Math Problem Statement
Solution
To solve the problem:
Problem Breakdown:
The map has a scale of 1:50,000, meaning 1 cm on the map corresponds to 50,000 cm in real life.
The given length of the road on the map is 8.5 cm.
Conversion Steps:
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Convert the map length into real-world length:
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Convert the real-world length from centimeters to kilometers: Therefore:
Final Answer:
The real length of the road is 4.25 kilometers.
Let me know if you’d like a detailed explanation of the steps or assistance with another question!
Follow-up Questions to Enhance Understanding:
- What would the real length be if the road on the map measured 10 cm?
- How does changing the scale to 1:100,000 affect the real-world calculation?
- How do we convert real lengths to map lengths given a specific scale?
- What units are most convenient for large-scale conversions, and why?
- How can map scales be used to calculate areas in real-world dimensions?
Tip: Always double-check the scale units (e.g., cm, km
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Math Problem Analysis
Mathematical Concepts
Scales and ratios
Unit conversion
Proportional reasoning
Formulas
Real length = map length × scale factor
1 kilometer = 100,000 centimeters
Theorems
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Suitable Grade Level
Grades 6-8
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