Question

martina made a scale drawing of a house. in real life, the living room is 8 meters wide. it is 4 centimeters wide in the drawing. what is the drawing’s scale factor? simplify your answer and write it as a fraction.

Explanation:

Step1: Convert units to be consistent

First, convert the real - life width from meters to centimeters. Since 1 meter = 100 centimeters, 8 meters = \(8\times100 = 800\) centimeters. The width in the drawing is 4 centimeters.

Step2: Calculate the scale factor

The scale factor is the ratio of the drawing length to the real - life length. So the scale factor \(=\frac{\text{drawing width}}{\text{real - life width}}=\frac{4}{800}\).

Step3: Simplify the fraction

To simplify \(\frac{4}{800}\), divide both the numerator and the denominator by their greatest common divisor, which is 4. \(\frac{4\div4}{800\div4}=\frac{1}{200}\).

Answer:

\(\frac{1}{200}\)