To find out how many sections George can cut from the board, we need to divide the length of the board by the length of each section.
The length of the board is \(3 + \frac{1}{4}\) feet, which can be converted to an improper fraction:
\[ 3 + \frac{1}{4} = \frac{12}{4} + \frac{1}{4} = \frac{13}{4} \text{ feet} \]
The length of each section is \(\frac{3}{4}\) foot.
Now, we perform the division:
\[ \text{Number of sections} = \frac{\text{Length of board}}{\text{Length of each section}} = \frac{\frac{13}{4}}{\frac{3}{4}} \]
When dividing fractions, we can multiply by the reciprocal:
\[ \frac{13}{4} \div \frac{3}{4} = \frac{13}{4} \times \frac{4}{3} = \frac{13 \times 4}{4 \times 3} = \frac{13}{3} \]
Now, we can convert \(\frac{13}{3}\) into a mixed number:
\[ \frac{13}{3} = 4 \frac{1}{3} \]
This means George can cut out 4 full sections of \(\frac{3}{4}\) foot, with \(\frac{1}{3}\) of a section remaining.
Thus, George can cut 4 sections from the board.
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