Question

Ethan drew a scale drawing of the high school. The scale of the drawing was 6 centimeters = 9 meters. What is the scale factor of the drawing?

Simplify your answer and write it as a fraction.

Answer 1

To find the scale factor of the drawing, we begin with the scale provided: 6 centimeters = 9 meters.

We can express this as a fraction:

\[
\text{Scale Factor} = \frac{\text{Length in drawing (cm)}}{\text{Actual Length (m)}}
\]

Substituting the values gives us:

\[
\text{Scale Factor} = \frac{6 \text{ cm}}{9 \text{ m}}
\]

To simplify this fraction, we need to convert the meters to centimeters since we're comparing lengths in the same units. We know that 1 meter = 100 centimeters, so:

\[
9 \text{ m} = 9 \times 100 \text{ cm} = 900 \text{ cm}
\]

Now, we can substitute this back into our scale factor:

\[
\text{Scale Factor} = \frac{6 \text{ cm}}{900 \text{ cm}}
\]

This fraction can be simplified by dividing both the numerator and the denominator by 6:

\[
\text{Scale Factor} = \frac{6 \div 6}{900 \div 6} = \frac{1}{150}
\]

Thus, the simplified scale factor of the drawing is:

\[
\boxed{\frac{1}{150}}
\]