To solve the expression $6 + (-4 \frac{3}{4}) + (-2 \frac{1}{8})$, follow these steps:

1. Convert mixed numbers to improper fractions:

   • $-4 \frac{3}{4} = -\frac{19}{4}$
   • $-2 \frac{1}{8} = -\frac{17}{8}$

2. Add $6$ as a fraction:

   • $6 = \frac{24}{4}$

3. Find a common denominator for all fractions:

   • The common denominator between 4 and 8 is 8.
   • $\frac{24}{4} = \frac{48}{8}$
   • $-\frac{19}{4} = -\frac{38}{8}$
   • $-\frac{17}{8}$ remains unchanged.

4. Add the fractions:

   • $\frac{48}{8} + (-\frac{38}{8}) + (-\frac{17}{8})$
   • $= \frac{48 - 38 - 17}{8} = \frac{-7}{8}$

Thus, the result is $-\frac{7}{8}$.

Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How do you convert mixed numbers to improper fractions?
2. What is the process to find a common denominator?
3. How would the process change if one of the numbers was positive?
4. Can you simplify negative fractions further?
5. How do you subtract fractions with unlike denominators?

Tip: Always convert mixed numbers to improper fractions before performing operations.