To find out how many sections of \( \frac{3}{4} \) foot can be cut from a board that is \( 3 \frac{1}{4} \) feet long, we first need to convert \( 3 \frac{1}{4} \) into an improper fraction.
- Convert \( 3 \frac{1}{4} \) to an improper fraction:
\[ 3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4} \]
- Now, we divide the length of the board by the length of each section:
\[ \text{Number of sections} = \frac{13/4}{3/4} \]
- Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \frac{13}{4} \div \frac{3}{4} = \frac{13}{4} \times \frac{4}{3} \]
- Simplifying this, we get:
\[ \frac{13 \times 4}{4 \times 3} = \frac{13}{3} \]
- Now, we need to find out how many whole sections we can cut, which is the whole number part of \( \frac{13}{3} \):
\[ \frac{13}{3} \approx 4.33 \]
Since George can only cut whole sections, he can cut 4 sections of \( \frac{3}{4} \) foot from the board.