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Quincy measured a house and made a scale drawing. The living room, which is $4$ meters long in real life, is $2$ millimeters long in the drawing. What is the scale of the drawing? $\newline$ $1$ millimeter : $\_\_\_$ meters $\newline$

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Scale drawings: word problems

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Q. Quincy measured a house and made a scale drawing. The living room, which is

4

meters long in real life, is

2

millimeters long in the drawing. What is the scale of the drawing?

\newline

1

millimeter :

\_\_\_

meters

\newline

Identify Measurements: Identify the real-life measurement and the corresponding measurement on the drawing. $\newline$ Real-life length of the living room = $4$ meters $\newline$ Length of the living room in the drawing = $2$ millimeters $\newline$ We need to find the ratio of the drawing length to the real-life length to determine the scale.
Set Up Ratio: Set up the ratio to find the scale of the drawing. $\newline$ Scale = $\frac{\text{Drawing measurement}}{\text{Real-life measurement}}$ $\newline$ Scale = $\frac{2\,\text{mm}}{4\,\text{m}}$
Convert Units: Convert meters to millimeters to have the same units for the ratio. $\newline$ $1$ meter $= 1000$ millimeters $\newline$ So, $4$ m $= 4 \times 1000$ mm $= 4000$ mm
Calculate Scale: Calculate the scale using the converted measurements. Scale = $\frac{2\,\text{mm}}{4000\,\text{mm}}$
Simplify Ratio: Simplify the ratio to find the scale. $\newline$ Divide both the numerator and the denominator by $2$ . $\newline$ Scale = $\frac{2}{4000}$ mm = $\frac{1}{2000}$ mm
Write Final Scale: Write the scale in the format requested in the question prompt. $\newline$ $1$ millimeter : ____ meters $\newline$ Since $2000$ mm is $2$ m (because $2000$ mm $/$ $1000$ mm/m $=$ $2$ m), the scale is: $\newline$ $1$ millimeter : $0.002$ meters

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