To determine how many \( \frac{5}{16} \)-foot pieces of wood can be cut from a board that is \( 1 \frac{9}{16} \) feet long, we first need to convert \( 1 \frac{9}{16} \) into an improper fraction.
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Convert \( 1 \frac{9}{16} \): \[ 1 \frac{9}{16} = \frac{16}{16} + \frac{9}{16} = \frac{25}{16} \]
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Now divide the total length by the length of each piece: \[ \text{Number of pieces} = \frac{\frac{25}{16}}{\frac{5}{16}} = \frac{25}{16} \times \frac{16}{5} \]
The \( \frac{16}{16} \) cancels out: \[ \frac{25}{5} = 5 \]
Thus, you can cut 5 pieces of wood that are \( \frac{5}{16} \) feet each from a board that is \( 1 \frac{9}{16} \) feet long.
The correct answer is: C. 5 pieces of wood