题目内容

计算:
(1)2.52×[5
1
2
-1.75×(
2
3
+
19
21
)]

(2)(
1
143
+
1
77
+
1
91
)÷(
20
99
+
1
9
)-
2
91

(3)[15.5-(1.5×
5
7
+1
1
2
×
2
7
)]÷14%

(4)[1
1
10
+2
7
20
÷(3
1
12
-1.125)]×
9
23
-
1
6
分析:(1)把小数化为分数,先算小括号内的,再算中括号内的乘法,然后算中括号内的减法,最后算括号外的乘法;
(2)把所有的分母写成这样的形式:143=11×13,77=11×7,91=7×13,被除数通分,除数通分,相除
9
7×13
,然后计算即可;
(3)把1
1
2
化为小数,小括号内运用乘法分配律简算,然后按运算顺序计算;
(4)把小数化为分数,先算小括号内的,再算中括号内的除法,然后算中括号内的加法,再算括号外的乘法,最后算括号外的减法.
解答:解:(1)2.52×[5
1
2
-1.75×(
2
3
+
19
21
)],
=
63
25
×[5
1
2
-
7
4
×
11
7
],
=
63
25
×[5
1
2
-
11
4
],
=
63
25
×
11
4

=
693
100

=6.93;

(2)(
1
143
+
1
77
+
1
91
)÷(
20
99
+
1
9
)-
2
91

=(
1
11×13
+
1
7×11
+
1
7×13
)÷(
20
99
+
11
99
)-
2
91

=
7+13+11
7×11×13
÷
31
99
-
2
91

=
31
7×11×13
×
99
31
-
2
91

=
9
91
-
2
91

=
1
13


(3)[15.5-(1.5×
5
7
+1
1
2
×
2
7
)]÷14%,
=[15.5-(1.5×
5
7
+1.5×
2
7
)]÷0.14,
=[15.5-1.5×(
5
7
+
2
7
)]÷0.14,
=[15.5-1.5×1]÷0.14,
=14÷0.14,
=100;

(4)[1
1
10
+2
7
20
÷(3
1
12
-1.125)]×
9
23
-
1
6

=[1
1
10
+2
7
20
÷(3
1
12
-1
1
8
)]×
9
23
-
1
6

=[1
1
10
+2
7
20
÷
47
24
9
23
-
1
6

=[1
1
10
+
47
20
×
24
47
9
23
-
1
6

=[1
1
10
+
6
5
9
23
-
1
6

=
23
10
×
9
23
-
1
6

=
9
10
-
1
6

=
11
15
点评:脱式计算,注意运算顺序和运算法则,根据题目特点,灵活进行数字转化.
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