Question

dave made a scale drawing of a city. the scale of the drawing was 5 inches = 1 yard. what is the drawing’s scale factor? simplify your answer and write it as a fraction.

Explanation:

Step1: Convert yards to inches

1 yard = 36 inches, so the actual length is 36 inches. The drawing length is 5 inches.

Step2: Find the scale factor

Scale factor = drawing length / actual length = $\frac{5}{36}$ (Wait, no, scale factor for drawing to actual is drawing over actual, but wait, the scale is drawing : actual. Wait, the problem says "the scale of the drawing was 5 inches = 1 yard". So scale factor is (drawing size) / (actual size). So actual size is 1 yard = 36 inches. So scale factor is 5 inches / 36 inches = $\frac{5}{36}$? Wait, no, maybe I got it reversed. Wait, scale factor for a drawing: if the drawing is smaller than actual, the scale factor is less than 1. Wait, 5 inches represents 36 inches (1 yard). So the scale factor (drawing to actual) is 5/36? Wait, no, let's think again. The scale factor is the ratio of the drawing's dimensions to the actual dimensions. So if 5 inches on the drawing equals 1 yard (36 inches) in real life, then the scale factor is (drawing length) / (actual length) = 5 / 36. Wait, but let's confirm. The formula for scale factor (when drawing is a reduction) is drawing length divided by actual length. So yes, 5 inches (drawing) / 36 inches (actual) = 5/36. Wait, but maybe I made a mistake. Wait, 1 yard is 36 inches. So the scale is 5 inches : 36 inches. So the scale factor is 5/36. Wait, but let's check. If the drawing is 5 inches, actual is 36 inches, so the scale factor is 5/36. Yes, that makes sense.

Answer:

$\frac{5}{36}$