Question: Which expression could be used to determine the product of $-4$ and $3 \frac{1}{4}$?
1. **State the problem:** We need to find an expression to determine the product of $-4$ and $3 \frac{1}{4}$.
2. **Convert the mixed number to an improper fraction:**
$$3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{13}{4}$$
3. **Write the product expression:**
$$-4 \times 3 \frac{1}{4} = -4 \times \frac{13}{4}$$
4. **Rewrite $-4$ as a fraction:**
$$-4 = \frac{-4}{1}$$
5. **Multiply the fractions:**
$$\frac{-4}{1} \times \frac{13}{4} = \frac{-4 \times 13}{1 \times 4} = \frac{-52}{4}$$
6. **Simplify the fraction:**
$$\frac{-52}{4} = \frac{\cancel{-52}}{\cancel{4}} = -13$$
**Final answer:** The expression to determine the product is $$-4 \times \frac{13}{4}$$ and the product equals $$-13$$.