Let's break down the expression step by step:

$-1 \frac{1}{2} + \frac{-1}{-2} - \left( \frac{-3}{5} \right)$

Step 1: Convert mixed number to an improper fraction

Convert $-1 \frac{1}{2}$ to an improper fraction: $-1 \frac{1}{2} = -\frac{3}{2}$

Step 2: Simplify the second term

$\frac{-1}{-2}$ simplifies to: $\frac{1}{2}$

Step 3: Remove the negative sign in the third term

$-\left(\frac{-3}{5}\right)$ becomes: $\frac{3}{5}$

Step 4: Add all the fractions

Now the expression becomes: $-\frac{3}{2} + \frac{1}{2} + \frac{3}{5}$

Step 5: Combine $-\frac{3}{2}$ and $\frac{1}{2}$

$-\frac{3}{2} + \frac{1}{2} = -\frac{2}{2} = -1$

Step 6: Add $-1$ and $\frac{3}{5}$

$-1 + \frac{3}{5}$ To combine these, convert $-1$ to a fraction with a denominator of 5: $-1 = -\frac{5}{5}$

Now, add the fractions: $-\frac{5}{5} + \frac{3}{5} = \frac{-5 + 3}{5} = \frac{-2}{5}$

Final Answer:

$-1 \frac{1}{2} + \frac{-1}{-2} - \left( \frac{-3}{5} \right) = -\frac{2}{5}$

Would you like more details on any of these steps?

Here are 5 related questions for further practice:

1. What is the result of $-2 \frac{1}{4} + \frac{-3}{6} - \left(\frac{-4}{7}\right)$?
2. How do you convert a mixed number to an improper fraction?
3. What happens when both numerator and denominator are negative in a fraction?
4. How do you add fractions with different denominators?
5. How would you solve $2 \frac{3}{4} - 1 \frac{5}{6}$?

Tip: Always simplify negative signs before performing arithmetic with fractions to avoid confusion.