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 solve the problem, we need to divide the length of the large piece of wood by the length of each board.
To convert 10 1/4 yards into a fraction, we can write it as a mixed number: 10 + 1/4 = 10 + 0.25 = 10.25 yards
Now let's write the length of the large piece of wood as a fraction: 10 1/4 = 10.25 yards
We want to cut boards that are 4/5 yard long.
Since we want whole boards and we can't have fractions of boards, we need to see how many times 4/5 can go into 10.25.
To do this, we divide 10.25 by 4/5:
10.25 ÷ (4/5)
To divide by a fraction, we multiply by its reciprocal:
10.25 × (5/4)
Multiplying gives us: 10.25 × 5 /4 = 51.25/4
Now let's write 51.25/4 as a mixed number:
51.25/4 = 12 13/4
So Andre can cut 12 whole boards from this piece of wood.