# 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)     $0 \square \frac{-7}{6}$

(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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