Answer
$-\dfrac{5}{12}$
Work Step by Step
The product of two numbers with opposite signs is negative. Furthermore, to multiply fractions, multiply the numerators and multiply the denominators. Then cancel any common factor between the numerator and the denominator. Hence, the product of the given expression, $
-\dfrac{5}{9}\cdot\dfrac{3}{4}
$, is
\begin{array}{l}\require{cancel}
-\dfrac{5(3)}{9(4)}
\\\\=
-\dfrac{15}{36}
\\\\=
-\dfrac{\cancel{3}\cdot5}{\cancel{3}\cdot12}
\\\\=
-\dfrac{5}{12}
.\end{array}
