The problem asks us to evaluate the expression $-\frac{8}{5} - (-2\frac{1}{4}) - \frac{1}{2}$.

1. Problem Description

The problem asks us to evaluate the expression $-\frac{8}{5} - (-2\frac{1}{4}) - \frac{1}{2}$.

2. Solution Steps

First, convert the mixed number $2\frac{1}{4}$ to an improper fraction:

$2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8+1}{4} = \frac{9}{4}$.

So, the expression becomes $-\frac{8}{5} - (-\frac{9}{4}) - \frac{1}{2}$.

Next, simplify the expression by removing the parentheses:

$-\frac{8}{5} + \frac{9}{4} - \frac{1}{2}$.

Now, we need to find a common denominator for the fractions. The least common multiple (LCM) of 5, 4, and 2 is

2

0. Convert each fraction to an equivalent fraction with a denominator of 20:

$-\frac{8}{5} = -\frac{8 \times 4}{5 \times 4} = -\frac{32}{20}$

$\frac{9}{4} = \frac{9 \times 5}{4 \times 5} = \frac{45}{20}$

$-\frac{1}{2} = -\frac{1 \times 10}{2 \times 10} = -\frac{10}{20}$

Substitute these equivalent fractions back into the expression:

$-\frac{32}{20} + \frac{45}{20} - \frac{10}{20}$

Now, combine the fractions:

$\frac{-32 + 45 - 10}{20} = \frac{13 - 10}{20} = \frac{3}{20}$

3. Final Answer

$\frac{3}{20}$