# Write four more rational numbers in each of the following patterns:$(i)$. $\frac{-3}{5},\ \frac{-6}{10},\ \frac{-9}{15},\ \frac{-12}{20}$........$(ii)$. $\frac{-1}{4},\ \frac{-2}{8},\ \frac{-3}{12}$.....$(iii)$. $\frac{-1}{6},\ \frac{2}{-12},\ \frac{3}{-18},\ \frac{4}{-24}$......$(iv)$. $\frac{-2}{3},\ \frac{2}{-3},\ \frac{4}{-6},\ \frac{6}{-9}$.....

Given:

(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) $\frac{-2}{3},\ \frac{2}{-3},\ \frac{4}{-6},\ \frac{6}{-9}$.....

To do: To write four more rational numbers in each of the given patterns.

Solution:

(i) $\frac{-3}{5},\ \frac{-6}{10},\ \frac{-9}{15},\ \frac{-12}{20}$........
This given pattern of rational numbers can be written as below:

$\frac{-3}{5}\times\frac{1}{1},\ -\frac{3}{5}\times\frac{2}{2},\ -\frac{3}{5}\times\frac{3}{3},\ -\frac{3}{5}\times\frac{4}{4}......$

In this sequence, the next four rational numbers can be written as:

$-\frac{3}{5}\times\frac{5}{5},\ -\frac{3}{5}\times\frac{6}{6},\ -\frac{3}{5}\times\frac{7}{7},\ -\frac{3}{5}\times\frac{8}{8}$

Or $-\frac{15}{25},\ -\frac{18}{30},\ -\frac{21}{35},\ -\frac{24}{40}$

(ii) $\frac{-1}{4},\ \frac{-2}{8},\ \frac{-3}{12}.....$

This given pattern of rational numbers can be written as below:

$-\frac{1}{4}\times\frac{1}{1},\ -\frac{1}{4}\times\frac{2}{2},\ -\frac{1}{4}\times\frac{3.}{3}.....$

In this sequence, the next four rational numbers can be written as:

$\frac{-1}{4}\times\frac{4}{4},\ \frac{-1}{4}\times\frac{5}{5},\ \frac{-1}{4}\times\frac{6}{6},\ \frac{-1}{4}\times\frac{7}{7}$

$\frac{-4}{16},\ \frac{-5}{20},\ \frac{-6}{24},\ \frac{-7}{28}$

(iii) $\frac{-1}{6},\ \frac{2}{-12},\ \frac{3}{-18},\ \frac{4}{-24}......$

This given pattern of rational numbers can be written as below:

$\frac{-1}{6}\times\frac{1}{1},\ \frac{-1}{6}\times\frac{2}{2},\ \frac{-1}{6}\times\frac{3}{3},\ \frac{-1}{6}\times\frac{4}{4}$

In this sequence, the next four rational numbers can be written as:

$\frac{-1}{6}\times\frac{5}{5},\ \frac{-1}{6}\times\frac{6}{6},\ \frac{-1}{6}\times\frac{7}{7},\ \frac{-1}{6}\times\frac{8}{8}$

Or $\frac{-5}{30},\ \frac{-1}{36},\ \frac{-7}{42},\ \frac{-8}{48}$

(iv) $\frac{-2}{3},\ \frac{2}{-3},\ \frac{4}{-6},\ \frac{6}{-9}.....$

This given pattern of rational numbers can be written as below:

$\frac{-2}{3}\times\frac{1}{1},\ \frac{2}{-3}\times\frac{1}{1},\ \frac{2}{-3}\times\frac{2}{2},\ \frac{2}{-3}\times\frac{3}{3}......$

In this sequence, the next four rational numbers can be written as:

$\frac{2}{-3}\times\frac{4}{4},\ \frac{2}{-3}\times\frac{5}{5},\ \frac{2}{-3}\times\frac{6}{6},\ \frac{2}{-3}\times\frac{7}{7}$

Or $\frac{8}{-12},\ \frac{10}{-15},\ \frac{12}{-18},\ \frac{14}{-21}$

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Updated on: 10-Oct-2022

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