To determine how many whole boards of length \( \frac{4}{5} \) yard Andre can cut from a piece of wood that is \( 10 \frac{1}{4} \) yards long, we first need to convert \( 10 \frac{1}{4} \) yards into an improper fraction.
-
Convert \( 10 \frac{1}{4} \) to an improper fraction: \[ 10 \frac{1}{4} = \frac{10 \times 4 + 1}{4} = \frac{40 + 1}{4} = \frac{41}{4} \text{ yards} \]
-
Now, we divide the total length of wood by the length of each board: \[ \text{Number of boards} = \frac{\frac{41}{4}}{\frac{4}{5}} \]
-
To divide by a fraction, multiply by its reciprocal: \[ \frac{41}{4} \div \frac{4}{5} = \frac{41}{4} \times \frac{5}{4} = \frac{41 \times 5}{4 \times 4} = \frac{205}{16} \]
-
Now, we convert \( \frac{205}{16} \) into a whole number to find how many whole boards can be cut: \[ 205 \div 16 = 12.8125 \] This means Andre can cut 12 whole boards.
Thus, the number of whole, equal-sized boards Andre can cut is 12.
1 answer