解:(1)(
![](http://thumb.1010pic.com/pic5/latex/520251.png)
)
![](http://thumb.1010pic.com/pic5/latex/520252.png)
,
=(
![](http://thumb.1010pic.com/pic5/latex/520253.png)
![](http://thumb.1010pic.com/pic5/latex/520254.png)
)
![](http://thumb.1010pic.com/pic5/latex/520252.png)
,
=
![](http://thumb.1010pic.com/pic5/latex/257652.png)
-
![](http://thumb.1010pic.com/pic5/latex/21045.png)
×
![](http://thumb.1010pic.com/pic5/latex/257652.png)
![](http://thumb.1010pic.com/pic5/latex/454020.png)
×
![](http://thumb.1010pic.com/pic5/latex/257652.png)
,
=
![](http://thumb.1010pic.com/pic5/latex/257652.png)
;
(2)5
![](http://thumb.1010pic.com/pic5/latex/520255.png)
(2.375-1
![](http://thumb.1010pic.com/pic5/latex/15657.png)
)
![](http://thumb.1010pic.com/pic5/latex/520256.png)
,
=5
![](http://thumb.1010pic.com/pic5/latex/21045.png)
-(2
![](http://thumb.1010pic.com/pic5/latex/597.png)
-1
![](http://thumb.1010pic.com/pic5/latex/15657.png)
)-3
![](http://thumb.1010pic.com/pic5/latex/5192.png)
,
=5
![](http://thumb.1010pic.com/pic5/latex/21045.png)
+1
![](http://thumb.1010pic.com/pic5/latex/15657.png)
-(2
![](http://thumb.1010pic.com/pic5/latex/597.png)
+3
![](http://thumb.1010pic.com/pic5/latex/5192.png)
),
=7-6,
=1;
(3)2001×20022002-2002×20012001,
=2001×2002×1001-2002×2001×1001,
=0;
(4)2000-1+9×111×999,
=1999+999×999,
=1000+999+999×999,
=1000+999×(999+1),
=1000+999×1000,
=1000+999000,
=1000000;
(5)2008-1+2-3+4-…+2006-2007,
=-1+2-3+4-+…-2005+2006-2007+2008,
=2008÷2,
=1004.
分析:算式(1)先把除数转化为乘它的倒数,再根据从被除数里减去一个数再加上一个相同的数还得原数.
算式(2)先把2.375化成分数2
![](http://thumb.1010pic.com/pic5/latex/597.png)
,再根据减法的运算性质进行简算.
算式(3)原式转化为:2001×2002×1001-2002×2001×1001,根据两个相同的数相减差是0.
算式(4)运用乘法分配律进行简算.
算式(5)原式可化为:-1+2-3+4+…-2005+2006-2007+2008,按次序每两个分为一组,且和为1,2008个数中分为2008÷2=1004组,所以其和为1004.
点评:此题考查的目的是使学生运用“转化”的思想和方法,再灵活运用简便方法进行计算.