Question: Evaluate $x + y$ when $x = -\frac{4}{5}$ and $y = \frac{1}{3}$. Write your answer as a fraction or mixed number in simplest form.
1. **State the problem:** We need to find the value of the expression $x + y$ given $x = -\frac{4}{5}$ and $y = \frac{1}{3}$.
2. **Write the expression:**
$$x + y = -\frac{4}{5} + \frac{1}{3}$$
3. **Find a common denominator:**
The denominators are $5$ and $3$. The least common denominator (LCD) is $15$.
4. **Rewrite each fraction with denominator $15$:
$$-\frac{4}{5} = -\frac{4 \times 3}{5 \times 3} = -\frac{12}{15}$$
$$\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}$$
5. **Add the fractions:**
$$-\frac{12}{15} + \frac{5}{15} = \frac{-12 + 5}{15} = \frac{-7}{15}$$
6. **Simplify the fraction:**
The fraction $\frac{-7}{15}$ is already in simplest form because $7$ and $15$ have no common factors other than $1$.
7. **Final answer:**
$$x + y = -\frac{7}{15}$$