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"The volume of a box is given by the product of its length, width, and height. Suppose the length of the box is $2 \frac{1}{2}$ feet, the width is $1 \frac{3}{4}$ feet, and the height is $1 \frac{1}{2}$ feet. Calculate the volume of the box in cubic feet."

Let's solve this step-by-step.

1. Convert the mixed numbers to improper fractions:

   • Length: $2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}$
   • Width: $1 \frac{3}{4} = 1 + \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{7}{4}$
   • Height: $1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}$

2. Use the formula for the volume of a box: $\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}$ Substitute the values: $\text{Volume} = \frac{5}{2} \times \frac{7}{4} \times \frac{3}{2}$

3. Multiply the fractions: $\text{Volume} = \frac{5 \times 7 \times 3}{2 \times 4 \times 2} = \frac{105}{16}$

4. Convert the improper fraction to a mixed number for the final answer: $\frac{105}{16} = 6 \frac{9}{16}$

So, the volume of the box is $6 \frac{9}{16}$ cubic feet.

Would you like any more details or explanations? Here are some related questions you might be interested in:

1. How do you convert a mixed number to an improper fraction?
2. What is the formula for the volume of a rectangular prism?
3. How do you multiply fractions?
4. What are the steps to simplify a fraction?
5. How do you convert an improper fraction to a mixed number?
6. What are some applications of calculating volume in real life?
7. How do you add or subtract mixed numbers?
8. What are the units of volume in the metric and imperial systems?

Tip: When converting mixed numbers to improper fractions, always multiply the whole number by the denominator and add the numerator for accuracy.