Andre is cutting fence boards from a large piece of wood 10 1/4 yards long. Each board needs to be 4/5 yard. How many whole, equal-sized boards can he cut from this piece of wood?
To find out how many boards Andre can cut from the piece of wood, we need to divide the length of the wood by the length of each board.
First, let's convert the length of the wood from yards to fraction yards: 10 1/4 yards = 10 + 1/4 = 10 + 0.25 = 10.25 yards.
The length of each board is 4/5 yard.
To divide 10.25 yards by 4/5 yard, we can multiply 10.25 yards by the reciprocal of 4/5 yard: 10.25 * (5/4) = 10.25 * 5/4 = 51.25/4.
To simplify the fraction, we can divide the numerator and denominator by their greatest common divisor, which is 25: 51.25/4 = (51.25/25) / (4/25) = 2.05/1.
Therefore, Andre can cut 2 whole, equal-sized boards from this piece of wood. Answer: \boxed{2}.