Q 8.     Fill in the boxes with the correct symbol out of >, <, and =.

(i)     \frac{-5}{7} \square \frac{2}{3}                (ii)     \frac{-4}{5} \square \frac{-5}{7}               (iii)     \frac{-7}{8} \square \frac{14}{-16}           

(iv)     \frac{-8}{5} \square \frac{-7}{4}          (v)     \frac{1}{-3} \square \frac{-1}{4}                (vi)     \frac{5}{-11} \square \frac{-5}{11}

(vii)     0 \square \frac{-7}{6}    

Answers (1)

(i) \frac{-5}{7} \square \frac{2}{3} 

\Rightarrow \frac{-5\times3}{7\times 3}\square \frac{2\times7}{3\times7}

\Rightarrow \frac{-15}{21} < \frac{14}{21}

Hence, \frac{-5}{7} < \frac{2}{3}

 

(ii) \frac{-4}{5} \square \frac{-5}{7} 

\Rightarrow \frac{-4\times7}{5\times 7}\square \frac{-5\times5}{7\times5}

\Rightarrow \frac{-28}{35} < \frac{-25}{35}

Hence, \frac{-4}{5} < \frac{-5}{7}

 

(iii) \frac{-7}{8} \square \frac{14}{-16} 

\Rightarrow \frac{-7\times-16}{8\times -16}\square \frac{14\times8}{-16\times8}

\Rightarrow \frac{112}{-128} = \frac{112}{-128}

Hence, \frac{-7}{8} = \frac{14}{-16}

 

(iv) \frac{-8}{5} \square \frac{-7}{4} 

\Rightarrow \frac{-8\times4}{5\times 4}\square \frac{-7\times5}{4\times5}

\Rightarrow \frac{-32}{20} > \frac{-35}{20}

Hence, \frac{-8}{5} > \frac{-7}{4}

 

(v) \frac{1}{-3} \square \frac{-1}{4} 

\Rightarrow \frac{1\times4}{-3\times 4}\square \frac{-1\times-3}{4\times-3}

\Rightarrow \frac{4}{-12} < \frac{3}{-12}

Hence, \frac{1}{-3} < \frac{1}{-4}

 

(vi) \frac{5}{-11} \square \frac{-5}{11}

\Rightarrow \frac{5\times11}{-11\times 11}\square \frac{-5\times-11}{11\times-11}

\Rightarrow \frac{55}{-121} = \frac{55}{-121}

Hence, \frac{5}{-11} = \frac{-5}{11}

 

(viI)  0 \square \frac{-7}{6}

Zero is always greater than every negative number.

Therefore, 0 > \frac{-7}{6}

 

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