问题 解答题
简便计算
(1)(
1
15
-
1
51
)×17×5
(2)
1
5
×27+41÷
5
3

(3)(1+
1
2
)×(1-
1
2
)×(1+
1
3
)×(1-
1
3
)×…×(1+
1
9
)×(1-
1
9
答案

(1)(

1
15
-
1
51
)×17×5,

=

1
15
×17×5-
1
51
×17×5,

=

17
3
-
5
3

=4;

(2)

1
5
×27+41÷
5
3

=

1
5
×27+41×
3
5

=

3
5
×9+41×
3
5

=

3
5
×(9+41),

=

3
5
×50,

=30;

(3)(1+

1
2
)×(1-
1
2
)×(1+
1
3
)×(1-
1
3
)×…×(1+
1
9
)×(1-
1
9
),

=

3
2
×
1
2
×
4
3
×
2
3
×…×
10
9
×
8
9

=

1
2
×(
3
2
×
2
3
)×(
4
3
×
3
4
)×…×(
9
8
×
8
9
)×
10
9

=

1
2
×
10
9

=

5
9

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