4

5

÷

–

1

3

–

–

1

5

×

–

3

5

Let's solve the given expression step by step:

The expression can be interpreted as:

\[
\frac{4}{5} \div \left(-\frac{1}{3} - \left(-\frac{1}{5} \times -\frac{3}{5}\right)\right)
\]

### Step 1: Simplify the multiplication inside the parentheses.

\[
-\frac{1}{5} \times -\frac{3}{5} = \frac{3}{25}
\]

### Step 2: Simplify the subtraction.

\[
-\frac{1}{3} - \frac{3}{25}
\]

To subtract these, find a common denominator (75):

\[
-\frac{1}{3} = -\frac{25}{75}, \quad \frac{3}{25} = \frac{9}{75}
\]

Now, subtract:

\[
-\frac{25}{75} - \frac{9}{75} = -\frac{34}{75}
\]

### Step 3: Divide \(\frac{4}{5}\) by the result from Step 2.

Dividing by a fraction is the same as multiplying by its reciprocal:

\[
\frac{4}{5} \div -\frac{34}{75} = \frac{4}{5} \times -\frac{75}{34} = -\frac{4 \times 75}{5 \times 34} = -\frac{300}{170} = -\frac{30}{17}
\]

So, the final answer is:

\[
-\frac{30}{17}
\]

Would you like further details or have any questions?

Here are five related questions to expand on this concept:

1. How do you multiply fractions with negative signs?
2. What is the process for dividing by a fraction?
3. How can you simplify complex fraction operations?
4. Why is it necessary to find a common denominator when subtracting fractions?
5. How do you interpret division involving complex fractions?

**Tip:** When dividing by a fraction, remember to multiply by its reciprocal to simplify the operation effectively.

Learn how to solve the complex fraction operation involving division and subtraction of fractions. This problem covers key concepts such as fraction operations with negative fractions and division of fractions. Suitable for Grades 7-9.

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