To solve the expression:

\[
-1\dfrac{1}{3} \div 2\dfrac{2}{5}
\]

### Step 1: Convert the mixed numbers to improper fractions.

1. Convert \(-1\dfrac{1}{3}\):
   \[
   -1\dfrac{1}{3} = -\left(\frac{3 \times 1 + 1}{3}\right) = -\frac{4}{3}
   \]

2. Convert \(2\dfrac{2}{5}\):
   \[
   2\dfrac{2}{5} = \frac{5 \times 2 + 2}{5} = \frac{12}{5}
   \]

### Step 2: Rewrite the division as multiplication by the reciprocal.

The expression becomes:
\[
-\frac{4}{3} \div \frac{12}{5} = -\frac{4}{3} \times \frac{5}{12}
\]

### Step 3: Multiply the fractions.

Multiply the numerators and denominators:
\[
-\frac{4 \times 5}{3 \times 12} = -\frac{20}{36}
\]

### Step 4: Simplify the fraction.

Simplify \(\frac{20}{36}\) by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 4:
\[
-\frac{20 \div 4}{36 \div 4} = -\frac{5}{9}
\]

Thus, the solution is:

\[
-\frac{5}{9}
\]

Would you like more details on any of the steps? Here are some related questions:

1. How do you find the reciprocal of a fraction?
2. How do you simplify fractions after multiplying?
3. What is the process for converting mixed numbers to improper fractions?
4. How do you divide fractions without converting to decimals?
5. What is the greatest common divisor (GCD), and how do you find it?

**Tip**: Always simplify fractions after any multiplication or division for the cleanest result.

Learn how to solve the division of mixed numbers: -1 1/3 ÷ 2 2/5. This problem demonstrates how to convert mixed numbers to improper fractions, divide fractions, and simplify the result. Suitable for students in Grades 6-8.

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