Add two fractions with different denominators, one negative.

1. Identify the problem: The problem is to add two fractions, $-\frac{7}{8}$ and $\frac{1}{4}$.
2. Find a common denominator: To add fractions, they must have the same denominator. The denominators are 8 and 4. The least common multiple (LCM) of 8 and 4 is 8.
3. Convert the second fraction: Convert $\frac{1}{4}$ to an equivalent fraction with a denominator of 8. To do this, multiply both the numerator and the denominator by 2:
$$ \frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8} $$
4. Add the fractions: Now that both fractions have the same denominator, add their numerators:
$$ -\frac{7}{8} + \frac{2}{8} = \frac{-7 + 2}{8} $$
5. Calculate the sum:
$$ \frac{-5}{8} $$
6. Simplify the answer: The fraction $-\frac{5}{8}$ is already in its simplest form because 5 and 8 have no common factors other than 1.