《2025年实验班提优训练暑假衔接版五升六年级数学苏教版》

例 计算:$\frac {1}{2}+\frac {1}{4}+\frac {1}{8}+\frac {1}{16}+\frac {1}{32}$

答案：
思路点拨 用正方形的面积表示单位“1”,算式的意思可以用右图表示。
答案详解 从右图中可以看出:
$\frac {1}{2}+\frac {1}{4}+\frac {1}{8}+\frac {1}{16}+\frac {1}{32}$
$=1-\frac {1}{32}$
$=\frac {31}{32}$

1. 计算下面各题。
$\frac {1}{3}+\frac {1}{6}+\frac {1}{12}+\frac {1}{24}+\frac {1}{48}+\frac {1}{96}$ $\frac {1}{2}+\frac {3}{4}+\frac {7}{8}+\frac {15}{16}+\frac {31}{32}+\frac {63}{64}$

答案： $\frac {1}{3}+\frac {1}{6}+\frac {1}{12}+\frac {1}{24}+\frac {1}{48}+\frac {1}{96}$
$=\frac {1}{1×3}+\frac {1}{3×2}+\frac {1}{3×4}+\frac {1}{3×8}+$
$\frac {1}{3×16}+\frac {1}{3×32}$
$=\frac {1}{3}×(1+\frac {1}{2}+\frac {1}{4}+\frac {1}{8}+\frac {1}{16}+\frac {1}{32})$
$=\frac {1}{3}×(1+1-\frac {1}{32})$
$=\frac {2}{3}-\frac {1}{96}$
$=\frac {21}{32}$
$\frac {1}{2}+\frac {3}{4}+\frac {7}{8}+\frac {15}{16}+\frac {31}{32}+\frac {63}{64}$
$=(1-\frac {1}{2})+(1-\frac {1}{4})+(1-\frac {1}{8})+(1-\frac {1}{16})+$
$(1-\frac {1}{32})+(1-\frac {1}{64})$
$=6-(1-\frac {1}{64})$
$=5\frac {1}{64}$

例 计算:$\frac {1}{2}+\frac {1}{6}+\frac {1}{12}+\frac {1}{20}+\frac {1}{30}+\frac {1}{42}$

答案： 思路点拨 每个分数的分母都可以分解为两个连续自然数的积,再把每个分数都拆分为两个分数的差。
$\frac {1}{2}= \frac {1}{1×2}= \frac {1}{1}-\frac {1}{2},\frac {1}{6}= \frac {1}{2×3}= \frac {1}{2}-\frac {1}{3},\frac {1}{12}= \frac {1}{3×4}= \frac {1}{3}-\frac {1}{4},...$,拆开后的一些分数在计算过程中可以互相抵消,这样就可简化运算。
答案详解 $\frac {1}{2}+\frac {1}{6}+\frac {1}{12}+\frac {1}{20}+\frac {1}{30}+\frac {1}{42}$
$=1-\frac {1}{2}+\frac {1}{2}-\frac {1}{3}+\frac {1}{3}-\frac {1}{4}+\frac {1}{4}-\frac {1}{5}+\frac {1}{5}-\frac {1}{6}+\frac {1}{6}-\frac {1}{7}$
$=1-\frac {1}{7}$
$=\frac {6}{7}$