To find the quotient of -27.374 divided by 7.5, you perform the division:
\[ \text{Quotient} = \frac{-27.374}{7.5} \]
Calculating this gives:
\[ \text{Quotient} \approx -3.64986667 \]
Rounding this value to two decimal places gives approximately -3.65.
Therefore, the answer is:
\(-3.65\)