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巧算下面各题
343+345+347+349+351
115+120+125+130+135+140+145
1+2+3+…+100
2+4+6+…+100
1001×999
1001+1002+1003+…+2000
646+647+648+649+650+651+652+653+654
666×222+333×556
1320÷33+1980÷33+495÷33.
分析:(1)(2)运用加法交换律与结合律简算;
(3)(4)(6)运用高斯求和公式,计算即可;
(5)把1001看做1000+1,运用乘法分配律简算;
(7)根据数字特点,把原式变为600×9+(46+47+49+51+52+53+54),计算即可;
(8)把666看做333×2,运用乘法分配律简算;
(9)把除法改为乘法,运用乘法分配律简算.
解答:解:(1)343+345+347+349+351,
=(343+347)+(349+351)+345,
=690+700+345,
=(700-10)+700+(300+45),
=(700+300+700)+(45-10),
=1700+35,
=1735;

(2)115+120+125+130+135+140+145,
=(115+125+135+145)+(120+130+140),
=(100+100+100+100)+(10+20+30+40)+5×4+(100+100+100+20+30+40),
=100×4+100+100×3+20+90,
=100×8+100+10,
=100×9+10,
=910;

(3)1+2+3+…+100,
=(1+100)×100÷2,
=(100+1)×50,
=5000+50,
=5050;

(4)2+4+6+…+100,
=(2+100)×50÷2,
=(2+100)×25,
=50+2500,
=2550;

(5)1001×999,
=(1000+1)×999,
=999000+999,
=999999;

(6)1001+1002+1003+…+2000,
=(1001+2000)×1000÷2,
=3001×500,
=1500500;

(7)646+647+648+649+650+651+652+653+654,
=600×9+(46+47+49+51+52+53+54),
=5400+(46+54)+(47+53)+(49+51),
=5400+100+100+100,
=5700;

(8)666×222+333×556,
=333×2×222+333×556,
=333×(444+556),
=333×1000,
=333000;

(9)1320÷33+1980÷33+495÷33,
=1320×
1
33
+1980×
1
33
+495×
1
33

=(1320+1980+495)×
1
33

=3795×
1
33

=115.
点评:完成此题,注意分析式中数据,运用运算定律或运算技巧进行灵活简算.
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