A board 3 5/8 feet long must be sawed. from a 6-foot board. how long is the remaining piece?

6 is the same as 5 8/8

So,

5 8/8 - 3 5/8 = 2 3/8

To find the length of the remaining piece, we need to subtract the length that needs to be sawed from the original length of the board.

First, let's convert the mixed fraction 3 5/8 to an improper fraction.
3 5/8 is equal to (3 * 8) + 5 divided by 8, which is equal to 24 + 5 divided by 8, which is equal to 29/8.

Now, subtracting the length that needs to be sawed, which is 29/8 feet, from the original length of the board, which is 6 feet:

6 feet - 29/8 feet

To subtract these values, we need to find a common denominator. The denominator of 29/8 is 8, so let's convert 6 feet to a fraction with a denominator of 8:

6 feet is equal to (6 * 8) divided by 8, which is equal to 48/8.

Now we can subtract the fractions:

48/8 - 29/8 = (48 - 29)/8 = 19/8

So, the remaining piece is 19/8 feet long.