a carpenter has a board that is 8 ft long. he cuts off two piece.one piece is 3 1/2 ft long and other is 2 1/3ft long.How much off the board is left.
3 1/2 = 3 3/6
2 1/3 = 2 2/6
The carpenter cuts off 5 5/6 ft of the board.
7 6/6 - 5 5/6 = 2 1/6 ft of the board is left.
There is 2 1/6 feet left.
To find out how much of the board is left after cutting off two pieces, we need to subtract the sum of the lengths of the two pieces from the original length of the board.
First, let's convert the mixed fractions to improper fractions for easier calculation:
3 1/2 ft = (3 * 2 + 1) / 2 = 7/2 ft
2 1/3 ft = (2 * 3 + 1) / 3 = 7/3 ft
Now, let's add the lengths of the two pieces:
7/2 ft + 7/3 ft = (7 * 3 + 7 * 2) / (2 * 3) = 35/6 ft
Since the sum of the lengths of the two pieces is 35/6 ft, we can calculate the amount of board left by subtracting this sum from the original length of the board:
8 ft - 35/6 ft
When subtracting a whole number from a fraction, it's often easier to convert the whole number to a fraction with the same denominator:
8 ft = 8 * 6/6 = 48/6 ft
Now, we can subtract:
48/6 ft - 35/6 ft = (48 - 35) / 6 = 13/6 ft
Therefore, there are 13/6 ft or 2 1/6 ft of the board left after cutting off two pieces.