leave the answer improper give your answer in simplest terms

We will take the common denominator and add the fractions.
The common denominator is the multiplication of the two denominators.
9 x 8 = 72
Now, multiplying the numerators with respective values, we find the answer. The process is shown below:
[tex]\begin{gathered} -\frac{4}{9}+\frac{-5}{8} \\ =\frac{-4(8)-5(9)}{72} \\ =\frac{-32-45}{72} \\ =-\frac{77}{72} \end{gathered}[/tex]The answer is:
[tex]-\frac{77}{72}[/tex]