Final answer:
To determine the fraction of the floor covered with tile, multiply 1/2 (the fraction of the length covered) by 1/5 (the fraction of the width covered), resulting in 1/10 of the floor being covered.
Step-by-step explanation:
To find the fraction of the floor that has been covered, we multiply the fraction of the length that has been covered by the fraction of the width covered. If half (1/2) the length and one-fifth (1/5) of the width are covered, we calculate the covered area by multiplying these fractions together:
(1/2) * (1/5) = 1/10
The area covered is 1/2 of the length and 1/5 of the width. Let's assume the length of the floor is x and the width is y.
The area covered = (1/2) * x * (1/5) * y = (1/10) * x * y.
The total area of the floor = x * y.
Therefore, the fraction of the floor that has been covered = (1/10) * x * y / (x * y) = 1/10.
This means 1/10 of the floor has been covered with tile. It's important to multiply the two fractions representing the lengths along each dimension to determine the fraction of the overall area that they cover.