Multiply.
\[
-5 \frac{1}{2} \cdot 6 \frac{3}{4}
\]

Step 1 ：\(-5 \frac{1}{2} = -\frac{11}{2}\) because \(5 \times 2 + 1 = 11\)

Step 2 ：\(6 \frac{3}{4} = \frac{27}{4}\) because \(6 \times 4 + 3 = 27\)

Step 3 ：So, the problem becomes: \(-\frac{11}{2} \cdot \frac{27}{4}\)

Step 4 ：To multiply fractions, we multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together: \((-11 \times 27) / (2 \times 4) = -\frac{297}{8}\)

Step 5 ：To convert an improper fraction to a mixed number, we divide the numerator by the denominator: \(297 \div 8 = 37\) with a remainder of \(1\)

Step 6 ：So, the final answer is \(-37 \frac{1}{8}\)

Step 7 ：To check our work, we convert \(-37 \frac{1}{8}\) back into an improper fraction, we get \(-\frac{297}{8}\)

Step 8 ：\(\boxed{-37 \frac{1}{8}}\) is the final answer