Final answer:
Mary can cut a maximum of 4 whole pieces, each 2/3 of a yard long, from the 9-foot wood piece, since 2/3 of a yard equals 2 feet.
Step-by-step explanation:
Mary wants to cut an 9-foot piece of wood into multiple pieces, with each piece being 2/3 of a yard long. To determine the maximum number of pieces she can cut from the 9-foot wood, we first need to convert either the length of the wood to yards or the length of the cut pieces to feet. Since there are 3 feet in a yard, we know that 2/3 of a yard is equal to 2/3 x 3 feet = 2 feet. To find out how many 2-foot pieces can be cut from the 9-foot wood, we divide 9 feet by 2 feet per piece.
9 feet / 2 feet per piece = 4.5 pieces
Since Mary cannot have half a piece, the greatest number of whole pieces she can cut from the 9-foot piece of wood is 4 pieces.