To solve \(-4 \frac{5}{11} - 2 \frac{4}{11}\), we first convert the mixed numbers into improper fractions.
-
Convert \(-4 \frac{5}{11}\) to an improper fraction:
\[
-4 \frac{5}{11} = -\left(4 \times 11 + 5\right)/11 = -\frac{44 + 5}{11} = -\frac{49}{11}
\]
-
Convert \(2 \frac{4}{11}\) to an improper fraction:
\[
2 \frac{4}{11} = \left(2 \times 11 + 4\right)/11 = \frac{22 + 4}{11} = \frac{26}{11}
\]
Now, we can perform the subtraction:
\[
-\frac{49}{11} - \frac{26}{11}
\]
Since the denominators are the same, we can combine the numerators:
\[
-\frac{49 + 26}{11} = -\frac{75}{11}
\]
Next, we convert \(-\frac{75}{11}\) back to a mixed number. Divide \(75\) by \(11\):
- \(11\) goes into \(75\) a total of \(6\) times, since \(11 \times 6 = 66\).
- The remainder is \(75 - 66 = 9\).
Thus,
\(-\frac{75}{11} = -6 \frac{9}{11}\).
So, the final answer is:
\[
-6 \frac{9}{11}
\]