Simplifying a Map Scale
Simplify a map scale \( 2 \text{ cm} : 1 \text{ km} \).
\( \begin{align} 2 \text{ cm} : 1 \text{ km} &= 2 \text{ cm} : 1000 \text{ m} \\ &= 2 \text{ cm} : 100 \ 000 \text{ cm} \\ &= 1 \text{ cm} : 50 \ 000 \text{ cm} \\ &= 1 : 50 \ 000 \end{align} \)
Finding an Actual Value by a Scale Ratio
A map has a scale of \( 1 : 25 \ 000 \). Find the actual distance if the scaled distance is \( 5 \text{ cm} \).
\( \begin{align} \text{actual distance} &= 5 \times 25 \ 000 \text{ cm} \\ &= 125 \ 000 \text{ cm} \\ &= 1250 \text{ m} \\ &= 1.25 \text{ km} \end{align} \)
Finding a Scaled Value by a Scale Ratio
A map has a scale of \( 1 : 500 \ 000 \). Find the scaled distance if the actual distance is \( 2 \text{ km} \).
\( \begin{align} \text{scaled distance} &= 2 \text{ km} \div 500 \ 000 \\ &= 2000 \text{ m} \div 500 \ 000 \\ &= 200 \ 000 \text{ cm} \div 500 \ 000 \\ &= 0.4 \text{ cm} \\ &= 4 \text{ mm} \end{align} \)
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