解:(1)0.9-(0.15+0.35÷
![](http://thumb.zyjl.cn/pic5/latex/5886.png)
),
=0.9-(0.15+0.35×
![](http://thumb.zyjl.cn/pic5/latex/1412.png)
),
=0.9-(0.15+0.49),
=0.9-0.64,
=0.26;
(2)159×
![](http://thumb.zyjl.cn/pic5/latex/50470.png)
-105×
![](http://thumb.zyjl.cn/pic5/latex/50471.png)
,
=159×
![](http://thumb.zyjl.cn/pic5/latex/519699.png)
-105×
![](http://thumb.zyjl.cn/pic5/latex/50471.png)
,
=105-105×
![](http://thumb.zyjl.cn/pic5/latex/50471.png)
,
=(1-
![](http://thumb.zyjl.cn/pic5/latex/50471.png)
)×105,
=
![](http://thumb.zyjl.cn/pic5/latex/196677.png)
×105,
=
![](http://thumb.zyjl.cn/pic5/latex/519700.png)
;
(3)
![](http://thumb.zyjl.cn/pic5/latex/6232.png)
+5×
![](http://thumb.zyjl.cn/pic5/latex/6232.png)
+
![](http://thumb.zyjl.cn/pic5/latex/6232.png)
×5,
=(1+5+5)×
![](http://thumb.zyjl.cn/pic5/latex/6232.png)
,
=11×
![](http://thumb.zyjl.cn/pic5/latex/6232.png)
,
=5;
(4)0.85×104,
=0.85×(100+4),
=0.85×100+4×0.85,
=85+3.4,
=88.4;
(5)(10-
![](http://thumb.zyjl.cn/pic5/latex/50472.png)
×1)+(9-
![](http://thumb.zyjl.cn/pic5/latex/50472.png)
×2)+(8-
![](http://thumb.zyjl.cn/pic5/latex/50472.png)
×3)+…+(2-
![](http://thumb.zyjl.cn/pic5/latex/50472.png)
×9)+(1-
![](http://thumb.zyjl.cn/pic5/latex/50472.png)
×10),
=(10+9+8+…+2+1)-(
![](http://thumb.zyjl.cn/pic5/latex/50472.png)
×1+
![](http://thumb.zyjl.cn/pic5/latex/50472.png)
×2+…+
![](http://thumb.zyjl.cn/pic5/latex/50472.png)
×9+
![](http://thumb.zyjl.cn/pic5/latex/50472.png)
×10),
=(10+9+8+…+2+1)-(10+9+8+…+2+1)×
![](http://thumb.zyjl.cn/pic5/latex/50472.png)
,
=(10+9+8+…+2+1)×(1-
![](http://thumb.zyjl.cn/pic5/latex/50472.png)
),
=(10+1)×10÷2×
![](http://thumb.zyjl.cn/pic5/latex/519701.png)
,
=55×
![](http://thumb.zyjl.cn/pic5/latex/519701.png)
,
=51;
(6)9.81×0.1+0.5×98.1+0.049×981,
=9.81×0.1+0.5×98.1+0.049×981,
=9.81×0.1+5×9.81+4.9×9.81,
=(0.1+5+4.9)×9.81,
=10×9.81,
=98.1.
分析:(1)按運算順序計算,先算小括號內(nèi)的除法,再算小括號內(nèi)的加法,最后算括號外的減法;
(2)把
![](http://thumb.zyjl.cn/pic5/latex/50470.png)
化為
![](http://thumb.zyjl.cn/pic5/latex/519699.png)
,然后約分結果為105,再用乘法分配律的逆運算簡算;
(3)運用乘法分配律的逆運算簡算;
(4)把104看作100+4,運用乘法分配律簡算;
(5)把整數(shù)與整數(shù)部分相加,分數(shù)與分數(shù)部分相加,再運用乘法分配律簡算;
(6)先把原式改為9.81×0.1+5×9.81+4.9×9.81,運用乘法分配律簡算.
點評:完成本題要注意分析式中數(shù)據(jù),靈活運用所學的運算律進行簡便計算的能力.