To find the volume of a rectangular prism, you can use the formula:
\[ \text{Volume} = \text{length} \times \text{height} \times \text{width} \]
First, convert the mixed numbers to improper fractions:
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For the length \(4 \frac{2}{3}\): \[ 4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3} \]
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For the height \(3 \frac{1}{3}\): \[ 3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3} \]
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For the width \(2 \frac{1}{2}\): \[ 2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} \]
Now substituting these values into the volume formula:
\[ \text{Volume} = \frac{14}{3} \times \frac{10}{3} \times \frac{5}{2} \]
First, multiply the numerators:
\[ 14 \times 10 \times 5 = 700 \]
Then, multiply the denominators:
\[ 3 \times 3 \times 2 = 18 \]
Now combine these:
\[ \text{Volume} = \frac{700}{18} \]
Next, simplify the fraction. Both 700 and 18 can be divided by 2:
\[ \frac{700 \div 2}{18 \div 2} = \frac{350}{9} \]
Now convert \(\frac{350}{9}\) into a mixed number. Divide 350 by 9:
\[ 350 \div 9 = 38 \quad \text{(whole number)}, \quad \text{remainder} = 350 - (9 \times 38) = 350 - 342 = 8 \]
Thus, we can express \(\frac{350}{9}\) as:
\[ 38 \frac{8}{9} \]
Therefore, the volume of the rectangular prism is:
\[ \boxed{\frac{350}{9}} \text{ or } \boxed{38 \frac{8}{9}} \text{ ft}^3 \]