Scale Drawings and Unit Conversions
A free Pre-Algebra lesson from the “Proportional Reasoning” unit, with a worked example and practice problems including step-by-step solutions.
Scale drawings and unit conversions both depend on equivalent ratios. A scale tells how drawing length compares to real length. A conversion factor tells how one unit compares to another, such as 12 inches in 1 foot or 100 centimeters in 1 meter. In Proportional Reasoning, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.
What you'll learn
- Use scale drawings to find real distances
- Convert common measurement units
- Choose units that fit the situation
Worked example
Problem. A map scale says 1 inch = 25 miles. How many miles are represented by 3.5 inches?
- Each inch represents 25 miles.
- Multiply 3.5 by 25.
- 3.5 x 25 = 87.5 miles.
- Connect the calculation back to Scale Drawings and Unit Conversions so the method, not just the arithmetic, is clear.
Answer: 87.5
Practice problems
1. How many inches are in 5 feet?
Show solution
- Warm-up: First identify exactly what the question is asking: How many inches are in 5 feet?
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- There are 12 inches in 1 foot.
- 5 x 12 = 60.
- Check the result by substituting or estimating: the response should match 60 and make sense in the original problem.
Answer: 60
2. How many centimeters are in 3 meters?
Show solution
- Warm-up: First identify exactly what the question is asking: How many centimeters are in 3 meters?
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- There are 100 centimeters in 1 meter.
- 3 x 100 = 300.
- Check the result by substituting or estimating: the response should match 300 and make sense in the original problem.
Answer: 300
3. A map uses 1 inch for 10 miles. How many miles are shown by 6 inches?
Show solution
- Warm-up: First identify exactly what the question is asking: A map uses 1 inch for 10 miles. How many miles are shown by 6 inches?
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Multiply 6 by 10.
- 6 inches represents 60 miles.
- Check the result by substituting or estimating: the response should match 60 and make sense in the original problem.
Answer: 60
4. A drawing scale is 2 inches = 5 feet. How many feet are represented by 8 inches?
Show solution
- Core Practice: First identify exactly what the question is asking: A drawing scale is 2 inches = 5 feet. How many feet are represented by 8 inches?
- For similarity and scale problems, match corresponding parts and use a constant scale factor or proportion.
- 8 inches is 4 times 2 inches.
- 5 feet x 4 = 20 feet.
- Check the result by substituting or estimating: the response should match 20 and make sense in the original problem.
Answer: 20
5. A model uses 1 centimeter for every 4 meters. How many centimeters are needed for 28 meters?
Show solution
- Core Practice: First identify exactly what the question is asking: A model uses 1 centimeter for every 4 meters. How many centimeters are needed for 28 meters?
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Divide 28 by 4.
- The model length is 7 centimeters.
- Check the result by substituting or estimating: the response should match 7 and make sense in the original problem.
Answer: 7
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