1. **State the problem:** We need to verify the unit conversion and multiplication steps in the equation converting salt and aluminum quantities to HF production per year. 2. **Given equation:** $$\frac{100\ \text{lb SALT}}{\text{Ton Al}} \times \frac{42000\ \text{tons Al}}{\text{YEAR}} \times \frac{2.32\ \text{lb HF}}{100\ \text{lb SALT}} \times \frac{8760\ \text{hours}}{\text{YEAR}} = 11.12\ \text{lb HF/hour}$$ 3. **Check units and simplification:** - Cancel lb SALT: $100\ \text{lb SALT}$ in numerator and denominator. - Cancel tons Al: $\text{Ton Al}$ and $42000\ \text{tons Al}$. - Cancel YEAR in numerator and denominator. 4. **Simplify numeric part:** $$100 \times 42000 \times \frac{2.32}{100} \times 8760 = 42000 \times 2.32 \times 8760$$ 5. **Calculate intermediate multiplication:** $$42000 \times 2.32 = 97440$$ 6. **Multiply by 8760 hours:** $$97440 \times 8760 = 853094400$$ 7. **Check the units:** The result is in lb HF per year, but the equation states lb HF per hour, so divide by hours per year: $$\frac{853094400}{8760} = 97440\ \text{lb HF/hour}$$ This contradicts the given 11.12 lb HF/hour, so the original equation seems inconsistent. 8. **Check the second line:** $$11.12\ \text{lb HF/hour} \times 4.38 = 48.7\ \text{tons HF/year}$$ Convert 48.7 tons to lb: $$48.7 \times 2000 = 97400\ \text{lb/year}$$ Convert 11.12 lb/hour to lb/year: $$11.12 \times 8760 = 97411.2\ \text{lb/year}$$ Multiply by 4.38: $$11.12 \times 4.38 = 48.7\ \text{tons/year}$$ This part is consistent. **Final conclusion:** The first equation's unit conversion and numeric values do not match the stated 11.12 lb HF/hour, but the second multiplication is correct.