Scale drawings: scale factor word problems KCM Zane measured a hotel and made a scale drawing. He used the scale 4 inches \( =2 \) feet, at is the scale factor of the drawing? Simplify your answer and write it as a fraction.

To find the scale factor, we need to express the relationship between the measurements in the drawing and the actual measurements. Since Zane used a scale where 4 inches corresponds to 2 feet, we start by converting 2 feet into inches (2 feet = 24 inches). Therefore, the scale is 4 inches (drawing) = 24 inches (actual size). To find the scale factor, we set up the ratio: \[\text{Scale factor} = \frac{\text{Drawing length}}{\text{Actual length}} = \frac{4}{24}\]. This simplifies to \(\frac{1}{6}\) when we divide both the numerator and denominator by 4. So, the scale factor of Zane's drawing is \(\frac{1}{6}\). Zane's scale drawing is a fantastic example of how architects and designers visualize large spaces, helping them make proportional estimates that fit on paper. Such drawings are essential for planning layouts in everything from home designs to urban planning, enabling people to see how structures will fit in a given area before they are built! When tackling scale factor problems, a common mistake is to forget to convert all units to the same measurement system. Ensure that you're always working in the same unit—such as inches to inches or feet to feet—before calculating. Always double-check the scale and unit conversions to avoid confusion, especially when the dimensions get larger or more complex!