Let's solve the given expression step by step:

1. The expression provided can be interpreted as:

   \[
   \left( - \frac{1}{2} + \left( -\frac{4}{5} \times \left( -\frac{1}{4} - \left( -\frac{3}{4} \right) \right) \right) \right)
   \]

2. Simplify the innermost expression:

   \[
   -\frac{1}{4} - \left( -\frac{3}{4} \right) = -\frac{1}{4} + \frac{3}{4} = \frac{2}{4} = \frac{1}{2}
   \]

3. Now multiply by \(-\frac{4}{5}\):

   \[
   -\frac{4}{5} \times \frac{1}{2} = -\frac{4}{10} = -\frac{2}{5}
   \]

4. Add this to \(-\frac{1}{2}\):

   \[
   -\frac{1}{2} + \left( -\frac{2}{5} \right)
   \]

   To add these, find a common denominator (10):

   \[
   -\frac{5}{10} + \left( -\frac{4}{10} \right) = -\frac{9}{10}
   \]

So, the final answer is:

\[
-\frac{9}{10}
\]

Would you like further details or have any questions?

Here are five related questions to expand on this concept:

1. How do you find a common denominator when adding fractions?
2. What is the result of multiplying a fraction by a negative fraction?
3. How can you simplify a complex fraction expression?
4. How does subtraction of negative numbers work in a fraction context?
5. What are some strategies to solve nested fraction expressions?

**Tip:** Always simplify expressions step by step to avoid errors in complex calculations.

Learn how to simplify and solve a complex fraction expression involving negative numbers step-by-step. This problem covers operations with fractions, negative number arithmetic, and simplification techniques. Suitable for students in Grades 6-8.

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