《2025年重点中学招生分班五年真题分类卷数学》

1. (2024陕西JDFZ)$1\frac {1}{2}×1\frac {1}{3}×1\frac {1}{4}×1\frac {1}{5}×... ×1\frac {1}{2006}×1\frac {1}{2007}$

答案： 解:原式=$\frac{3}{2}×\frac{4}{3}×\frac{5}{4}×\frac{6}{5}×\cdots×\frac{2007}{2006}×\frac{2008}{2007}$
=$\frac{1}{2}×2008$
=1004

2. (2024陕西TYZBH学校)$2017÷2017\frac {2017}{2018}+2018\frac {1}{2019}$

答案： 解:原式=$2017÷\frac{2017×2018+2017}{2018}+\frac{2018×2019+1}{2019}$
=$2017×\frac{2018}{2017×2018+2017}+\frac{2018×2019+1}{2019}$
=$2017×\frac{2018}{2017×(2018+1)}+\frac{2018×2019+1}{2019}$
=$\frac{2018}{2019}+\frac{2018×2019+1}{2019}$
=$\frac{2018×2019+2019}{2019}$
=$\frac{2019×(2018+1)}{2019}$
=2019

3. (2024陕西GX3C)$(1-\frac {1}{2})×(1-\frac {1}{3})×(1-\frac {1}{4})×(1-\frac {1}{5})×... ×(1-\frac {1}{100})$

答案： 解:原式=$\frac{1}{2}×\frac{2}{3}×\frac{3}{4}×\frac{4}{5}×\cdots×\frac{99}{100}$
=$\frac{1}{100}$

4. (2024陕西GXYZ)$(1+\frac {1}{51})×(1-\frac {1}{51})×(1+\frac {1}{52})×(1-\frac {1}{52})×... ×(1+\frac {1}{152})×(1-\frac {1}{152})$

答案： 解:原式=$\frac{52}{51}×\frac{50}{51}×\frac{53}{52}×\frac{51}{52}×\cdots×\frac{153}{152}×\frac{151}{152}$
=$\frac{50}{51}×\frac{153}{152}$
=$\frac{75}{76}$

5. (2021北京BSDFZ)$(57×85×105×117×121)÷(1×3×5×7×9×11×13×15×17×19)$

答案： 解:原式=(57×85×105×117×121)÷[1×(3×19)×(5×17)×(7×15)×(9×13)×11]
=(57×85×105×117×121)÷(57×85×105×117×11)
=121÷11
=11