(i)
\(\frac{9}{8}\div\text{x}(let)=\frac{-3}{2}\)
\(\Rightarrow\) \(\text{x} =\frac{9}{8}\div\frac{-3}{2}\)
\(\Rightarrow\) \(\text{x} =\frac{9}{8}\times\frac{2}{-3}\)
\(\Rightarrow\) \(\text{x}=\frac{9\times2}{8\times-3}\)
\(\Rightarrow\) \(\text{x}= \frac{18}{-24}= \frac{18\times-1}{-24\times-1}=\frac{-18}{24}\)
\(\Rightarrow\) \(\text{x}= \frac{-18}{24}= \frac{-18\div6}{24\div6}=\frac{-3}{4}\)
Therefore,
\(\frac{9}{8}\div\frac{-3}{4}= \frac{-3}{2}\)
(ii)
\(\text{x}(let)\div\frac{-7}{5}=\frac{10}{19}\)
\(\Rightarrow\) \(\text{x}=\frac{10}{19}\times\frac{-7}{5}\)
\(\Rightarrow\) \(\text{x} = \frac{10\times-7}{19\times5}\)
\(\Rightarrow\) \(\text{x} = \frac{-70}{95}=\frac{-70\div5}{95\div5}= \frac{-14}{19}\)
Therefore,
\(\frac{-14}{19}\div\frac{-7}{5}=\frac{10}{19}\)
(iii)
\(\text{x}(let) \div(-3)=\frac{-4}{15}\)
\(\Rightarrow\) \(\text{x}= \frac{-4}{15}\times(-3)\)
\(\Rightarrow\) \(\text{x}= \frac{-4\times-3}{15\times1}\)
\(\Rightarrow\) \(\text{x}= \frac{12}{15}=\frac{12\div3}{15\div3}=\frac{4}{5}\)
Therefore,
\(\frac{4}{5}\div(-3)=\frac{-4}{15}\)
(iv)
\(-12\div\text{x}(let)= \frac{-6}{5}\)
\(\Rightarrow
\) \(\text{x}=-12\div\frac{-6}{5}\)
\(\Rightarrow
\) \(\text{x}= -12\times\frac{5}{-6}\)
\(\Rightarrow
\) \(\text{x}=\frac{-12\times5}{1\times-6}\)
\(\Rightarrow
\) \(\text{x}= \frac{-60}{-6}=\frac{-60\times-1}{-6\times-1}=\frac{60}{6}\)
\(\Rightarrow
\) \(\text{x} =\frac{60}{6}= \frac{60\div6}{6\div6}=10\)
Therefore,
\(-12\div10=\frac{-6}{5}\)
