The expression you're asking about involves dividing two fractions: \( \frac{2}{3} \) divided by \( -\frac{1}{1 \frac{1}{3}} \).

### Let's simplify step-by-step:

1. Convert \( -1 \frac{1}{3} \) into an improper fraction:
   \[
   -1 \frac{1}{3} = -\left( \frac{4}{3} \right)
   \]
2. Now, the expression becomes:
   \[
   \frac{2}{3} \div -\frac{4}{3}
   \]

3. Division of fractions means multiplying by the reciprocal. So, flip \( -\frac{4}{3} \) and multiply:
   \[
   \frac{2}{3} \times -\frac{3}{4}
   \]

4. Multiply the numerators and denominators:
   \[
   \frac{2 \times -3}{3 \times 4} = \frac{-6}{12}
   \]

5. Simplify the fraction:
   \[
   \frac{-6}{12} = -\frac{1}{2}
   \]

Thus, the result is:
\[
\boxed{-\frac{1}{2}}
\]

Would you like more details or have any questions?

Here are five related questions to extend this concept:
1. How do you divide fractions in general?
2. How do you convert mixed numbers to improper fractions?
3. How can you simplify fractions after multiplying?
4. What are the steps to handle negative numbers in fraction division?
5. Can you apply these steps to solve \(\frac{5}{6} \div \left(-2 \frac{1}{2}\right)\)?

**Tip:** Always remember that dividing by a fraction is the same as multiplying by its reciprocal!

Learn how to divide fractions with negative numbers, specifically solving the problem 2/3 divided by -1 1/3. This step-by-step guide explains the key concepts of fraction division, conversion of mixed numbers to improper fractions, and handling negative numbers. Perfect for students in Grades 5-7.

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