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Question

Give four rational numbers equivalent to: (i) \(\frac{{-{2}}}{{7}}\) (ii) \(\frac{{5}}{{-{3}}}\) (iii) \(\frac{{4}}{{9}}\)

Answer

(i) Four numbers equivalent to \(-\frac{{2}}{{7}}\) are

\(-\frac{{2}}{{7}}\ast\frac{{2}}{{2}}=-\frac{{4}}{{14}}\)

\(-\frac{{2}}{{7}}\ast\frac{{3}}{{3}}=-\frac{{6}}{{21}}\)

\(-\frac{{2}}{{7}}\ast\frac{{4}}{{4}}=-\frac{{8}}{{28}}\)

\(-\frac{{2}}{{7}}\ast\frac{{5}}{{5}}=-\frac{{10}}{{35}}\)



(ii)Four numbers equivalent to \(-\frac{{5}}{{3}}\) are

\(-\frac{{5}}{{3}}\ast\frac{{2}}{{2}}=-\frac{{10}}{{6}}\)

\(-\frac{{5}}{{3}}\ast\frac{{3}}{{3}}=-\frac{{15}}{{9}}\)

\(-\frac{{5}}{{3}}\ast\frac{{4}}{{4}}=-\frac{{20}}{{12}}\)

\(-\frac{{5}}{{3}}\ast\frac{{5}}{{5}}=-\frac{{25}}{{15}}\)



(iii)Four numbers equivalent to \(\frac{{4}}{{9}}\) are

\(\frac{{4}}{{9}}\ast\frac{{2}}{{2}}=\frac{{8}}{{18}}\)

\(\frac{{4}}{{9}}\ast\frac{{3}}{{3}}=\frac{{12}}{{27}}\)

\(\frac{{4}}{{9}}\ast\frac{{4}}{{4}}=\frac{{16}}{{36}}\)

\(\frac{{4}}{{9}}\ast\frac{{5}}{{5}}=\frac{{20}}{{45}}\)


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