解:(1)(
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)
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,
=(
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)
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,
=
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-
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×
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×
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,
=
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;
(2)5
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(2.375-1
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)
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,
=5
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-(2
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-1
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)-3
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,
=5
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+1
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-(2
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+3
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),
=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)先把除數(shù)轉(zhuǎn)化為乘它的倒數(shù),再根據(jù)從被除數(shù)里減去一個(gè)數(shù)再加上一個(gè)相同的數(shù)還得原數(shù).
算式(2)先把2.375化成分?jǐn)?shù)2
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,再根據(jù)減法的運(yùn)算性質(zhì)進(jìn)行簡(jiǎn)算.
算式(3)原式轉(zhuǎn)化為:2001×2002×1001-2002×2001×1001,根據(jù)兩個(gè)相同的數(shù)相減差是0.
算式(4)運(yùn)用乘法分配律進(jìn)行簡(jiǎn)算.
算式(5)原式可化為:-1+2-3+4+…-2005+2006-2007+2008,按次序每?jī)蓚€(gè)分為一組,且和為1,2008個(gè)數(shù)中分為2008÷2=1004組,所以其和為1004.
點(diǎn)評(píng):此題考查的目的是使學(xué)生運(yùn)用“轉(zhuǎn)化”的思想和方法,再靈活運(yùn)用簡(jiǎn)便方法進(jìn)行計(jì)算.