Performed the indicated operation and reduced to lowest terms.    [(-2/5)×(3/4)] ÷ (-4/5) and type an integer or a simplified fraction

Let's perform the indicated operation step by step and reduce it to the lowest terms.

We have the expression:

\[
\left(\frac{-2}{5} \times \frac{3}{4}\right) \div \frac{-4}{5}
\]

### Step 1: Multiply the fractions
First, multiply \(\frac{-2}{5}\) and \(\frac{3}{4}\):

\[
\frac{-2}{5} \times \frac{3}{4} = \frac{-2 \times 3}{5 \times 4} = \frac{-6}{20}
\]

### Step 2: Simplify the fraction
Simplify \(\frac{-6}{20}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

\[
\frac{-6}{20} = \frac{-6 \div 2}{20 \div 2} = \frac{-3}{10}
\]

### Step 3: Divide by the second fraction
Now, divide \(\frac{-3}{10}\) by \(\frac{-4}{5}\). Dividing by a fraction is the same as multiplying by its reciprocal:

\[
\frac{-3}{10} \div \frac{-4}{5} = \frac{-3}{10} \times \frac{5}{-4}
\]

### Step 4: Multiply the fractions
Multiply \(\frac{-3}{10}\) by \(\frac{5}{-4}\):

\[
\frac{-3}{10} \times \frac{5}{-4} = \frac{-3 \times 5}{10 \times -4} = \frac{-15}{-40}
\]

### Step 5: Simplify the fraction
The fraction \(\frac{-15}{-40}\) simplifies because the negatives cancel each other out:

\[
\frac{-15}{-40} = \frac{15}{40}
\]

Finally, simplify \(\frac{15}{40}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 5:

\[
\frac{15}{40} = \frac{15 \div 5}{40 \div 5} = \frac{3}{8}
\]

So, the simplified result is:

\[
\boxed{\frac{3}{8}}
\]

Would you like more details or have any questions? 

Here are 5 related questions:

1. How do you multiply two fractions with different signs?
2. How do you divide one fraction by another?
3. What are the steps to simplify a fraction?
4. Can you explain how to find the greatest common divisor of two numbers?
5. What happens when you multiply or divide fractions with negative numerators and denominators?

**Tip:** When dividing fractions, always remember to multiply by the reciprocal of the second fraction.

Learn how to simplify and divide fractions step-by-step with a detailed solution. This problem involves multiplying fractions with different signs, dividing fractions by multiplying their reciprocal, and simplifying fractions using the greatest common divisor method. Suitable for students in Grades 6-8.

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