Question

20．计算下面各组算式，从计算结果中你发现了什么？你能再写出两组这样的式子吗？
$\left\{\begin{array}{l}{\frac{1}{2}-\frac{1}{3}=}\\{\frac{1}{3}-\frac{1}{4}=}\end{array}\right.$
$\left\{\begin{array}{l}{\frac{1}{4}-\frac{1}{5}=}\\{\frac{1}{5}-\frac{1}{6}=}\end{array}\right.$
$\left\{\begin{array}{l}{\frac{1}{8}-\frac{1}{9}=}\\{\frac{1}{9}-\frac{1}{10}=}\end{array}\right.$．

Answer 1

分析 根据分数减法的计算方法进行计算，然后再根据每个算式的差进行总结规律，并举例说明即可．

解答 解：$\left\{\begin{array}{l}{\frac{1}{2}-\frac{1}{3}=\frac{1}{6}}\\{\frac{1}{3}-\frac{1}{4}=\frac{1}{12}}\end{array}\right.$
$\left\{\begin{array}{l}{\frac{1}{4}-\frac{1}{5}=\frac{1}{20}}\\{\frac{1}{5}-\frac{1}{6}=\frac{1}{30}}\end{array}\right.$
$\left\{\begin{array}{l}{\frac{1}{8}-\frac{1}{9}=\frac{1}{72}}\\{\frac{1}{9}-\frac{1}{10}=\frac{1}{90}}\end{array}\right.$
从计算结果中发现：当分子是1，分母分别为两个相邻的自然数时，它们的差就是两个相邻自然数的乘积，分子仍然是1，
例如：$\left\{\begin{array}{l}{\frac{1}{6}-\frac{1}{7}=\frac{1}{42}}\\{\frac{1}{7}-\frac{1}{8}=\frac{1}{56}}\end{array}\right.$和$\left\{\begin{array}{l}{\frac{1}{10}-\frac{1}{11}=\frac{1}{110}}\\{\frac{1}{11}-\frac{1}{12}=\frac{1}{132}}\end{array}\right.$．

点评 解答此题的关键是根据分数减法的计算方法进行计算，然后再从计算结果中总结规律且应用规律．