Let's go through each problem one by one.

1. $6 + (-8) = -2$

2. $(-8) - 7 = -15$

3. $(-2) + 4 = 2$

4. $(-4) - 3 = -7$

5. $(-8) - 3 = -11$

6. $(-7) + (-8) = -15$

7. $3 \frac{1}{2} - 3 \frac{1}{6}$

   Convert mixed numbers to improper fractions: $3 \frac{1}{2} = \frac{7}{2} \quad \text{and} \quad 3 \frac{1}{6} = \frac{19}{6}$ Find a common denominator (6): $\frac{7}{2} = \frac{21}{6} \Rightarrow \frac{21}{6} - \frac{19}{6} = \frac{2}{6} = \frac{1}{3}$

8. $\left(-\frac{1}{4}\right) - \left(-\frac{3}{4}\right)$

   This becomes: $-\frac{1}{4} + \frac{3}{4} = \frac{2}{4} = \frac{1}{2}$

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

   Find a common denominator (28): $\frac{1}{7} = \frac{4}{28} \quad \text{and} \quad -\frac{7}{4} = -\frac{49}{28}$ $\frac{4}{28} - \frac{49}{28} = -\frac{45}{28}$

10. $1 \frac{3}{8} + \left(-\frac{7}{4}\right)$

    Convert the mixed number to an improper fraction: $1 \frac{3}{8} = \frac{11}{8}$ Convert $-\frac{7}{4}$ to a denominator of 8: $-\frac{7}{4} = -\frac{14}{8}$ $\frac{11}{8} - \frac{14}{8} = -\frac{3}{8}$

Let me know if you'd like further clarification on any of these solutions!

Here are five related questions to explore further:

1. What is the process for adding and subtracting negative numbers?
2. How do you convert mixed numbers to improper fractions?
3. What are some tips for finding a common denominator in fraction operations?
4. Why does subtracting a negative number result in addition?
5. How can visual aids like number lines help in understanding positive and negative numbers?

Tip: When working with fractions, always ensure the denominators are the same before adding or subtracting.