Q 2.     Write four more rational numbers in each of the following patterns:

 

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

Answers (1)

We have the pattern:

\frac{-2}{3} = \frac{-2\times1}{3\times1}           \frac{2}{-3} =\frac{2}{-3} = \frac{2\times1}{-3\times1}              \frac{4}{-6} = \frac{-2\times2}{3\times2}              \frac{-6}{9} = \frac{-2\times3}{3\times3}    

Now, following the same pattern, we have

\frac{-2\times4}{3\times4} = \frac{-8}{12}\ or\ \frac{8}{-12}                         \frac{-2\times5}{3\times5} = \frac{-10}{15}\ or\ \frac{10}{-15}           

 \frac{-2\times6}{3\times6} = \frac{-12}{18}\ or\ \frac{12}{-18}                     \frac{-2\times7}{3\times7} = \frac{-14}{21}\ or\ \frac{14}{-21}

Hence, the required rational numbers are:

\frac{8}{-12},\ \frac{10}{-15},\ \frac{12}{-18},and\ \frac{14}{-21}.

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