To solve the problem $-\frac{1}{2} + \frac{3}{5}$, we need to find a common denominator for the fractions.

Steps:

1. Find the Least Common Denominator (LCD): The denominators are $2$ and $5$. The LCD is $10$.

2. Rewrite the Fractions with the LCD: $-\frac{1}{2} = -\frac{5}{10}, \quad \frac{3}{5} = \frac{6}{10}.$

3. Add the Fractions: $-\frac{5}{10} + \frac{6}{10} = \frac{-5 + 6}{10} = \frac{1}{10}.$

Final Answer:

$\boxed{\frac{1}{10}}$

Would you like a further breakdown or a visual explanation?

Related Questions:

1. How do you find the least common denominator for fractions?
2. How does subtracting a fraction differ from adding one?
3. Can fractions always be simplified before adding or subtracting?
4. What happens when you add fractions with negative numbers?
5. How do improper fractions affect the addition or subtraction process?

Tip:

Always simplify fractions first if possible; it can make the arithmetic easier!