To determine how many whole boards Andre can cut from a piece of wood that is \( 10 \frac{1}{4} \) yards long when each board needs to be \( \frac{4}{5} \) yard, we can follow these steps:
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Convert \( 10 \frac{1}{4} \) yards to an improper fraction: \[ 10 \frac{1}{4} = 10 + \frac{1}{4} = \frac{40}{4} + \frac{1}{4} = \frac{41}{4} \text{ yards} \]
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Find out how many \( \frac{4}{5} \) yard boards can be cut from \( \frac{41}{4} \) yards. To do this, we divide \( \frac{41}{4} \) by \( \frac{4}{5} \): \[ \text{Number of boards} = \frac{\frac{41}{4}}{\frac{4}{5}} = \frac{41}{4} \times \frac{5}{4} = \frac{41 \times 5}{4 \times 4} = \frac{205}{16} \]
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Now we convert \( \frac{205}{16} \) to a mixed number to find the whole boards: \[ 205 \div 16 = 12 \quad \text{(whole number part)} \] The remainder when dividing is: \[ 205 - (16 \times 12) = 205 - 192 = 13 \] Thus, \[ \frac{205}{16} = 12 \frac{13}{16} \]
Therefore, Andre can cut 12 whole boards from the \( 10 \frac{1}{4} \) yard piece of wood.
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