Verify whether the given statement is true or false:
(i) $\frac{13}{5} \div \frac{26}{10}=\frac{26}{10} \div \frac{13}{5}$
(ii) $-9 \div \frac{3}{4}=\frac{3}{4} \div(-9)$
(iii) $\frac{-8}{9} \div \frac{-4}{3}=\frac{-4}{3} \div \frac{-8}{9}$
(iv) $\frac{-7}{24} \div \frac{3}{-16}=\frac{3}{-16} \div \frac{-7}{24}$
(i) $\frac{13}{5} \div \frac{26}{10}=\frac{26}{10} \div \frac{13}{5}$
LHS
$\frac{13}{5} \div \frac{26}{10}$
$=\frac{13}{5} \times \frac{10}{26}$
$=\frac{130}{130}$
$=1$
RHS
$\frac{26}{10} \div \frac{13}{5}$
$=\frac{26}{10} \times \frac{5}{13}$
$=\frac{130}{130}$
$=1$
TRUE
(ii) $-9 \div \frac{3}{4}=\frac{3}{4} \div(-9)$
LHS
$-9 \div \frac{3}{4}$
$=-9 \times \frac{4}{3}$
$=\frac{-36}{3}$
$=-12$
RHS
$\frac{3}{4} \div(-9)$
$=\frac{3}{4} \times \frac{1}{-9}$
$=\frac{3}{-36}$
$=\frac{-1}{12}$
FALSE
(iii) $\frac{-8}{9} \div \frac{-4}{3}=\frac{-4}{3} \div \frac{-8}{9}$
LHS
$\frac{-8}{9} \div \frac{-4}{3}$
$=\frac{-8}{9} \times \frac{3}{-4}$
$=\frac{24}{36}$
$=\frac{2}{3}$
RHS
$\frac{-4}{3} \div \frac{-8}{9}$
$=\frac{-4}{3} \times \frac{9}{-8}$
$=\frac{36}{24}$
$=\frac{3}{2}$
FALSE
(iv) $\frac{-7}{24} \div \frac{3}{-16}=\frac{3}{-16} \div \frac{-7}{24}$
LHS
$\frac{-7}{24} \times \frac{-16}{3}$
$=\frac{112}{72}$
RHS
$\frac{3}{-16} \div \frac{-7}{24}$
$=\frac{3}{-16} \times \frac{24}{-7}$
$=\frac{72}{112}$
FALSE