The expression you provided is:

$\left(- \frac{1}{5}\right) + \frac{7}{4}$

To add these fractions, we need a common denominator. The least common denominator (LCD) of 5 and 4 is 20.

First, convert both fractions to have a denominator of 20:

$\left(- \frac{1}{5}\right) = -\frac{4}{20}$ $\frac{7}{4} = \frac{35}{20}$

Now, add the two fractions:

$-\frac{4}{20} + \frac{35}{20} = \frac{-4 + 35}{20} = \frac{31}{20}$

So, the result is:

$\frac{31}{20} \quad \text{or} \quad 1 \frac{11}{20} \quad \text{(as a mixed number)}$

Would you like a further breakdown of the steps?

Here are some related questions for practice:

1. Simplify $\frac{3}{8} + \frac{5}{12}$.
2. What is $\frac{2}{3} - \frac{5}{6}$?
3. Solve $- \frac{7}{9} + \frac{11}{15}$.
4. What is $\frac{5}{6} - \frac{7}{12} + \frac{1}{4}$?
5. Find the sum $\frac{4}{9} + \frac{8}{15}$.

Tip: Always find the least common denominator when adding or subtracting fractions to simplify the process!