Question
Zane drew a scale drawing of a city. The scale of the drawing was 5 inches = 1 yard. What scale factor does the drawing use?
Simplify your answer and write it as a fraction.
Simplify your answer and write it as a fraction.
Answers
GPT-4o mini
To determine the scale factor for Zane's drawing, we need to express the relationship between the inches in the drawing and the actual yards.
The scale given is:
\[
5 \text{ inches} = 1 \text{ yard}
\]
To find the scale factor, we need to express it as a ratio of drawing distance to actual distance. Here, we have:
\[
\text{Scale Factor} = \frac{\text{drawing distance}}{\text{actual distance}} = \frac{5 \text{ inches}}{1 \text{ yard}}
\]
To write this scale factor as a fraction with consistent units, we can convert yards to inches. Since there are 36 inches in one yard, we can rewrite the scale factor as follows:
\[
\text{Scale Factor} = \frac{5 \text{ inches}}{1 \text{ yard}} = \frac{5 \text{ inches}}{36 \text{ inches}} = \frac{5}{36}
\]
Thus, the simplified scale factor for Zane's drawing is:
\[
\boxed{\frac{5}{36}}
\]
The scale given is:
\[
5 \text{ inches} = 1 \text{ yard}
\]
To find the scale factor, we need to express it as a ratio of drawing distance to actual distance. Here, we have:
\[
\text{Scale Factor} = \frac{\text{drawing distance}}{\text{actual distance}} = \frac{5 \text{ inches}}{1 \text{ yard}}
\]
To write this scale factor as a fraction with consistent units, we can convert yards to inches. Since there are 36 inches in one yard, we can rewrite the scale factor as follows:
\[
\text{Scale Factor} = \frac{5 \text{ inches}}{1 \text{ yard}} = \frac{5 \text{ inches}}{36 \text{ inches}} = \frac{5}{36}
\]
Thus, the simplified scale factor for Zane's drawing is:
\[
\boxed{\frac{5}{36}}
\]