(1 )0.125×2.5×5×64 (2)1-2+3-4+5-6+…+1991-1992+1993 (3)9999×2222-3333×3334 (4)94×2003-93×2004 (5)25×6

(1 )0.125×2.5×5×64 (2)1-2+3-4+5-6+…+1991-1992+1993 (3)9999×2222-3333×3334 (4)94×2003-93×2004 (5)25×6

题目
(1 )0.125×2.5×5×64
(2)1-2+3-4+5-6+…+1991-1992+1993
(3)9999×2222-3333×3334 
(4)94×2003-93×2004
(5)25×6.78+25×3.47+125×0.0382
(6)1993×1997+1993+1999×1993-1993.
答案
(1 )0.125×2.5×5×64,
=0.125×2.5×5×4×2×8,
=0.125×8×(2.5×4)×(5×2),
=1×10×10,
=100;
(2)1-2+3-4+5-6+…+1991-1992+1993,
=1+(3-2)+(5-4)+(7-6)+…+(1993-1992),
=1+1+1+1+…+1,
=997;
(3)9999×2222+3333×3334,
=3333×3×2222-3333×3334,
=3333×(6666+3334),
=3333×10000,
=3330000;
(4)94×2003-93×2004,
=94×2003-93×(2003+1),
=94×2003-93×2003-93,
=2003×(94-93)-93,
=2003×1-93,
=2003-93,
=1910;
(5)25×6.78+25×3.47+125×0.0382,
=25×6.78+25×3.47+25×5×0.0382,
=25×6.78+25×3.47+25×0.191,
=25×(6.78+3.47+0.191),
=25×10.441,
=25×(10+0.4+0.04+0.001),
=25×10+25×0.4+25×0.04+25×0.01,
=250+10+1+0.025,
=261.025;
(6)1993×1997+1993+1999×1993-1993,
=1993×1997+1999×1993,
=1993×(1997+1999),
=1993×(2000-3+2000-1),
=1993×(4000-4),
=1993×4×(1000-1),
=7972×(1000-1),
=7972×1000-7972,
=7972000-7972,
=7964028.
(1)把64看作4×2×8,运用乘法交换律与结合律简算;
(2)通过观察,原式可变成1+(3-2)+(5-4)+(7-6)+…+(1993-1992),每个括号内的结果都是1,简算即可;
(3)把9999卡座3333×3,运用乘法分配律简算;
(4)把2004看作2003+1,这样可以使运算简便;
(5)根据数字特点,原式变为25×6.78+25×3.47+25×5×0.0382,运用乘法分配律简算;
(6)原式先变为1993×1997+1999×1993,运用乘法分配律计算为1993×(1997+1999),然后把1997看作(2000-3),把1999看作(2000-1),进一步计算即可.

四则混合运算中的巧算.

完成此题,注意分析算式中的数据,选择合理正确的方法进行简算.

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