(i)
\(\frac{4}{9}\div\frac{-5}{12}\)
= \(\frac{4}{9}\times\frac{12}{-5}\)
= \(\frac{4\times12}{9\times-5}\)
= \(\frac{48}{-45}=\frac{48\times-1}{-45\times-1}=\frac{-48}{45}\)
In lowest terms,
\(\frac{-48}{45} = \frac{-48\div3}{45\div3} = \frac{-16}{15}\)
(ii)
\(-8\div\frac{-7}{16}\)
= \(\frac{-8}{1}\div\frac{-7}{16}\)
= \(\frac{-8}{1}\times\frac{16}{-7}\)
= \(\frac{-8\times16}{1\times-7}\)
= \(\frac{-128}{-7}= \frac{-128\times-1}{-7\times-1}=\frac{128}{7}\)
(iii)
\(\frac{-12}{7}\div-18\)
= \(\frac{-12}{7}\div\frac{-18}{1}\)
= \(\frac{-12}{7}\times\frac{1}{-18}\)
= \(\frac{-12\times1}{7\times-18}\)
= \(\frac{-12\times1}{7\times-18}\)
= \(\frac{-12}{-126}=\frac{-12\times-1}{-126\times-1}=\frac{12}{126}\)
In lowest terms,
\(\frac{12}{126}=\frac{12\div6}{126\div6}=\frac{2}{21}\)
(iv)
\(\frac{-1}{10}\div\frac{-8}{5}\)
= \(\frac{-1}{10}\times\frac{5}{8}\)
= \(\frac{-1\times5}{10\times-8}\)
= \(\frac{-5}{-80}= \frac{-5\times-1}{-80\times-1}=\frac{5}{80}\)
In lowest terms,
\(\frac{5}{80}=\frac{5\div5}{80\div5}=\frac{1}{16}\)
(v)
\(\frac{-16}{35}\div\frac{-15}{14}\)
= \(\frac{-16}{35}\times\frac{14}{-15}\)
= \(\frac{-224}{-525}= \frac{-224\times-1}{-525\times-1}= \frac{224}{525}\)
In lowest terms,
\(\)\(\frac{224}{525}=\frac{224\div7}{525\div7} =\frac{32}{75}\)
(vi)
\(\frac{-65}{14}\div\frac{13}{7}\)
= \(\frac{-65}{14}\times\frac{7}{13}\)
= \(\frac{-65\times7}{14\times13}\)
= \(\frac{-455}{182}= \frac{-455\times-1}{182\times-1}= \frac{-455}{182}\)
In lowest terms,
\(\frac{-455}{182}= \frac{-455\div7}{182\div7}= \frac{-65}{26}\)
Further,
\(\frac{-65}{182}= \frac{-65\div13}{26\div13}= \frac{-5}{2}\)
