(i)
\(\frac{25}{8}\div\text{x}=-10\)
\(\Rightarrow\) \(\text{x}=\frac{25}{8}\div-10\)
\(\Rightarrow\) \(\text{x}=\frac{25}{8}\times\frac{1}{-10}\)
\(\Rightarrow\) \(\text{x}=\frac{25\times1}{8\times-10}\)
\(\Rightarrow\) \(\text{x}=\frac{25}{-80}=\frac{25\times-1}{-80\times-1}=\frac{-25}{80}\)
\(\Rightarrow\) \(\text{x}=\frac{-25}{80}=\frac{-25\div5}{80\div5}=\frac{-5}{16}\)
(ii)
\(\frac{-8}{9}\times\text{x}=\frac{-2}{3}\)
\(\Rightarrow\) \(\text{x}=\frac{-2}{3}\div\frac{-8}{9}\)
\(\Rightarrow\) \(\text{x}=\frac{-2}{3}\times\frac{9}{-8}\)
\(\Rightarrow\) \(\text{x}=\frac{-2\times-9}{3\times-8}\)
\(\Rightarrow\) \(\text{x}=\frac{-18}{-24}=\frac{-18\times-1}{-24\times-1}=\frac{18}{24}\)
\(\Rightarrow\) \(\text{x}=\frac{18}{24}=\frac{18\div6}{24\div6}=\frac{3}{4}\)
(iii)
\(-1+\text{x}=\frac{-2}{9}\)
\(\Rightarrow\) \(\text{x}=\frac{-2}{9}-(-1)\)
\(\Rightarrow\) \(\text{x}=\frac{-2\times1-(-1)\times9}{9}\)
\(\Rightarrow\) \(\text{x}=\frac{-2+9}{9}\)
\(\Rightarrow\) \(\text{x}=\frac{7}{9}\)
(iv)
\(\frac{2}{3}-\text{x}=\frac{1}{15}\)
\(\Rightarrow\) \(\text{x}=\frac{2}{3}-\frac{1}{15}\)
\(\Rightarrow\) \(\text{x}=\frac{2\times5-1\times1}{15}\)
\(\Rightarrow\) \(\text{x}=\frac{10-1}{15}\)
\(\Rightarrow\) \(\text{x}=\frac{9}{15}=\frac{9\div3}{15\div3}=\frac{3}{5}\)
