To find the quotient of \(-\frac{3}{4}\) and \(\frac{2}{5}\), we divide \(-\frac{3}{4}\) by \(\frac{2}{5}\).

### Step-by-Step Solution:

1. **Rewrite the Division as Multiplication**:
   \[
   -\frac{3}{4} \div \frac{2}{5} = -\frac{3}{4} \times \frac{5}{2}
   \]

2. **Multiply the Fractions**:
   \[
   -\frac{3 \times 5}{4 \times 2} = -\frac{15}{8}
   \]

3. **Simplify if Possible**:
   The fraction \(-\frac{15}{8}\) is already in its simplest form.

### Answer:
The quotient of \(-\frac{3}{4}\) and \(\frac{2}{5}\) is \(-\frac{15}{8}\).

Would you like more details or have any questions?

Here are some related questions you might find helpful:
1. What is the reciprocal of a fraction, and how is it used in division?
2. How do you multiply and divide mixed numbers?
3. How can you convert improper fractions to mixed numbers?
4. What are some strategies for simplifying fractions?
5. How do you add and subtract fractions with different denominators?

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

Learn how to find the quotient of -3/4 and 2/5 by converting the division into multiplication. This problem covers key concepts of fractions, reciprocals, and multiplication, ideal for students in Grades 6-8.

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