Imagine 4-inch tiles laid out on top of a 16-inch square tile. There would be 4 rows of 4-inch squares, with 4 tiles in each row. Each 4-inch square tile has an area of 16 square inches (4 x 4), each row of 4-inch tiles has an area of 64...

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Imagine 4-inch tiles laid out on top of a 16-inch square tile. There would be 4 rows of 4-inch squares, with 4 tiles in each row. Each 4-inch square tile has an area of 16 square inches (4 x 4), each row of 4-inch tiles has an area of 64 square inches (4 x 16), and the total area of the 4 rows of 4-inch tiles would be 256 square inches, matching the total area of the 16-inch square tile (16 x 16). (Of course, grout would add slightly to the area covered the tiles, but is probably not being included in the consideration of this problem.)

The builder would use 16 times as many tiles if she uses 4-inch square tiles instead of 16-inch square tiles.