Question

Write four more rational numbers of the following pattern:

$\frac{-7}{4},\frac{14}{-8},\frac{-21}{12},\frac{28}{-16}.......$

Answer 1

Given,

$\frac{-7}{4},\frac{14}{-8},\frac{-21}{12},\frac{28}{-16}.......$

We have,

$\frac{-7}{4}=\frac{-7\times 1}{4\times 1},\frac{14}{-8}=\frac{-7\times (-2)}{4\times (-2)},\frac{-7}{4}=\frac{-7\times 3}{4\times 3},\frac{28}{-16}=\frac{-7\times (-4)}{4\times (-4)}$

Thus the following pattern is observed as

$\frac{-7\times 1}{4\times 1},\frac{-7\times (-2)}{4\times (-2)},\frac{-7\times 3}{4\times 3},\frac{-7\times (-4)}{4\times (-4)}$

Therefore following the same pattern next four rational numbers will be

$\frac{-7\times 5}{4\times 5},\frac{-7\times (-6)}{4\times (-6)},\frac{-7\times 7}{4\times 7},\frac{-7\times (-8)}{4\times (-8)}$

or,$\frac{-35}{20},\frac{42}{-24},\frac{-49}{28},\frac{56}{-32}$

Hence, the required four rational numbers will be

$\frac{-35}{20},\frac{42}{-24},\frac{-49}{28}and\frac{56}{-32}$