1.25)+1.25*19
=412+88+11*1.25+1.25*19
=500+1.25*(11+19)
=500+1.25*30
=500+37.5
=537.5

Answer 2

（1+1/2+1/3+1/4）x（1/2+1/3+1/4+1/5）-（1+1/2+1/3+1/4+1/5）x（1/2+1/3+1/4）
中间该是减号.
设1/2+1/3+1/4+1/5=M,1/2+1/3+1/4=N
原式=(1+N)*(M)-(1+M)*N
=M+NM-N-NM
=M-N
=1/5
或者是这样：(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)×(1/2+1/3+1/4)
=1 x(1/2+1/3+1/4+1/5）+ (1/2+1/3+1/4) x(1/2+1/3+1/4+1/5) -[1 x(1/2+1/3+1/4)+(1/2+1/3+1/4+1/5)x(1/2+1/3+1/4)]
=1 x(1/2+1/3+1/4+1/5）+ (1/2+1/3+1/4) x(1/2+1/3+1/4+1/5) -1 x(1/2+1/3+1/4)-(1/2+1/3+1/4+1/5)x(1/2+1/3+1/4)
=(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4)
=1/5
同学这是我努力打出来的，给好评吧。

Answer 3

设1/2+1/3+1/4为x
=(x+1)*(x+1/5)-x*(x+1+1/5)
=1*1/5
=1/5

Answer 4

897654-=9