Let's simplify the given expression step by step:

The expression is:

\[
- \frac{2}{5a} \left( -5 + \frac{1}{3a} - 4 \right)
\]

### Step 1: Simplify inside the parentheses.
\[
-5 + \frac{1}{3a} - 4 = -9 + \frac{1}{3a}
\]

### Step 2: Distribute \(- \frac{2}{5a}\) to each term inside the parentheses.
\[
- \frac{2}{5a} \times \left( -9 + \frac{1}{3a} \right) = - \frac{2}{5a} \times (-9) + - \frac{2}{5a} \times \frac{1}{3a}
\]

### Step 3: Multiply each term.
For the first term:
\[
- \frac{2}{5a} \times (-9) = \frac{18}{5a}
\]

For the second term:
\[
- \frac{2}{5a} \times \frac{1}{3a} = - \frac{2}{15a^2}
\]

### Step 4: Combine the results.
\[
\frac{18}{5a} - \frac{2}{15a^2}
\]

This is the simplified form of the expression:

\[
\frac{18}{5a} - \frac{2}{15a^2}
\]

Would you like any further details or clarifications?

Here are 5 related questions to expand on this concept:
1. How would the expression change if a different constant was added inside the parentheses?
2. Can you factor this expression further?
3. How would the result differ if \(a\) had a specific value?
4. What happens if \(a\) is negative in this expression?
5. Can you simplify other similar expressions with fractions?

**Tip:** When distributing fractions, always multiply both the numerator and denominator separately to avoid confusion.

Discover how to simplify the algebraic expression -2/5a(-5+1/3a -4) using distributive property and fraction multiplication. This step-by-step solution is ideal for high school students in Grades 9-10 learning algebraic simplification.

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