Let's solve the given expression step by step:

The expression is: 

\[
2 \frac{2}{5} \times \left(-\frac{1}{3}\right) \div \frac{1}{9} \times (-1)
\]

### Step 1: Convert the mixed number to an improper fraction

The mixed number \(2 \frac{2}{5}\) can be converted to an improper fraction:

\[
2 \frac{2}{5} = \frac{10}{5} + \frac{2}{5} = \frac{12}{5}
\]

### Step 2: Rewrite the expression

Now, substitute the improper fraction into the expression:

\[
\frac{12}{5} \times \left(-\frac{1}{3}\right) \div \frac{1}{9} \times (-1)
\]

### Step 3: Simplify multiplication and division operations

First, multiply \(\frac{12}{5} \times \left(-\frac{1}{3}\right)\):

\[
\frac{12}{5} \times \left(-\frac{1}{3}\right) = -\frac{12 \times 1}{5 \times 3} = -\frac{12}{15}
\]

Simplify \(-\frac{12}{15}\):

\[
-\frac{12}{15} = -\frac{4}{5} \quad (\text{after dividing the numerator and the denominator by 3})
\]

Now, divide by \(\frac{1}{9}\):

\[
-\frac{4}{5} \div \frac{1}{9} = -\frac{4}{5} \times 9 = -\frac{4 \times 9}{5 \times 1} = -\frac{36}{5}
\]

### Step 4: Simplify multiplication with \(-1\)

Finally, multiply by \(-1\):

\[
-\frac{36}{5} \times (-1) = \frac{36}{5}
\]

So, the result is:

\[
\frac{36}{5} \text{ or } 7 \frac{1}{5}
\]

Would you like more details or have any questions about this solution? 

Here are some related questions to explore:

1. How do you convert a mixed number to an improper fraction?
2. What are the rules for multiplying and dividing fractions?
3. How do you simplify a fraction?
4. How does the order of operations affect solving this expression?
5. How do you handle negative signs in multiplication and division?

**Tip:** Always simplify fractions at each step to make calculations easier!

Learn how to solve the expression 2 2/5 x [-1/3] ÷ 1/9 x [-1] step by step. This problem covers fraction multiplication, division, and handling negative numbers, perfect for Grades 6-8 students.

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