To solve \(-1 \frac{1}{3} - 1 \frac{2}{3}\), we first convert the mixed numbers to improper fractions.

\[
-1 \frac{1}{3} = -\left( \frac{3}{3} + \frac{1}{3} \right) = -\frac{4}{3}
\]

\[
1 \frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3}
\]

Now, subtract:

\[
- \frac{4}{3} - \frac{5}{3} = -\frac{4+5}{3} = -\frac{9}{3} = -3
\]

Thus, the solution is:

\[
\boxed{-3}
\]

Would you like more details on any step?

Here are some related questions you can explore:
1. How do you add and subtract mixed numbers?
2. What are improper fractions, and how do you convert them back to mixed numbers?
3. How do you simplify fractions after subtraction?
4. What happens when both numbers are negative in subtraction?
5. How does subtraction work with decimals instead of fractions?

**Tip**: When subtracting fractions, always ensure they have the same denominator for easy calculations!

Learn how to solve the subtraction of mixed numbers -1 1/3 - 1 2/3 by converting them to improper fractions. This solution covers the concepts of mixed number conversion, subtraction of fractions, and simplification. Ideal for students in Grades 5-7.

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