(1)9.6×42+3.8×96+4.8×40
(2)
1
2
+
1
3
+
2
3
+
1
4
+
2
4
+
3
4
+…+
1
20
+
2
20
+…+
19
20

(3)
2004+2005×2003
2004×2005-1

(4)
1
8
+
1
24
+
1
48
+
1
80
+…+
1
360
分析:(1)根據(jù)乘法分配律進(jìn)行計(jì)算;
(2)根據(jù)題意,把同分母的分?jǐn)?shù)結(jié)合起來(lái),原式=
1
2
+1+
3
2
+2+…+
19
2
,變成一個(gè)等差是
1
2
,共有19項(xiàng)的等差數(shù)列,然后再根據(jù)求和公式進(jìn)一步計(jì)算;
(3)把分子2004+2005×2003根據(jù)乘法分配律進(jìn)行化簡(jiǎn),然后再進(jìn)一步計(jì)算;
(4)根據(jù)分?jǐn)?shù)的拆項(xiàng)進(jìn)行計(jì)算.
解答:解:(1)9.6×42+3.8×96+4.8×40,
=9.6×42+38×9.6+4.8×40,
=9.6×(42+38)+4.8×40,
=9.6×80+4.8×40,
=9.6×80+(2.4×2)×40,
=9.6×80+2.4×80,
=(9.6+2.4)×80,
=12×80,
=960;

(2)
1
2
+
1
3
+
2
3
+
1
4
+
2
4
+
3
4
+…+
1
20
+
2
20
+…+
19
20
,
=
1
2
+
1+2
3
+
1+2+3
4
+…+
1+2+…+19
20
,
=
1
2
+1+
3
2
+…+
(1+19)×19÷2
20
,
=
1
2
+1+
3
2
+…+
19
2

=(
1
2
+
19
2
)×19÷2,
=10×19÷2,
=95;

(3)
2004+2005×2003
2004×2005-1

=
2004+2005×(2004-1)
2004×2005-1
,
=
2004+2005×2004-2005×1
2004×2005-1
,
=
2004+2005×2004-2005
2004×2005-1
,
=
2005×2004-(2005-2004)
2004×2005-1
,
=
2005×2004-1
2004×2005-1
,
=1;

(4)
1
8
+
1
24
+
1
48
+
1
80
+…+
1
360
,
=(
1
2×4
)+(
1
4×6
)+(
1
6×8
)+(
1
8×10
)+…+(
1
18×20
),
=
1
2
×(
1
2
-
1
4
+
1
4
-
1
6
+
1
6
-
1
8
+
1
8
-
1
10
+…+
1
18
-
1
20
),
=
1
2
×(
1
2
-
1
20
),
=
1
2
×
9
20
,
=
9
40
點(diǎn)評(píng):根據(jù)題意,找準(zhǔn)巧算的方法,然后再進(jìn)一步計(jì)算即可.
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