To find the number of tiles required, we need to calculate the area of the floor and the area of each tile.

The area of the floor is given by: Area of floor = length × width = 15 m × 8 m = 120 m²

The area of each tile is given by: Area of tile = length × width = 0.5 m × 0.25 m = 0.125 m²

To find the number of tiles required, we divide the area of the floor by the area of each tile: Number of tiles = Area of floor / Area of tile = 120 m² / 0.125 m² = 960 tiles

Therefore, 960 tiles are required to cover the floor.

Now, let’s calculate the area of the carpet. The length and width of the carpet will be 2 meters more than the length and width of the floor, respectively.

Length of carpet = 15 m + 2 m = 17 m Width of carpet = 8 m + 2 m = 10 m

The area of the carpet is given by: Area of carpet = length × width = 17 m × 10 m = 170 m²

To find the fraction of the floor that is uncovered, we subtract the area of the carpet from the area of the floor and divide by the area of the floor: Fraction of floor uncovered = (Area of floor - Area of carpet) / Area of floor = (120 m² - 170 m²) / 120 m² = -50 m² / 120 m² = -5/12

However, the fraction cannot be negative, so we take the absolute value: Fraction of floor uncovered = |-5/12| = 5/12

Therefore, the correct fraction of the floor that is uncovered is 5/12, not 7/20.