1. **Stating the problem:** We are given several unit rates and fractions involving pounds and quarts: - 1/4 pound - 1/32 pound per quart - 1/8 quart - 4 pounds per quart We want to understand and possibly relate these quantities. 2. **Understanding the units and relationships:** - Pounds (lb) measure weight. - Quarts (qt) measure volume. - "Pound per quart" is a density-like unit (weight per volume). 3. **Analyzing each given quantity:** - 1/4 pound is a weight. - 1/32 pound per quart means for every quart, the weight is 1/32 pound. - 1/8 quart is a volume. - 4 pounds per quart means for every quart, the weight is 4 pounds. 4. **Example calculation:** Suppose we want to find the weight corresponding to 1/8 quart using the density 4 pounds per quart. Using the formula: $$\text{Weight} = \text{Density} \times \text{Volume}$$ Substitute values: $$\text{Weight} = 4 \frac{\text{pounds}}{\text{quart}} \times \frac{1}{8} \text{quart} = \frac{4}{8} \text{pounds} = \frac{1}{2} \text{pound}$$ 5. **Summary:** - To find weight from volume and density, multiply density by volume. - Units must be consistent. Final answer for the example: The weight of 1/8 quart at 4 pounds per quart is $\frac{1}{2}$ pound.