To solve \(-8 \frac{3}{4} + 4 \frac{3}{5}\), we need to convert the mixed numbers into improper fractions, then add them together.

1. Convert \(-8 \frac{3}{4}\) to an improper fraction:
   \[
   -8 \frac{3}{4} = -\left(\frac{8 \times 4 + 3}{4}\right) = -\frac{35}{4}
   \]

2. Convert \(4 \frac{3}{5}\) to an improper fraction:
   \[
   4 \frac{3}{5} = \frac{4 \times 5 + 3}{5} = \frac{23}{5}
   \]

3. Now add the fractions:
   \[
   -\frac{35}{4} + \frac{23}{5}
   \]

4. Find the least common denominator (LCD) of 4 and 5, which is 20. Convert both fractions to have a denominator of 20:
   \[
   -\frac{35}{4} = -\frac{175}{20}, \quad \frac{23}{5} = \frac{92}{20}
   \]

5. Now add the fractions:
   \[
   -\frac{175}{20} + \frac{92}{20} = \frac{-175 + 92}{20} = \frac{-83}{20}
   \]

6. The result is:
   \[
   \frac{-83}{20} \text{ or } -4 \frac{3}{20}
   \]

Thus, \(-8 \frac{3}{4} + 4 \frac{3}{5} = -4 \frac{3}{20}\).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you subtract mixed numbers?
2. Can you add two negative mixed numbers?
3. How do you simplify improper fractions?
4. What is the method to find the least common denominator?
5. How do you convert a mixed number to an improper fraction?

**Tip:** Always simplify fractions when possible to get the final answer in its simplest form.

Learn how to add mixed numbers like -8 3/4 and 4 3/5 with a step-by-step guide. This detailed solution covers key concepts such as converting mixed numbers to improper fractions, finding the least common denominator, and performing the addition. Suitable for Grades 5-7.

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