《2025年实验班提优训练暑假衔接版五升六年级数学苏教版》

2. 计算下面各题。
$\frac {1}{2}+\frac {1}{6}+\frac {1}{12}+\frac {1}{20}+\frac {1}{30}+\frac {1}{42}+\frac {1}{7}$ $\frac {1}{2}+\frac {1}{6}+\frac {1}{12}+\frac {1}{20}+... +\frac {1}{2450}$

答案： $\frac {1}{2}+\frac {1}{6}+\frac {1}{12}+\frac {1}{20}+\frac {1}{30}+\frac {1}{42}+\frac {1}{7}$
$=1-\frac {1}{2}+\frac {1}{2}-\frac {1}{3}+\frac {1}{3}-\frac {1}{4}+\frac {1}{4}-\frac {1}{5}+\frac {1}{5}-$
$\frac {1}{6}+\frac {1}{6}-\frac {1}{7}+\frac {1}{7}$
$=1$
$\frac {1}{2}+\frac {1}{6}+\frac {1}{12}+\frac {1}{20}+... +\frac {1}{2450}$
$=1-\frac {1}{2}+\frac {1}{2}-\frac {1}{3}+\frac {1}{3}-\frac {1}{4}+\frac {1}{4}-\frac {1}{5}+... +$
$\frac {1}{49}-\frac {1}{50}$
$=1-\frac {1}{50}$
$=\frac {49}{50}$

例 计算:$\frac {5}{6}-\frac {7}{12}+\frac {9}{20}-\frac {11}{30}+\frac {13}{42}$

答案： 思路点拨 常用的分数巧算技巧如“拆”的方法,即先把某些分数分裂成两个分数相加或相减的形式,再相互抵消或合并成一个分数,达到简化运算的目的。此题可以先把每个分数拆分成两个分数的和的形式再进行巧算。
$\frac {5}{6}= \frac {1}{2}+\frac {1}{3}$ $\frac {7}{12}= \frac {1}{3}+\frac {1}{4}$ $\frac {9}{20}= \frac {1}{4}+\frac {1}{5}$ $\frac {11}{30}= \frac {1}{5}+\frac {1}{6}$ $\frac {13}{42}= \frac {1}{6}+\frac {1}{7}$
答案详解 $\frac {5}{6}-\frac {7}{12}+\frac {9}{20}-\frac {11}{30}+\frac {13}{42}$
$=(\frac {1}{2}+\frac {1}{3})-(\frac {1}{3}+\frac {1}{4})+(\frac {1}{4}+\frac {1}{5})-(\frac {1}{5}+\frac {1}{6})+(\frac {1}{6}+\frac {1}{7})$
$=\frac {1}{2}+\frac {1}{3}-\frac {1}{3}-\frac {1}{4}+\frac {1}{4}+\frac {1}{5}-\frac {1}{5}-\frac {1}{6}+\frac {1}{6}+\frac {1}{7}$
$=\frac {1}{2}+\frac {1}{7}$
$=\frac {9}{14}$

3. 计算下面各题。
$\frac {9}{20}-\frac {11}{30}+\frac {13}{42}-\frac {15}{56}+\frac {17}{72}$ $\frac {5}{6}-\frac {7}{12}+\frac {9}{20}-\frac {11}{30}+\frac {13}{42}-\frac {15}{56}+\frac {17}{72}-\frac {19}{90}+\frac {21}{110}-\frac {23}{132}+\frac {25}{156}$

答案： $\frac {9}{20}-\frac {11}{30}+\frac {13}{42}-\frac {15}{56}+\frac {17}{72}$
$=(\frac {1}{4}+\frac {1}{5})-(\frac {1}{5}+\frac {1}{6})+(\frac {1}{6}+\frac {1}{7})-(\frac {1}{7}+\frac {1}{8})$
$+(\frac {1}{8}+\frac {1}{9})$
$=\frac {1}{4}+\frac {1}{5}-\frac {1}{5}-\frac {1}{6}+\frac {1}{6}+\frac {1}{7}-\frac {1}{7}-\frac {1}{8}+\frac {1}{8}+\frac {1}{9}$
$=\frac {1}{4}+\frac {1}{9}$
$=\frac {13}{36}$
$\frac {5}{6}-\frac {7}{12}+\frac {9}{20}-\frac {11}{30}+\frac {13}{42}-\frac {15}{56}+\frac {17}{72}-\frac {19}{90}+$
$\frac {21}{110}-\frac {23}{132}+\frac {25}{156}$
$=(\frac {1}{2}+\frac {1}{3})-(\frac {1}{3}+\frac {1}{4})+(\frac {1}{4}+\frac {1}{5})-(\frac {1}{5}+\frac {1}{6})$
$+(\frac {1}{6}+\frac {1}{7})-(\frac {1}{7}+\frac {1}{8})+(\frac {1}{8}+\frac {1}{9})-(\frac {1}{9}+$
$\frac {1}{10})+(\frac {1}{10}+\frac {1}{11})-(\frac {1}{11}+\frac {1}{12})+(\frac {1}{12}+\frac {1}{13})$
$=\frac {1}{2}+\frac {1}{13}$
$=\frac {15}{26}$