#### Answer

$-\dfrac{9}{10}
$

#### Work Step by Step

Use the rule $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$.
Note that the product and quotient of two numbers with different signs is negative.
$\require{cancel}
=\dfrac{4}{5} \times \left(-\dfrac{9}{8}\right)
\\=\dfrac{\cancel{4}}{5} \times \left(-\dfrac{9}{\cancel{8}^2}\right)
\\=-\dfrac{1(9)}{5(2)}
\\=-\dfrac{9}{10}
$