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The problem presented is:

\[
\frac{3 \frac{4}{5}}{-1 \frac{1}{10}} \, \text{(What is \( 3 \frac{4}{5} \div -1 \frac{1}{10} \)? Write the answer as a mixed number.)}
\]

Let's break this down:

1. Convert the mixed numbers into improper fractions:
   - \( 3 \frac{4}{5} = \frac{19}{5} \)
   - \( -1 \frac{1}{10} = -\frac{11}{10} \)

2. To divide fractions, multiply by the reciprocal:
   \[
   \frac{19}{5} \div -\frac{11}{10} = \frac{19}{5} \times -\frac{10}{11} = -\frac{19 \times 10}{5 \times 11} = -\frac{190}{55}
   \]

3. Simplify the fraction:
   \[
   \frac{190}{55} = \frac{38}{11} \, \text{(since 5 is a common divisor)}
   \]

4. Now convert the improper fraction \( \frac{38}{11} \) into a mixed number:
   - \( 38 \div 11 = 3 \) remainder \( 5 \), so:
   \[
   \frac{38}{11} = 3 \frac{5}{11}
   \]

Thus, the answer is:

\[
-3 \frac{5}{11}
\]

Would you like more details on any of the steps or further clarification? Here are some related questions you could explore:

1. How do you convert a mixed number to an improper fraction?
2. What is the reciprocal of a fraction, and how do you use it in division?
3. How do you simplify fractions?
4. How do you convert an improper fraction to a mixed number?
5. What are the steps for dividing two mixed numbers?

**Tip:** Always simplify the fractions as much as possible to ensure the answer is in its simplest form.

What is 3 4/5 ÷ (-1 1/10)? Write the answer as a mixed number in simplest form.

Learn how to solve the division of mixed numbers: 3 4/5 ÷ (-1 1/10). Convert the mixed numbers to improper fractions, apply the reciprocal, and simplify to get the final answer in mixed number form. This problem is ideal for students in Grades 6-8.

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