To divide 11 by -4, we start by performing the division:
\[ 11 \div -4 = -\frac{11}{4} \]
Next, we convert \(-\frac{11}{4}\) into a mixed number. To do this, we divide 11 by 4:
\[ 11 \div 4 = 2 \quad \text{(whole number part)} \]
Calculating the remainder:
\[ 11 - (4 \times 2) = 11 - 8 = 3 \quad \text{(remainder)} \]
Thus, we can express \(-\frac{11}{4}\) as a mixed number:
\[ -\frac{11}{4} = -2 \frac{3}{4} \]
Therefore, the answer is:
\[ -2 \frac{3}{4} \]