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1%5/6+7/12%9/20+11/30/42,加15/56/72,加19/90。

这道题要用“分数拆分法”来做,就是说把题中的各个分数拆分成下面的算式,达到正负抵消,从而使计算简便.题中的“14/72”错啦,应该是“17/72”;还有“90/19”的分子分母写反啦,应该是“19/90”5/6=1/2+1/37/12=1/3+1/49/20=1/4

1-5/6+7/12-9/20+11/30-13/42+15/56-17/72 =1-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)+(1/7+1/8)-(1/8+1/9) =1-1/2-1/3+1/3+1/4-1/4-1/5+1/5+1/6-1/6-1/7+1/7+1/8-1/8-1/9 =1-1/2-1/9 =7/18

=1-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+……+(1/9+1/10)=1-1/2-1/3+1/3+1/4-1/4-1/5+……+1/9+1/10=1+1/10=11/10

1-5/6+7/12-9/20+11/30-13/42+15/56=1-(1/2+1/3)+1/3+1/4-(1/4+1/5)+1/5+1/6-(1/6+1/7)+1/7+1/8=1-1/2-1/3+1/3+1/4++1/7+1/8=1-1/2+1/8=1/2-1/8=3/87.6乘31又2/5加43.9乘2又2/5=(7+3/5)*(3+2/5)+(43+9/10)*(2+2/5)=38/5*17/5+439/10*12/5=1/

5/6=1/2+1/3,7/12=1/3+1/4,同理可得后面的9/20,11/30,13/42,15/56,17/72.所以原式=1+1/2-(1/2+1/3)+1/3+1/4……-(1/6+1/7)+1/7+1/8-(1/8+1/9)=1-1/9=8/9

=(7/12-17/72)-(9/20-11/30)-(13/42-15/56)=(42/72-17/72)-(27/60-22/60)-(52/168-45/168)=25/72-1/12-1/24=25/72-6/72-3/72=16/72=2/9

1+5/67/12+9/2011/30+13/4215/56+17/72=-1+(1/2+1/3)-(1/3+1/4)+(1/4+1/5)-(1/5+1/6)+(1/6+1/7)-(1/7+1/8)+(1/8+1/9)=-1+1/2+1/3-1/3-1/4+1/4+1/5-1/5-1/6+1/6+1/7-1/7-1/8+1/8+1/9=-1+1/2+1/9=-7/18

拆分数5/6拆成1/3+1/2 7/12拆成1/3+1/4 9/20拆成1/4+1/5 11/30拆成1/5+1/6 13/42拆成1/6+1/7 15/56拆成1/7+1/8 17/72拆成1/8+1/9 19/90拆成1/10+1/9 这样算就简单了得出结果为3/5

=(1/2+1/3)-(1/3+1/4)+(1/4+1/5)-(1/5+1/6)+(1/6+1/7)-(1/7+1/8)+(1/8+1/9)-(1/9+1/10)=1/2-1/10=0.4

如图

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