问题 解答题
两千多年前,古埃及人总喜欢把分数转化为分子是1的分数来计算,所以后人常把分子是1的分数称为埃及分数.埃及分数在计算中有着一些什么规律呢?请观察下面几组算式并填空:
(1)
1
3
-
1
4
=
(4)-(3)
3×4
=
1
3×4

1
7
-
1
8
=
()-()
7×8
=
1
7×8

1
20
-
1
21
=
()-()
20×21
=
1
20×21

1
100
-
1
101
=
()
()


1
a
-
1
a+1
=
a+1
a•a+1
-
1
a•(a+1)
=
1
a•(a+1)

(2)请你根据上面的规律,把下面各个分数写成两个分数的差.
1
2×3
=
1
()
-
1
()

1
5×6
=
1
()
-
1
()

1
40×41
=
1
()
-
1
()

1
1999×2000
=
1
()
-
1
()

1
42
=
1
()
-
1
()

1
9900
=
1
()
-
1
()

1
72
=
1
()
-
1
()

1
n•(n+1)
=
1
()
-
1
()
答案

1
7
-
1
8
=
8-7
7×8
=
1
7×8

1
20
-
1
21
=
21-20
20×21
=
1
20×21

1
100
-
1
101
=
101-100
100×101
=
1
100×101

1
2×3
=
1
2
-
1
3

1
5×6
=
1
5
-
1
6

1
40×41
=
1
40
-
1
41

1
1999×2000
=
1
1999
-
1
2000

1
42
=
1
6
-
1
7

1
9900
=
1
99
-
1
100

1
72
=
1
8
-
1
9

1
n•(n+1)
=
1
n
-
1
n+1

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