The problem asks to find the greatest edge length of cubes that Safara could use to fill a rectangular prism with given edge lengths of $3\frac{1}{2} \, \text{ft}, 2\frac{1}{4} \, \text{ft}, \text{and} 4\frac{1}{3} \, \text{ft}$. The cubes must have edge lengths that are unit fractions.

Step-by-Step Solution:

1. Convert the mixed numbers into improper fractions:

   • $3\frac{1}{2}$ becomes $\frac{7}{2}$.
   • $2\frac{1}{4}$ becomes $\frac{9}{4}$.
   • $4\frac{1}{3}$ becomes $\frac{13}{3}$.

2. Find the greatest common divisor (GCD): To determine the largest cube that can completely fill the prism, we need to find the greatest common divisor of these fractions' denominators. To do this, we will:

   • Find the GCD of the denominators 2, 4, and 3, which is 1 (because they have no common factor larger than 1).

3. The greatest edge length of the cube: Since the GCD of the denominators is 1, the largest cube that can fill the prism without leaving gaps must have an edge length of $\frac{1}{12} \, \text{ft}$ (which is the least common multiple (LCM) of 2, 4, and 3 for the numerators to form unit cubes).

Thus, the greatest edge length of the cubes Safara could use is 1/12 feet.

Do you want further details or have any questions?

Here are 5 related questions:

1. How do you find the LCM of fractions in a general case?
2. How do you calculate the volume of a cube given its edge length?
3. Can you explain how cube volume relates to prism volume in this scenario?
4. What happens if the cube's edge length is not a unit fraction?
5. How do improper fractions help in simplifying such problems?

Tip: Always convert mixed numbers into improper fractions for easier calculation when comparing or simplifying.