在下列每个模式中再写四个有理数
$(i)$. $\frac{-3}{5},\ \frac{-6}{10},\ \frac{-9}{15},\ \frac{-12}{20}$........
$(ii)$. $\frac{-1}{4},\ \frac{-2}{8},\ \frac{-3}{12}$.....
$(iii)$. $\frac{-1}{6},\ \frac{2}{-12},\ \frac{3}{-18},\ \frac{4}{-24}$......
$(iv)$. $\frac{-2}{3},\ \frac{2}{-3},\ \frac{4}{-6},\ \frac{6}{-9}$.....
已知：
(i) $\frac{-3}{5},\ \frac{-6}{10},\ \frac{-9}{15},\ \frac{-12}{20}$........
(ii) $\frac{-1}{4},\ \frac{-2}{8},\ \frac{-3}{12}$.....
(iii) $\frac{-1}{6},\ \frac{2}{-12},\ \frac{3}{-18},\ \frac{4}{-24}$......
(iv) $\frac{-2}{3},\ \frac{2}{-3},\ \frac{4}{-6},\ \frac{6}{-9}$.....
要求：在每个给定的模式中再写四个有理数。
解答
(i) $\frac{-3}{5},\ \frac{-6}{10},\ \frac{-9}{15},\ \frac{-12}{20}$........
给定的有理数模式可以写成如下形式：
$\frac{-3}{5}\times\frac{1}{1},\ -\frac{3}{5}\times\frac{2}{2},\ -\frac{3}{5}\times\frac{3}{3},\ -\frac{3}{5}\times\frac{4}{4}......$
在这个序列中，接下来的四个有理数可以写成：
$-\frac{3}{5}\times\frac{5}{5},\ -\frac{3}{5}\times\frac{6}{6},\ -\frac{3}{5}\times\frac{7}{7},\ -\frac{3}{5}\times\frac{8}{8}$
或者 $-\frac{15}{25},\ -\frac{18}{30},\ -\frac{21}{35},\ -\frac{24}{40}$
(ii) $\frac{-1}{4},\ \frac{-2}{8},\ \frac{-3}{12}.....$
给定的有理数模式可以写成如下形式：
$-\frac{1}{4}\times\frac{1}{1},\ -\frac{1}{4}\times\frac{2}{2},\ -\frac{1}{4}\times\frac{3}{3}.....$
在这个序列中，接下来的四个有理数可以写成：
$\frac{-1}{4}\times\frac{4}{4},\ \frac{-1}{4}\times\frac{5}{5},\ \frac{-1}{4}\times\frac{6}{6},\ \frac{-1}{4}\times\frac{7}{7}$
$\frac{-4}{16},\ \frac{-5}{20},\ \frac{-6}{24},\ \frac{-7}{28}$
(iii) $\frac{-1}{6},\ \frac{2}{-12},\ \frac{3}{-18},\ \frac{4}{-24}......$
给定的有理数模式可以写成如下形式：
$\frac{-1}{6}\times\frac{1}{1},\ \frac{-1}{6}\times\frac{2}{2},\ \frac{-1}{6}\times\frac{3}{3},\ \frac{-1}{6}\times\frac{4}{4}$
在这个序列中，接下来的四个有理数可以写成：
$\frac{-1}{6}\times\frac{5}{5},\ \frac{-1}{6}\times\frac{6}{6},\ \frac{-1}{6}\times\frac{7}{7},\ \frac{-1}{6}\times\frac{8}{8}$
或者 $\frac{-5}{30},\ \frac{-6}{36},\ \frac{-7}{42},\ \frac{-8}{48}$
(iv) $\frac{-2}{3},\ \frac{2}{-3},\ \frac{4}{-6},\ \frac{6}{-9}.....$
给定的有理数模式可以写成如下形式：
$\frac{-2}{3}\times\frac{1}{1},\ \frac{2}{-3}\times\frac{1}{1},\ \frac{2}{-3}\times\frac{2}{2},\ \frac{2}{-3}\times\frac{3}{3}......$
$\frac{2}{-3}\times\frac{4}{4},\ \frac{2}{-3}\times\frac{5}{5},\ \frac{2}{-3}\times\frac{6}{6},\ \frac{2}{-3}\times\frac{7}{7}$
或者 $\frac{8}{-12},\ \frac{10}{-15},\ \frac{12}{-18},\ \frac{14}{-21}$
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