计算.要简便 (1+0.12+0.23)*(0.12+0.23+0.34)-(1+0.12+0.23+0.34)*(0.12+0.23)

题目

计算.要简便 (1+0.12+0.23)*(0.12+0.23+0.34)-(1+0.12+0.23+0.34)*(0.12+0.23)
还有
一又二分之一+二又三分之一+三又四分之一+四又五分之一+五又六分之一+六又七分之一+七又八分之一
123+234+345+456+567+678+789+900
1+1/(2-1/3)/[1-1/(2+1/3)]
(9又7分之2+7又9分之2)/(7分之5+9分之7)
6-3/2-5/4-9/8-17/16-33/32
1-(101010/202020)的平方*(222002/333003)的平方*(300033/500055)的平方*(101010/141414)的平方

答案

(1+0.12+0.23)*(0.12+0.23+0.34)-(1+0.12+0.23+0.34)*(0.12+0.23)
=(1+0.12+0.23)*(0.12+0.23)+(1+0.12+0.23)*0.34-(1+0.12+0.23)*(0.12+0.23)-0.34*(0.12+0.23)
=0.34*(1+0.12+0.23)-0.34*(0.12+0.23)
=0.34+0.34*(0.12+0.23)-0.34*(0.12+0.23)
=0.34
一又二分之一+二又三分之一+三又四分之一+四又五分之一+五又六分之一+六又七分之一+七又八分之一
=1+2+3+4+5+6+7+1/2+1/3+1/4+1/5+1/6+1/7+1/8
=28+(1/2+1/3+1/6)+1/5+1/7+(1/4+1/8)
=28+1+1/5+1/7+3/8
=29+201/280
=29又201/280
123+234+345+456+567+678+789+900
=456-333+456-222+456-111+456+456+111+456+222+456+333+900
=7×456+900
=4092
1+1/(2-1/3)/[1-1/(2+1/3)]
=1+1/(5/3)/[1-1/(7/3)]
=1+3/5/(4/7)
=1+21/20
=41/20
(9又7分之2+7又9分之2)/(7分之5+9分之7)
=65×(2/7+2/9)/(5/7+7/9)
=65×(18+14)/(45+49)
=65×32/94
=1040/47
6-3/2-5/4-9/8-17/16-33/32
=6-1-1/2-1-1/4-1-1/8-1-1/16-1-1/32
=-(1/2+1/4+1/8+1/16+1/32)
=-31/32
1-(101010/202020)的平方*(222002/333003)的平方*(300033/500055)的平方*(101010/141414)的平方
=1-(1/2*2/3*3/5*10/14)的平方
=1-(1/7)的平方
=48/49