To solve and explain the expression $-\frac{1}{5} + \frac{1}{2}$:

Step 1: Find a common denominator

The denominators of the fractions are 5 and 2. The least common denominator (LCD) is 10.

Step 2: Rewrite the fractions

Convert each fraction so they have the same denominator:

$-\frac{1}{5} = -\frac{2}{10}, \quad \frac{1}{2} = \frac{5}{10}$

Step 3: Add the fractions

Now, add the numerators while keeping the denominator the same:

$-\frac{2}{10} + \frac{5}{10} = \frac{-2 + 5}{10} = \frac{3}{10}$

Step 4: Simplify if possible

The fraction $\frac{3}{10}$ is already in its simplest form.

Final Answer:

$-\frac{1}{5} + \frac{1}{2} = \frac{3}{10}$

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Related Questions:

1. How do you determine the least common denominator for fractions?
2. Why is it necessary to rewrite fractions with a common denominator before adding?
3. How do you handle subtraction of fractions like $-\frac{1}{5} - \frac{1}{2}$?
4. What are some practical applications of adding fractions?
5. How can mixed numbers be added or subtracted?

Tip:

Always simplify fractions as a final step to ensure your answer is in its simplest form!