We are asked to evaluate the following expression: $-1\frac{4}{11} - \frac{1}{11} + 1\frac{9}{11} - 1\frac{5}{11}$.

1. Problem Description

We are asked to evaluate the following expression:

$-1\frac{4}{11} - \frac{1}{11} + 1\frac{9}{11} - 1\frac{5}{11}$.

2. Solution Steps

First, convert the mixed numbers to improper fractions.

$a \frac{b}{c} = \frac{ac+b}{c}$

$-1\frac{4}{11} = -\frac{11(1)+4}{11} = -\frac{15}{11}$

$1\frac{9}{11} = \frac{11(1)+9}{11} = \frac{20}{11}$

$1\frac{5}{11} = \frac{11(1)+5}{11} = \frac{16}{11}$

Now, substitute these into the expression:

$-\frac{15}{11} - \frac{1}{11} + \frac{20}{11} - \frac{16}{11}$

Combine the numerators, keeping the common denominator:

$\frac{-15 - 1 + 20 - 16}{11} = \frac{-16 + 20 - 16}{11} = \frac{4-16}{11} = \frac{-12}{11}$

Convert back to mixed number:

$-\frac{12}{11} = -1\frac{1}{11}$

3. Final Answer

$-1\frac{1}{11}$