解:(1)306÷(201×47-9413),
=306÷(9447-9413),
=306÷34,
=9;
(2)
![](http://thumb.1010pic.com/pic5/latex/36.png)
÷[(
![](http://thumb.1010pic.com/pic5/latex/168.png)
+
![](http://thumb.1010pic.com/pic5/latex/36.png)
)×
![](http://thumb.1010pic.com/pic5/latex/848.png)
],
=
![](http://thumb.1010pic.com/pic5/latex/36.png)
÷[
![](http://thumb.1010pic.com/pic5/latex/60986.png)
×
![](http://thumb.1010pic.com/pic5/latex/848.png)
],
=
![](http://thumb.1010pic.com/pic5/latex/36.png)
÷
![](http://thumb.1010pic.com/pic5/latex/2132.png)
,
=
![](http://thumb.1010pic.com/pic5/latex/36.png)
×15,
=3;
(3)
![](http://thumb.1010pic.com/pic5/latex/597.png)
×35+35×
![](http://thumb.1010pic.com/pic5/latex/5192.png)
,
=(
![](http://thumb.1010pic.com/pic5/latex/597.png)
+
![](http://thumb.1010pic.com/pic5/latex/5192.png)
)×35,
=1×35,
=35;
(4)2007×2009×(
![](http://thumb.1010pic.com/pic5/latex/288778.png)
+
![](http://thumb.1010pic.com/pic5/latex/212801.png)
),
=2007×2009×
![](http://thumb.1010pic.com/pic5/latex/288778.png)
+2007×2009×
![](http://thumb.1010pic.com/pic5/latex/212801.png)
,
=
![](http://thumb.1010pic.com/pic5/latex/18486.png)
+
![](http://thumb.1010pic.com/pic5/latex/28261.png)
,
=1+
![](http://thumb.1010pic.com/pic5/latex/54677.png)
+(1-
![](http://thumb.1010pic.com/pic5/latex/54677.png)
),
=2;
(5)53.7×5.3+537×0.37+53.7,
=53.7×5.3+53.7×3.7+53.7,
=(5.3+3.7+1)×53.7,
=10×53.7,
=537;
(6)
![](http://thumb.1010pic.com/pic5/latex/156462.png)
+
![](http://thumb.1010pic.com/pic5/latex/112214.png)
+
![](http://thumb.1010pic.com/pic5/latex/156463.png)
+…+
![](http://thumb.1010pic.com/pic5/latex/520166.png)
,
=2×(
![](http://thumb.1010pic.com/pic5/latex/6902.png)
+
![](http://thumb.1010pic.com/pic5/latex/6903.png)
+
![](http://thumb.1010pic.com/pic5/latex/12344.png)
+…+
![](http://thumb.1010pic.com/pic5/latex/212801.png)
),
=2×(1-
![](http://thumb.1010pic.com/pic5/latex/13.png)
+
![](http://thumb.1010pic.com/pic5/latex/13.png)
-
![](http://thumb.1010pic.com/pic5/latex/8.png)
+
![](http://thumb.1010pic.com/pic5/latex/8.png)
-
![](http://thumb.1010pic.com/pic5/latex/96.png)
+…+
![](http://thumb.1010pic.com/pic5/latex/54677.png)
-
![](http://thumb.1010pic.com/pic5/latex/23405.png)
)
=2×(1-
![](http://thumb.1010pic.com/pic5/latex/23405.png)
)
=2×
![](http://thumb.1010pic.com/pic5/latex/28262.png)
=
![](http://thumb.1010pic.com/pic5/latex/144520.png)
.
分析:(1)先算括号内的乘法,再算扩阿红诶的剑法,最后算括号外的除法;
(2)先算小括号内的,再算中括号内的,最后算括号外的;
(3)运用乘法分配律的逆运算简算;
(4)运用乘法分配律简算;
(5)根据数字特点,把原式变为53.7×5.3+53.7×3.7+53.7,运用乘法分配律的逆运算简算;
(6)通过观察,每个分数的分子都是2,于是先把2拿出来,括号内的分数可以拆成两个分数相减的形式,然后通过加减相抵消的方法,得出结果.
点评:此题考查了四则混合运算的运算顺序,以及运用运算定律或运算技巧简算的能力.