Question

20．計算下面各組算式，從計算結(jié)果中你發(fā)現(xiàn)了什么？你能再寫出兩組這樣的式子嗎？
$\left\{\begin{array}{l}{\frac{1}{2}-\frac{1}{3}=}\\{\frac{1}{3}-\frac{1}{4}=}\end{array}\right.$
$\left\{\begin{array}{l}{\frac{1}{4}-\frac{1}{5}=}\\{\frac{1}{5}-\frac{1}{6}=}\end{array}\right.$
$\left\{\begin{array}{l}{\frac{1}{8}-\frac{1}{9}=}\\{\frac{1}{9}-\frac{1}{10}=}\end{array}\right.$．

Answer 1

分析 根據(jù)分?jǐn)?shù)減法的計算方法進(jìn)行計算，然后再根據(jù)每個算式的差進(jìn)行總結(jié)規(guī)律，并舉例說明即可．

解答 解：$\left\{\begin{array}{l}{\frac{1}{2}-\frac{1}{3}=\frac{1}{6}}\\{\frac{1}{3}-\frac{1}{4}=\frac{1}{12}}\end{array}\right.$
$\left\{\begin{array}{l}{\frac{1}{4}-\frac{1}{5}=\frac{1}{20}}\\{\frac{1}{5}-\frac{1}{6}=\frac{1}{30}}\end{array}\right.$
$\left\{\begin{array}{l}{\frac{1}{8}-\frac{1}{9}=\frac{1}{72}}\\{\frac{1}{9}-\frac{1}{10}=\frac{1}{90}}\end{array}\right.$
從計算結(jié)果中發(fā)現(xiàn)：當(dāng)分子是1，分母分別為兩個相鄰的自然數(shù)時，它們的差就是兩個相鄰自然數(shù)的乘積，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$\left\{\begin{array}{l}{\frac{1}{10}-\frac{1}{11}=\frac{1}{110}}\\{\frac{1}{11}-\frac{1}{12}=\frac{1}{132}}\end{array}\right.$．

點評 解答此題的關(guān)鍵是根據(jù)分?jǐn)?shù)減法的計算方法進(jìn)行計算，然后再從計算結(jié)果中總結(jié)規(guī)律且應(yīng)用規(guī)律．