题目内容

(2010?临海市)用递等式计算(能简算的简算,并写出简算过程)
345-2442÷37+34              
(4-3.5×
2
3
)÷1
1
9

180÷15+42×33-239         
8.59-2.07÷0.3×1.1
(2
2
5
-3.5÷2
5
8
)×(2
5
12
+4.25)
[6-(
4
9
×6.3+2
3
10
)]÷0.15.
分析:(1)345-2442÷37+34,此题应先算除法,再算减法和加法;
(2)(4-3.5×
2
3
)÷1
1
9
,先算括号内的,再算括号外的,在计算时把小数化为分数较简便;
(3)180÷15+42×33-239,先算除法和乘法,再算加法和减法;
(4)8.59-2.07÷0.3×1.1,先算除法和乘法,最后算减法;
(5)(2
2
5
-3.5÷2
5
8
)×(2
5
12
+4.25),注意把小数化为分数计算较简便;
(6)[6-(
4
9
×6.3+2
3
10
)]÷0.15,此题把分数化为小数计算较简便.
解答:解:(1)345-2442÷37+34,
=345-66+34,
=279+34,
=313;
(2)(4-3.5×
2
3
)÷1
1
9

=(4-
7
2
×
2
3
)×
9
10

=(4-
7
3
)×
9
10

=
5
3
×
9
10

=1
1
2

(3)180÷15+42×33-239,
=12+1386-239,
=1398-239,
=1159;
(4)8.59-2.07÷0.3×1.1,
=8.59-6.9×1.1,
=8.59-7.59,
=1;
(5)(2
2
5
-3.5÷2
5
8
)×(2
5
12
+4.25),
=(2
2
5
-3
1
2
×
8
21
)×(2
5
12
+4
1
4
),
=(2
2
5
-
7
2
×
8
21
)×6
2
3

=(2
2
5
-
4
3
)×6
2
3

=
16
15
×
20
3

=7
1
9

(6)[6-(
4
9
×6.3+2
3
10
)]÷0.15,
=[6-(2.8+2.3)]÷0.15,
=[6-5.1]÷0.15,
=0.9÷0.15,
=6.
点评:此题重点考查学生的运算顺序,在计算时要留心数的形式如何变化才能使计算简便的问题.
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