a carpenter needs to buy either an 8 foot or a 10 foot piece of wood that will be cut into three pieces. these pieces will be 4 3/4 feet, 1 5/6, and 2 2/3 feet long. what length of wood should the carpenter buy?

well, what is the total length of the pieces?

4 3/4 + 1 5/6 + 2 2/3
= 4+1+2 + 9/12 + 10/12 + 8/12
= 7 + 27/12
= 7 + 2 3/12
= 9 1/4 ft

What about part b: Later, the carpenter needs to go back to the lumber store for more lumber. He will cut 3 more pieces the same size as 9 3/12ft. In addition, he will cut a piece that is 3 3/4 feet long. The carpenter thinks he needs a 12-foot piece of lumber. Do you agree or disagree? Support your answer using information from the problem.

To determine the length of wood that the carpenter needs to buy, we need to calculate the total length required for all three pieces.

First, let's convert all the measurements to a common fraction:

- 4 3/4 feet can be written as 4 + 3/4 = 16/4 + 3/4 = 19/4 feet
- 1 5/6 feet can be written as 1 + 5/6 = 6/6 + 5/6 = 11/6 feet
- 2 2/3 feet can be written as 2 + 2/3 = 6/3 + 2/3 = 8/3 feet

Now, we can add up the three measurements:

19/4 + 11/6 + 8/3

To add these fractions, we need to find a common denominator for all three fractions, which in this case is 12.

19/4 can be rewritten as (19/4) * (3/3) = 57/12
11/6 can be rewritten as (11/6) * (2/2) = 22/12
8/3 remains the same

Now, we can add the fractions:

57/12 + 22/12 + 8/3 = (57 + 22 + 32)/12 = 111/12

So, the total length of wood required is 111/12 feet.

Since the carpenter needs to buy either an 8-foot or a 10-foot piece of wood, we should round up the total length to the next whole number to make sure we have enough wood.

111/12 is approximately 9.25 feet.

Therefore, the carpenter should buy at least a 10-foot piece of wood to have enough material for all three pieces.

Thanks,Steve

the carpenter will buy