Camilla measured a hotel and made a scale drawing. The scale of the drawing was 4 inches = 2 feet. What is the scale factor of the drawing?

Simplify your answer and write it as a fraction.

1 answer

To determine the scale factor of Camilla's drawing, we start with the scale provided:

\[ 4 \text{ inches} = 2 \text{ feet} \]

First, we need to express both quantities in the same unit. Let's convert 2 feet into inches. We know that:

\[ 1 \text{ foot} = 12 \text{ inches} \]

Thus,

\[ 2 \text{ feet} = 2 \times 12 \text{ inches} = 24 \text{ inches} \]

Now, we can rewrite the scale equation:

\[ 4 \text{ inches} = 24 \text{ inches} \]

Next, we set up the scale factor as the ratio of the drawing measurement (in inches) to the actual measurement (in inches):

\[ \text{Scale Factor} = \frac{\text{Drawing measurement}}{\text{Actual measurement}} = \frac{4 \text{ inches}}{24 \text{ inches}} \]

Now, simplify the fraction:

\[ \text{Scale Factor} = \frac{4}{24} = \frac{1}{6} \]

Therefore, the scale factor of the drawing is:

\[ \boxed{\frac{1}{6}} \]