You are installing a wood fence. the fence is 120 feet long. east wood slat to be installed vertically, is 3 3/4 inches wide. what is the total cost of the wood slats if each slat costs $1.40?

3 3/4 inches = (3 3/4 / 12) feet = 0.3125 feet
120 feet requires  x number of board.

120 feet/0.3125 feet / board = 384 boards.

1 board costs 1.40 
384 boards cost x

1.4 * 384.00= x*1 = x
537.60 dollars.

Note if you need to do this by dimensional analysis, it will look like this.

120 feet/fence [ 1 board / 3.75 inches] [ 12 inches/foot] [1.40 dollars / board]

All units that can be cancelled should be.
The result is 537.6 dollars / fence which is the answer you got.