The question asks for the following:

1. Expressions with the value $-\frac{3}{4}$:
   • A sum
   • A difference
   • A product
   • A quotient
   • One with at least two operations

Solutions:

1. Sum:
   $-\frac{1}{2} + (-\frac{1}{4})$
   $-\frac{1}{2} = -\frac{2}{4}$, so $-\frac{2}{4} + (-\frac{1}{4}) = -\frac{3}{4}$.

2. Difference:
   $-1 + \frac{1}{4}$
   $-1 = -\frac{4}{4}$, so $-\frac{4}{4} + \frac{1}{4} = -\frac{3}{4}$.

3. Product:
   $-\frac{3}{1} \cdot \frac{1}{4}$
   $-\frac{3}{1} \times \frac{1}{4} = -\frac{3}{4}$.

4. Quotient:
   $-\frac{3}{2} \div 2$
   $-\frac{3}{2} \div 2 = -\frac{3}{2} \times \frac{1}{2} = -\frac{3}{4}$.

5. Two operations:
   $-1 + \frac{1}{2} - \frac{1}{4}$
   $-1 = -\frac{4}{4}$, so
   $-\frac{4}{4} + \frac{2}{4} - \frac{1}{4} = -\frac{3}{4}$.

Would you like additional clarifications or step-by-step explanations?

5 Questions to Explore Further:

1. How can you represent $-\frac{3}{4}$ using fractions with different denominators?
2. What are the properties of operations involving negative fractions?
3. Can you create an equation where the solution is $-\frac{3}{4}$?
4. What happens when you multiply $-\frac{3}{4}$ by another fraction?
5. How does the concept of mixed numbers relate to these operations?

Tip:

Always simplify fractions in intermediate steps to avoid errors in operations!