Question

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 one third in.
and width one fourth in.
The actual tiles have length one fourth ft
and width three sixteenths 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.
Question content area bottom
Part 1
The ratio of the length of a tile in the model to the length of an actual tile is
  
enter your response here.
​(Type the ratio as a simplified​ fraction.)

Answer 1

The ratio is 1/9.

Two ways to see this:
1) Convert actual length to inches: 1/4 ft = 3 in. Then (1/3 in) ÷ (3 in) = (1/3)/3 = 1/9.
2) Convert the model length to feet: 1/3 in = (1/3)/12 = 1/36 ft. Then (1/36 ft) ÷ (1/4 ft) = (1/36)·4 = 4/36 = 1/9.