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（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.）
题目详情
（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.）
41.2X8.1+11X9.25+537X0.19= （请附计算过程.）
▼优质解答
答案和解析
（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
=（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
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