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To find the number of boards Andre can cut from the piece of wood, we need to divide the length of the wood by the length of each board.
10 1/4 yards = 10 + 1/4 yards = 40/4 + 1/4 yards = 41/4 yards
We then divide 41/4 yards by 4/5 yard/board:
(41/4) / (4/5) = (41/4) * (5/4) = (41 * 5) / (4 * 4) = 205 / 16
Since we cannot have a fraction of a board, we need to round down to the nearest whole number.
205 / 16 ≈ 12.8125
Therefore, Andre can cut approximately 12 boards from this piece of wood.