An artist is using tiles and boards for a project. A tile has length of 1 Thirds ft and width 1 thirds ft. a board has length 1 fourths yd and width 1 fourths yd. what is the ratio of the length of the tile to the length of the board? what is the ratio of the area of the tile to the area of the board

a. TILE: L = 1/3 Ft.

BOARD: L = 1/4 Yd. = 3/4 Ft.
RATIO = (1/3)/(3/4) = 1/3 * 4/3 = 4/9.

b. At = L*W = 1/3 * 1/3 = 1/9 Ft^2
Ab = 3/4 * 3/4 = 9/16 Ft^2.

At/Ab = (1/9)/(9/16) = 1/9 * 16/9=16/81.

an artist is using tiles and boards for a projects. A tile has a length 2/3ft and a width of 2/3ft. A board has a length of 1/6 yd and width of 1/6 yd. what is the ratio of the length of the tile to the board?

To find the ratio of the length of the tile to the length of the board, we need to convert the measurements to the same unit of measurement. In this case, we'll convert the tile length from feet to yards.

1 third ft = 1/3 ft
1 fourth yd = 1/4 yd

To convert feet to yards, we divide the length by 3:
1/3 ft ÷ 3 = 1/9 yd

Now we can find the ratio:
Length of tile: Length of board = 1/9 yd : 1/4 yd

To simplify the ratio, we can multiply both parts by 4:
(1/9 yd) * 4 = 4/9 yd
(1/4 yd) * 4 = 1 yd

Simplified ratio: 4/9 yd : 1 yd

Now, let's calculate the ratio of the area of the tile to the area of the board.

The area of the tile:
Length * Width = (1/3 ft) * (1/3 ft) = 1/9 ft^2

The area of the board:
Length * Width = (1/4 yd) * (1/4 yd) = 1/16 yd^2

To compare the areas, we need to convert the tile area to the same unit of measurement as the board. We'll convert the tile area from square feet to square yards.

1 ft^2 = (1/3 ft) * (1/3 ft) = 1/9 ft^2
1/9 ft^2 ÷ 9 = 1/81 yd^2

Now we can find the ratio:
Area of tile: Area of board = 1/81 yd^2 : 1/16 yd^2

To simplify the ratio, we can multiply both parts by 16:
(1/81 yd^2) * 16 = 16/81 yd^2
(1/16 yd^2) * 16 = 1 yd^2

Simplified ratio: 16/81 yd^2 : 1 yd^2

In summary:
- The ratio of the length of the tile to the length of the board is 4/9 yd : 1 yd
- The ratio of the area of the tile to the area of the board is 16/81 yd^2 : 1 yd^2.

To find the ratio of the length of the tile to the length of the board, we need to convert both measurements to the same unit. Let's convert the length of the tile from feet to yards:

1 third ft = 1/3 ft * (1 yd / 3 ft) = 1/9 yd

Now, we can calculate the ratio:

Length of the tile: 1/9 yd
Length of the board: 1/4 yd

Ratio of length of tile to length of board = (1/9) / (1/4)
= (1/9) * (4/1)
= 4/9

Therefore, the ratio of the length of the tile to the length of the board is 4:9.

Now, let's find the ratio of the area of the tile to the area of the board:

To calculate the area, we need to square the measurements. First, convert the width of the tile from feet to yards:

1 third ft = 1/3 ft * (1 yd / 3 ft) = 1/9 yd

Now, calculate the areas:

Area of the tile: (1/9 yd) * (1/9 yd) = 1/81 sq. yd
Area of the board: (1/4 yd) * (1/4 yd) = 1/16 sq. yd

Ratio of area of tile to area of board = (1/81) / (1/16)
= (1/81) * (16/1)
= 16/81

Therefore, the ratio of the area of the tile to the area of the board is 16:81.