题目内容

(2013?广州模拟)计算下列各题,能简便的要简便计算
3
1
6
÷(1+
1
3
×1
3
4
)

1
15
+
2
17
)×15×17
(9.6-10
1
2
÷1.25)÷(1
1
3
×0.75)

5.66×7.28-3.16×3.16-3.16×4.12
2012×0.875+201.2×1.25
1
1×2
+
1
2×3
+
1
3×4
+…+
1
99×100
分析:(1)按运算顺序进行计算,先算括号内的,再算括号外的;
(2)根据数字特点,运用乘法分配律简算;
(3)按运算顺序进行计算,两个括号同时运算,第一个括号内既有除法运算,也有减法运算,应先算除法,再算减法;
(4)根据数字特点,先运用乘法分配律的逆运算,把原式改写为5.66×7.28-3.16×(3.16+4.12),然后再运用乘法分配律的逆运算简算;
(5)根据积不变的规律,把201.2×1.25改写成2012×0.125,然后运用乘法分配律的逆运算计算;
(6)通过观察,分母是两个连续自然数的乘积,可以把每个分数改写成两个分数相减的形式,然后通过加、减相互抵消,求出结果.
解答:解:(1)3
1
6
÷(1+
1
3
×1
3
4
),
=3
1
6
÷(1+
1
3
×
7
4
),
=3
1
6
÷(1+
7
12
),
=
19
6
÷
19
12

=
19
6
×
12
19

=2;

(2)(
1
15
+
2
17
)×15×17,
=
1
15
×15×17+
2
17
×15×17,
=17+30,
=47;

(3)(9.6-10
1
2
÷1.25)÷(1
1
3
×0.75),
=(9.6-
21
2
÷
5
4
)÷(
4
3
×
3
4
),
=(9.6-
21
2
×
4
5
)÷1,
=(9.6-8.4)÷1,
=1.2;

(4)5.66×7.28-3.16×3.16-3.16×4.12,
=5.66×7.28-3.16×(3.16+4.12),
=5.66×7.28-3.16×7.28,
=(5.66-3.16)×7.28,
=2.5×7.28,
=18.2;

(5)2012×0.875+201.2×1.25,
=2012×0.875+2012×0.125,
=2012×(0.875+0.125),
=2012×1,
=2012;

(6)
1
1×2
+
1
2×3
+
1
3×4
+…+
1
99×100

=1-
1
2
+
1
2
-
1
3
+
1
3
-
1
4
+…+
1
99
-
1
100

=1-
1
100

=
99
100
点评:此题考查了学生对四则混合运算顺序的掌握情况,以及认真审题、灵活解答的能力.
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