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?

Answer 1

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.