To find out how many whole boards of size \( \frac{4}{5} \) yard can be cut from a piece of wood that is \( 10 \frac{1}{4} \) yards long, we first need to convert \( 10 \frac{1}{4} \) into an improper fraction.
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Convert \( 10 \frac{1}{4} \) to an improper fraction: \[ 10 \frac{1}{4} = 10 \times 4 + 1 = 40 + 1 = 41 \text{ (the numerator)} \] Therefore: \[ 10 \frac{1}{4} = \frac{41}{4} \text{ yards} \]
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Now we need to divide the total length by the length of each board: \[ \text{Number of boards} = \frac{\frac{41}{4}}{\frac{4}{5}} \] Dividing by a fraction is the same as multiplying by its reciprocal: \[ \text{Number of boards} = \frac{41}{4} \times \frac{5}{4} = \frac{41 \times 5}{4 \times 4} = \frac{205}{16} \]
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Now calculate \( \frac{205}{16} \): To find the whole number of boards, we can divide \( 205 \) by \( 16 \): \[ 205 \div 16 = 12.8125 \]
Since you can only cut whole boards, we take the whole number part: \[ \text{Whole boards} = 12 \]
Therefore, Andre can cut 12 whole, equal-sized boards from the piece of wood.
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