To find the length of each of the 7 smaller boards cut from the original board, we first need to convert the length of the original board into an improper fraction and then divide it by 7.
The length of the original board is 9 and one-third feet, which can be converted as follows:
-
Convert 9 to an improper fraction: \[ 9 = \frac{9 \times 3}{3} = \frac{27}{3} \]
-
Add the one-third: \[ 9 \frac{1}{3} = \frac{27}{3} + \frac{1}{3} = \frac{28}{3} \]
Next, we divide the total length by 7 to find the length of each smaller board: \[ \text{Length of each board} = \frac{\frac{28}{3}}{7} \]
To divide by a number, we multiply by its reciprocal: \[ \text{Length of each board} = \frac{28}{3} \times \frac{1}{7} = \frac{28}{3 \times 7} = \frac{28}{21} \]
Now, simplify \(\frac{28}{21}\): \[ \frac{28}{21} = \frac{4}{3} \]
Thus, the length of each of the smaller boards is \( \frac{4}{3} \) feet.
Looking at the provided options, the correct answer is: Four-thirds \( \frac{4}{3} \).