1、52又11/25*79.45+159*47.56+79又11/20*52.44 =52.44*79.45+159*47.56+79.55*52.44 =52.44*(79.45+79.55)+159*47.56 =52.44*159+159*47.56 =159*(52.44+47.56) =159*100 =15900 2、5/9*193+4/9*195 =5/9*（195-2）+4/9*195 =5/9*195-5/9*2+4/9*195 =195*（5/9+4/9）-5/9*2 =195-10/9 =193又8/9 3.2001*20022002-2002*20012001 =2002*20022002-2002*20012001-20022002 =2002*(20022002-20012001)-20022002 =2002*10001-20022002 =2002*(10001-10001) =0 4、1.9+19.9+199.9+1999.9+19999.9=(2+20+200+2000+20000)-(0.1+0.1+0.1+0.1+0.1)=22221.5 5.3901*99/（3901*198）*1110 =(3901/3901)*(99/198)*1110 =1*(1/2)*1110 =555 6.10又3/8*18.88+18.88*0.625-188.8*1/10 =10.375*18.88+18.88*0.625-18.88 =18.88*(10.375+0.625-1) =188.8 7.2002+2001-2000-1999+1998+1997-1996-1995+……+2+1 =(2002+2001-2000-1999)+(1998+1997-1996-1995)+……+2+1 =4+4+4+……+2+1 =4*500+2+1 =2003 8.1/1*2+1/2*3+1/3*4+……+1/10*11 =（1-1/2）+（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）+（1/10-1/11） =1-1/11 =10/11 9.1/3+1/15+1/35+1/63+1/99 =1/2*(1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+1/2*(1/7-1/9)+ 1/2*(1/9-1/11) =1/2*(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11) =1/2*10/11 =5/11 10、1又1/2-5/6+7/12+9/20+11/30-13/42+15/56 =（1+1/2）-(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+1/2-1/2-1/3+1/3+1/4+1/4+1/5+1/5+1/6-1/6-1/7+1/7+1/8 =1+1/4+1/4+1/5+1/5+1/8 =2.025 1、52又11/25*79.45+159*47.56+79又11/20*52.44 =52.44*79.45+159*47.56+79.55*52.44 =52.44*(79.45+79.55)+159*47.56 =52.44*159+159*47.56 =159*(52.44+47.56) =159*100 =15900 2、5/9*193+4/9*195 =5/9*（195-2）+4/9*195 =5/9*195-5/9*2+4/9*195 =195*（5/9+4/9）-5/9*2 =195-10/9 =193又8/9 3.2001*20022002-2002*20012001 =2002*20022002-2002*20012001-20022002 =2002*(20022002-20012001)-20022002 =2002*10001-20022002 =2002*(10001-10001) =0 4、1.9+19.9+199.9+1999.9+19999.9=(2+20+200+2000+20000)-(0.1+0.1+0.1+0.1+0.1)=22221.5 5.3901*99/（3901*198）*1110 =(3901/3901)*(99/198)*1110 =1*(1/2)*1110 =555 6.10又3/8*18.88+18.88*0.625-188.8*1/10 =10.375*18.88+18.88*0.625-18.88 =18.88*(10.375+0.625-1) =188.8 7.2002+2001-2000-1999+1998+1997-1996-1995+……+2+1 =(2002+2001-2000-1999)+(1998+1997-1996-1995)+……+2+1 =4+4+4+……+2+1 =4*500+2+1 =2003 8.1/1*2+1/2*3+1/3*4+……+1/10*11 =（1-1/2）+（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）+（1/10-1/11） =1-1/11 =10/11 9.1/3+1/15+1/35+1/63+1/99 =1/2*(1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+1/2*(1/7-1/9)+ 1/2*(1/9-1/11) =1/2*(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11) =1/2*10/11 =5/11 10、1又1/2-5/6+7/12+9/20+11/30-13/42+15/56 =（1+1/2）-(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+1/2-1/2-1/3+1/3+1/4+1/4+1/5+1/5+1/6-1/6-1/7+1/7+1/8 =1+1/4+1/4+1/5+1/5+1/8 =2.025