To find the length in feet of each board, we need to convert the length of each board from feet and inches to just feet.
Since 9 inches is equal to 3/4 of a foot (since there are 12 inches in a foot), we can write the length of each board as 2 feet + 3/4 of a foot. This can also be written as 2 + 3/4.
To multiply a whole number by a fraction, we can convert the whole number to a fraction with a denominator of 1. So 2 can be written as 2/1.
Now we can multiply the fractions: (2/1) multiplied by (3/4). When multiplying fractions, we multiply the numerators (2 x 3) to get the new numerator, and multiply the denominators (1 x 4) to get the new denominator. This gives us 6/4.
The fraction 6/4 can be simplified by dividing both the numerator and the denominator by their greatest common factor, which is 2. Dividing both 6 and 4 by 2 gives us 3/2.
Now we have the length of each board in feet as 3/2.
To find the total amount of board feet the carpenter needs, we multiply the number of boards (4) by the length of each board in feet (3/2).
4 multiplied by 3/2 is equal to (4/1) multiplied by (3/2). Multiplying the numerators (4 x 3) gives us 12, and multiplying the denominators (1 x 2) gives us 2. So the result is 12/2, which simplifies to 6.
Therefore, the carpenter needs to buy 6 feet of wood in total.
I hope this explanation helps you understand how to get the answer!