Question

2.6 ps - 8
an architect makes a model of a new house. the model shows a tile patio in the backyard. in the model, each tile has length \\(\frac{1}{4}\\) in. and width \\(\frac{1}{6}\\) in. the actual tiles have length \\(\frac{1}{3}\\) ft and width \\(\frac{2}{9}\\) ft. what is the ratio of the length of a tile in the model to the length of an actual tile? what is the ratio of the area of a tile in the model to the area of an actual tile? use pencil and paper. describe two ways to find each ratio.
the ratio of the length of a tile in the model to the length of an actual tile is
(type the ratio as a simplified fraction.)
enter your answer in the answer box and then click check answer.
1 part remaining

Explanation:

Step1: Convert model length to feet

The model length is $\frac{1}{4}$ in. Since 1 foot = 12 inches, convert inches to feet: $\frac{1}{4} \div 12 = \frac{1}{4} \times \frac{1}{12} = \frac{1}{48}$ ft.

Step2: Find the ratio of model length to actual length

The actual length is $\frac{1}{3}$ ft. The ratio is $\frac{\frac{1}{48}}{\frac{1}{3}}$.

Step3: Simplify the ratio

To divide fractions, multiply by the reciprocal: $\frac{1}{48} \times \frac{3}{1} = \frac{3}{48} = \frac{1}{16}$.

Answer:

$\frac{1}{16}$