To determine how many sections of 3/4 foot long can be cut from a board that is 3 and 1/4 feet long, we first convert the length of the board into an improper fraction.
3 and 1/4 feet can be converted as follows: \[ 3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4} \text{ feet} \]
Now, we divide the total length of the board by the length of each section: \[ \text{Number of sections} = \frac{\frac{13}{4}}{\frac{3}{4}} \]
To divide by a fraction, we multiply by its reciprocal: \[ \text{Number of sections} = \frac{13}{4} \times \frac{4}{3} \]
The 4 in the numerator and denominator cancel out: \[ = \frac{13}{3} \]
Now we convert \(\frac{13}{3}\) into a mixed number: \[ \frac{13}{3} = 4 \frac{1}{3} \]
This means that George can cut out 4 full sections of 3/4 foot, with a remainder that is not enough for another full section.
Thus, the answer is: 4 sections.
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