Final answer:
To cover a floor 222 inches wide with boards that are each 4 5/8 inches wide, divide the floor width by the board width. 48 boards are needed to cover the floor when rounding up to the nearest whole number.
Step-by-step explanation:
To determine how many boards will be needed to cover a floor that is 222 inches wide when each board is 4 5/8 inches wide, we need to divide the total width of the floor by the width of one board. First, convert 4 5/8 inches to an improper fraction: 4 5/8 inches = (4 × 8 + 5)/8 = 37/8 inches. Next, divide 222 inches by 37/8 inches to find the number of boards needed:
Number of boards = 222/(37/8) = 222 × (8/37) = 1776/37 ≈ 48 boards
Since we cannot have a fraction of a board, we round up to the nearest whole number, as the boards must cover the entire width without gaps. Therefore, the floor would require 48 boards.