问题 解答题
1999+9992
1
20
+
1
30
+
1
42
+…+
1
132

2008×20092009-2009×20082008
9
20
÷6+
1
20
×
1
6

5.58-
3
5
+5.42-
2
5

(2890+
5
6
+
7
8
+
7
10
)÷(
5
6
+
7
8
+
7
10

3333×3333+9999×8889
2005+2006×2004
2005×2006-1

若2!=2×3,3!=3×4×5,5!=5×6×7×8×9.按此规则计算
4!
61!
答案

(1)1999+9992,

=1999+999×999,

=1999+(1000-1)×999,

=1999+999000-999,

=(1999-999)+999000,

=1000+999000,

=1000000;

(2)

1
20
+
1
30
+
1
42
+…+
1
132

=

1
4
-
1
5
+
1
5
-
1
6
+
1
6
-
1
7
+…+
1
11
-
1
12

=

1
6

(3)2008×20092009-2009×20082008,

=2008×(2009×10001)-2009×(2008×10001)

=2008×10001×(2009-2009),

=2008×10001×0,

=0;

(4)

9
20
÷6+
1
20
×
1
6

=

9
20
×
1
6
+
1
20
×
1
6

=(

9
20
+
1
20
)×
1
6

=

1
2
×
1
6

=

1
12

(5)5.58-

3
5
+5.42-
2
5

=(5.58+5.42)-(

3
5
+
2
5
),

=11-1,

=10;

(6)(2890+

5
6
+
7
8
+
7
10
)÷(
5
6
+
7
8
+
7
10
),

=[2890+(

5
6
+
7
8
+
7
10
)]÷(
5
6
+
7
8
+
7
10
),

=2890÷(

5
6
+
7
8
+
7
10
)+(
5
6
+
7
8
+
7
10
)÷(
5
6
+
7
8
+
7
10
),

=2890×

120
289
+1,

=1200+1,

=1201;

(7)3333×3333+9999×8889

=9×1111×1111+9999×8889,

=9999×1111+9999×8889,

=9999×(1111+8889),

=9999×10000,

=99990000;

(8)

2005+2006×2004
2005×2006-1

=

2005+(2005+1)×2004
2005×(2005+1)-1

=

2005+2005×2004+2004
2005×2005+2005-1

=

2005×2005+2004
2005×2005+2004

=1;

(9)因为2!=2×3,3!=3×4×5,5!=5×6×7×8×9,

所以4!=4×5×6×7=840 6!=6×7×8×9×10×11,

所以

4!
6!
=
4×5×6×7
6×7×8×9×10×11
=
1
396

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