Verify whether the given statement is true or false:
(i) $\left(\frac{5}{9} \div \frac{1}{3}\right) \div \frac{5}{2}=\frac{5}{9} \div\left(\frac{1}{3} \div \frac{5}{2}\right)$
(ii) $\left\{(-16) \div \frac{6}{5}\right\} \div \frac{-9}{10}=(-16) \div\left\{\frac{6}{5} \div \frac{-9}{10}\right\}$
(iii) $\left(\frac{-3}{5} \div \frac{-12}{35}\right) \div \frac{1}{14}=\frac{-3}{5} \div\left(\frac{-12}{35} \div \frac{1}{4}\right)$
(i) $\left(\frac{5}{9} \div \frac{1}{3}\right) \div \frac{5}{2}=\frac{5}{9} \div\left(\frac{1}{3} \div \frac{5}{2}\right)$
LHS
$\left(\frac{5}{9} \div \frac{1}{3}\right) \div \frac{5}{2}$
$=\left(\frac{5}{9} \times \frac{3}{1}\right) \times \frac{2}{5}$
$=\frac{5 \times 3 \times 2}{9 \times 1 \times 5}$
$=\frac{30}{45}$
$=\frac{2}{3}$
RHS
$\frac{5}{9} \div\left(\frac{1}{3} \div \frac{5}{2}\right)$
$=\frac{5}{9} \div\left(\frac{1}{3} \times \frac{2}{5}\right)$
$=\frac{5}{9} \div\left(\frac{2}{15}\right)$
$=\frac{5}{9} \times\left(\frac{15}{2}\right)=\frac{75}{18}$
$=\frac{25}{6}$
$\mathrm{LHS} \neq \mathrm{RHS}$
FALSE
(ii) $\left[(-16) \div \frac{6}{5}\right] \div \frac{-9}{10}=(-16) \div\left[\frac{6}{5} \div \frac{-9}{10}\right]$
LHS
$=\left[(-16) \div \frac{6}{5}\right] \div \frac{-9}{10}$
$=\left[(-16) \times \frac{5}{6}\right] \times \frac{10}{-9}$
$=\frac{(-16) \times 5 \times 10}{6 \times(-9)}$
$=\frac{800}{54}$
$=\frac{400}{27}$
RHS
$(-16) \div\left(\frac{6}{5} \div \frac{-9}{10}\right)$
$=(-16) \div\left(\frac{6}{5} \times \frac{10}{-9}\right)$
$=-16 \div\left\{\frac{-60}{45}\right\}$
$=-16 \times\left(\frac{-45}{60}\right)$
$=-16 \times\left(\frac{-3}{4}\right)$
$=\frac{48}{4}$
$=12$
LHS $\neq$ RHS
FALSE
(iii) $\left(\frac{-3}{5} \div \frac{-12}{35}\right) \div \frac{1}{14}=\frac{-3}{5} \div\left(\frac{-12}{35} \div \frac{1}{4}\right)$
LHS
$=\left(\frac{-3}{5} \times \frac{35}{-12}\right) \times 14$
$=\frac{(-3) \times 35 \times 14}{5 \times(-12)}$
$=\frac{1470}{60}$
$=\frac{49}{2}$
RHS
$=\frac{-3}{5} \div\left(\frac{-12}{35} \div \frac{1}{4}\right)$
$=\frac{-3}{5} \div\left(\frac{-12}{35} \times \frac{4}{1}\right)$
$=\frac{-3}{5} \div\left(\frac{-12 \times 4}{35}\right)$
$=\frac{-3}{5} \div\left(\frac{-48}{35}\right)$
$=\frac{-3}{5} \times \frac{35}{-48}$
$=\frac{3 \times 35}{5 \times 48}$
$=\frac{105}{240}$
$\mathrm{LHS} \neq \mathrm{RHS}$
FALSE