Simplify:

Solution:

(i) $\frac{4}{9} \div \frac{-5}{12}$

$=\frac{4}{9} \times \frac{12}{-5}$

$=\frac{4 \times 12}{9 \times-5}$

$=\frac{48}{-45}$

$=\frac{-48}{45}$

$=\frac{-16}{15}$

(ii) $-8 \div \frac{-7}{16}$

$=-8 \times \frac{16}{-7}$

$=\frac{8 \times 16}{7}$

$=\frac{128}{7}$

(iii) $\frac{-12}{7} \div(-18)$

$=\frac{-12}{7} \times \frac{1}{-18}$

$=\frac{12}{126}$

$=\frac{12 \div 3}{126 \div 3}$

$=\frac{4}{42}$

$=\frac{4 \div 2}{42 \div 2}$

$=\frac{2}{21}$

(iv) $\frac{-1}{10} \div \frac{-8}{5}$

$=\frac{-1}{10} \times \frac{5}{-8}$

$=\frac{5}{80}$

$=\frac{5 \div 5}{80 \div 5}$

$=\frac{1}{16}$

(v) $\frac{-16}{35} \div \frac{-15}{14}$

$=\frac{-16}{35} \times \frac{14}{-15}$

$=\frac{224}{525}$

(vi) $\frac{-65}{14} \div \frac{13}{7}$

$=\frac{-65}{14} \times \frac{7}{13}$

$=\frac{-5}{2}$