Answer
$ad-bc=\dfrac{7}{72}$
Work Step by Step
Substituting $
a=-\dfrac{1}{3}
,$ $
b=\dfrac{1}{2}
,$ $
c=\dfrac{1}{4}
,$ $
d=-\dfrac{2}{3}
$ in the expression $ad-bc,$ then
\begin{align*}\require{cancel}
&
\left( -\dfrac{1}{3} \right)\left( -\dfrac{2}{3} \right)-\left( \dfrac{1}{2} \right)\left( \dfrac{1}{4} \right)
\\\\&=
\dfrac{2}{9}-\dfrac{1}{8}
\\\\&=
\dfrac{2}{9}\cdot\dfrac{8}{8}-\dfrac{1}{8}\cdot\dfrac{9}{9}
&\text{(change to similar fractions)}
\\\\&=
\dfrac{16}{72}-\dfrac{9}{72}
\\\\&=
\dfrac{7}{72}
.\end{align*}
Hence, $
ad-bc=\dfrac{7}{72}
$.
