A carpenter cut a board 3 3/4 feet long to make a shelf. Before he cut the board, it was 10 1/2 feet long.How long is the remaining piece of the board?Enter your answer, as a mixed number in simplest form

Subtract 3 3/4 from 10 1/2.  Note that the LCD is 4, so 10 1/2 = 10 2/4.

What is    10 2/4
               -  3 3/4
-------------------------
                     ?

Since 2/4 is smaller than 3/4, you must borrow 1 from that 10.

Now your problem looks like   9 6/4
                                               -3 3/4
                                             ----------
                                                 6 3/4   (answer)

The remnant of the board is 6 3/4 feet long.