To determine how many sections of \( \frac{3}{4} \) foot long can be cut from a board that is \( 3 \frac{1}{4} \) feet long, we first need to convert \( 3 \frac{1}{4} \) feet into an improper fraction.
-
Convert \( 3 \frac{1}{4} \) to an improper fraction: \[ 3 \frac{1}{4} = 3 + \frac{1}{4} = \frac{12}{4} + \frac{1}{4} = \frac{13}{4} \text{ feet} \]
-
Divide \( \frac{13}{4} \) feet by \( \frac{3}{4} \) feet to find the number of sections: \[ \frac{13}{4} \div \frac{3}{4} = \frac{13}{4} \times \frac{4}{3} = \frac{13 \times 4}{4 \times 3} = \frac{13}{3} \]
-
Calculate \( \frac{13}{3} \): \[ \frac{13}{3} = 4 \frac{1}{3} \]
Since George can only cut whole sections from the board, he can cut a total of 4 sections of \( \frac{3}{4} \) foot each from the \( 3 \frac{1}{4} \) foot board.
Thus, the answer is 4 sections.