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.

Learn how to solve the expression -1 1/2 + -1/-2 - -3/5 by converting mixed numbers to improper fractions, simplifying signs, and adding fractions. This step-by-step guide covers key concepts in fraction arithmetic, suitable for students in Grades 6-8.

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