1. **State the problem:** We need to find the volume of a rectangular prism with length $3 \frac{5}{8}$ inches, width $2 \frac{1}{2}$ inches, and height 4 inches. 2. **Formula for volume of a rectangular prism:** $$V = \text{length} \times \text{width} \times \text{height}$$ 3. **Convert mixed numbers to improper fractions:** - Length: $3 \frac{5}{8} = \frac{(3 \times 8) + 5}{8} = \frac{24 + 5}{8} = \frac{29}{8}$ - Width: $2 \frac{1}{2} = \frac{(2 \times 2) + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2}$ 4. **Calculate the volume:** $$V = \frac{29}{8} \times \frac{5}{2} \times 4$$ 5. **Simplify step-by-step:** First multiply $\frac{5}{2}$ and 4: $$\frac{5}{2} \times 4 = \frac{5}{2} \times \frac{4}{1} = \frac{5 \times 4}{2 \times 1} = \frac{20}{2}$$ Now simplify $\frac{20}{2}$: $$\frac{20}{2} = \cancel{\frac{20}{2}} = 10$$ 6. **Now multiply length by this result:** $$V = \frac{29}{8} \times 10 = \frac{29 \times 10}{8} = \frac{290}{8}$$ 7. **Simplify $\frac{290}{8}$ by dividing numerator and denominator by 2:** $$\frac{290}{8} = \frac{\cancel{290}145}{\cancel{8}4} = \frac{145}{4}$$ 8. **Convert $\frac{145}{4}$ to a mixed number:** Divide 145 by 4: $$145 \div 4 = 36 \text{ remainder } 1$$ So, $$\frac{145}{4} = 36 \frac{1}{4}$$ **Final answer:** The volume of the box is $36 \frac{1}{4}$ cubic inches.