Q 9.     Which is greater in each of the following:

 (i)     \frac{2}{3}, \frac{5}{2}                           (ii)     \frac{-5}{6}, \frac{-4}{3}           

(iii)   \frac{-3}{4}, \frac{2}{-3}                   (iv)     \frac{-1}{4}, \frac{1}{4}       

(v)  -3\frac{2}{7}, -3\frac{4}{5}

Answers (1)

(i)  \frac{2}{3}, \frac{5}{2}

\Rightarrow \frac{2\times2}{3\times2}, \frac{5\times3}{2\times3}

\Rightarrow \frac{4}{6}, \frac{15}{6}

Since, \frac{15}{6}> \frac{4}{6}

So, \frac{5}{2}> \frac{2}{3}.

 

(ii)  \frac{-5}{6}, \frac{-4}{3}

\Rightarrow \frac{-5\times3}{6\times3}, \frac{-4\times6}{3\times6}

\Rightarrow \frac{-15}{18}, \frac{-24}{18}

Since, \frac{-15}{18}> \frac{-24}{18}

So, \frac{-5}{6}> \frac{-4}{3}.

 

(iii)  \frac{-3}{4}, \frac{2}{-3}

\Rightarrow \frac{-3\times-3}{4\times-3}, \frac{2\times4}{-3\times4}

\Rightarrow \frac{9}{-12}, \frac{8}{-12}

Since, \frac{8}{-12}> \frac{9}{-12}

So, \frac{2}{-3}> \frac{-3}{4}

 

(iv)  \frac{-1}{4}, \frac{1}{4}

\Rightarrow \frac{1}{4}> \frac{-1}{4}

As each positive number is greater than its negative.

 

(v) -3\frac{2}{7}, -3\frac{4}{5}

\Rightarrow \frac{-23}{7}, \frac{-19}{5} =\frac{-23\times5}{7\times5}, \frac{-19\times7}{5\times7}

\Rightarrow \frac{-115}{35} > \frac{-133}{35}

So, -3\frac{2}{7}> -3\frac{4}{5}

 

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