0.9-(0.15+0.35÷
); 159×
-105×
;
+5×
+
×5; 0.85×104;
(10-
×1)+(9-
×2)+(8-
×3)+…+(2-
×9)+(1-
×10);9.81×0.1+0.5×98.1+0.049×981.解:(1)0.9-(0.15+0.35÷
),=0.9-(0.15+0.35×
),=0.9-(0.15+0.49),
=0.9-0.64,
=0.26;
(2)159×
-105×
,=159×
-105×
,=105-105×
,=(1-
)×105,=
×105,=
;(3)
+5×
+
×5,=(1+5+5)×
,=11×
,=5;
(4)0.85×104,
=0.85×(100+4),
=0.85×100+4×0.85,
=85+3.4,
=88.4;
(5)(10-
×1)+(9-
×2)+(8-
×3)+…+(2-
×9)+(1-
×10),=(10+9+8+…+2+1)-(
×1+
×2+…+
×9+
×10),=(10+9+8+…+2+1)-(10+9+8+…+2+1)×
,=(10+9+8+…+2+1)×(1-
),=(10+1)×10÷2×
,=55×
,=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)按运算顺序计算,先算小括号内的除法,再算小括号内的加法,最后算括号外的减法;
(2)把
化为
,然后约分结果为105,再用乘法分配律的逆运算简算;(3)运用乘法分配律的逆运算简算;
(4)把104看作100+4,运用乘法分配律简算;
(5)把整数与整数部分相加,分数与分数部分相加,再运用乘法分配律简算;
(6)先把原式改为9.81×0.1+5×9.81+4.9×9.81,运用乘法分配律简算.
点评:完成本题要注意分析式中数据,灵活运用所学的运算律进行简便计算的能力.