题目内容

(2012?麟游县)脱式计算(能简算的要简算)
①3
13
15
-2
13
14
+5
2
15
-1
1
14

②14.85-1.58×8+31.2÷1.2
③(1
1
3
+2
1
2
)÷(2-1
1
2

④2.25×
3
5
+2.75÷1
2
3
+60%
⑤9.81×0.1+0.5×98.1+0.049×981
⑥1000+999-998-997+996+995-994-993+…+104+103-102-101.
分析:①根据加法的交换律和连减的简便方法计算即可;
②先算乘除,再算加减;
③先计算括号里面的,再计算括号外面的除法;
④根据乘法分配律简便计算;
⑤先变形为9.81×0.1+5×9.81+4.9×9.81,再根据乘法分配律简便计算;
⑥将算式四个分为一组,然后找一下共有几组这样的数,然后根据规律解答.
解答:解:①3
13
15
-2
13
14
+5
2
15
-1
1
14

=(3
13
15
+5
2
15
)-(2
13
14
+1
1
14
),
=9-4,
=5;

②14.85-1.58×8+31.2÷1.2,
=14.85-12.64+26,
=2.21+26,
=28.21;

③(1
1
3
+2
1
2
)÷(2-1
1
2
),
=
23
6
÷
1
2

=7
1
2


④2.25×
3
5
+2.75÷1
2
3
+60%,
=2.25×
3
5
+2.75×
3
5
+
3
5

=(2.25+2.75+1)×
3
5

=6×
3
5

=3
3
5


⑤9.81×0.1+0.5×98.1+0.049×981,
=9.81×0.1+5×9.81+4.9×9.81,
=9.81×(0.1+5+4.9),
=9.81×10,
=98.1;

⑥1000+999-998-997+996+995-994-993+…+104+103-102-101,
=(1000+999-998-997)+(996+995-994-993)+…+(104+103-102-101),
=4×225,
=900.
点评:考查了运算定律与简便运算,四则混合运算.注意运算顺序和运算法则,灵活运用所学的运算律简便计算.
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