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Divide:
(i) 1 by $ \frac{1}{2} $
(ii) 5 by $ \frac{-5}{7} $
(iii) $ \frac{-3}{4} $ by $ \frac{9}{-16} $
(iv) $ \frac{-7}{8} $ by $ \frac{-21}{16} $
(v) $ \frac{7}{-4} $ by $ \frac{63}{64} $
(vi) 0 by $ \frac{-7}{5} $
(vii) $ \frac{-3}{4} $ by $ -6 $
(viii) $ \frac{2}{3} $ by $ \frac{-7}{12} $
(ix) -4 $ by $ \frac{-3}{5} $
(x) $ \frac{-3}{13} $ by $ \frac{-4}{65} $
To do:
We have to divide the given rational numbers.
Solution:
We know that,
$a \div b = a \times \frac{1}{b}$
Therefore,
(i) $1 \div \frac{1}{2} = 1 \times \frac{2}{1}$
$=2$
(ii) $5 \div \frac{-5}{7} = 5 \times \frac{7}{-5}$
$=-7$
(iii) $\frac{-3}{4} \div \frac{9}{-16} = \frac{-3}{4} \times \frac{-16}{9}$
$=\frac{-3\times(-16)}{4\times9}$
$=\frac{4}{3}$
(iv) $\frac{-7}{8} \div \frac{-21}{16} = \frac{-7}{8} \times \frac{16}{-21}$
$=\frac{-7\times16}{8\times(-21)}$
$=\frac{2}{3}$
(v) $\frac{7}{-4} \div \frac{63}{64} = \frac{7}{-4} \times \frac{64}{63}$
$=\frac{7\times64}{-4\times63}$
$=\frac{-16}{9}$
(vi) $0 \div \frac{-7}{5} = 0 \times \frac{5}{-7}$
$=\frac{0\times5}{-7}$
$=0$
(vii) $\frac{-3}{4} \div -6 = \frac{-3}{4} \times \frac{1}{-6}$
$=\frac{-3\times1}{4\times(-6)}$
$=\frac{1}{8}$
(viii) $\frac{2}{3} \div \frac{-7}{12} = \frac{2}{3} \times \frac{12}{-7}$
$=\frac{2\times12}{3\times(-7)}$
$=\frac{-8}{7}$
(ix) $-4 \div \frac{-3}{5} = -4 \times \frac{5}{-3}$
$=\frac{-4\times5}{-3}$
$=\frac{20}{3}$
(x) $\frac{-3}{13} \div \frac{-4}{65} = \frac{-3}{13} \times \frac{65}{-4}$
$=\frac{-3\times65}{13\times(-4)}$
$=\frac{15}{4}$