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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.

What you'll learn

Why it matters: Floor plans, maps, model train layouts, and clothing patterns are all read at a scaled size. Unit conversions are what let inches on paper translate to actual feet in a room.

Worked example

Problem. A map scale says 1 inch = 25 miles. How many miles are represented by 3.5 inches?

  1. Each inch represents 25 miles.
  2. Multiply 3.5 by 25.
  3. 3.5 x 25 = 87.5 miles.

Answer: 87.5

Practice problems

1. How many inches are in 5 feet?

Show solution
  1. Warm-up: First identify exactly what the question is asking: How many inches are in 5 feet?
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. There are 12 inches in 1 foot.
  4. 5 x 12 = 60.
  5. 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
  1. Warm-up: First identify exactly what the question is asking: How many centimeters are in 3 meters?
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. There are 100 centimeters in 1 meter.
  4. 3 x 100 = 300.
  5. 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
  1. 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?
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Multiply 6 by 10.
  4. 6 inches represents 60 miles.
  5. 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
  1. 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?
  2. For similarity and scale problems, match corresponding parts and use a constant scale factor or proportion.
  3. 8 inches is 4 times 2 inches.
  4. 5 feet x 4 = 20 feet.
  5. 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
  1. 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?
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Divide 28 by 4.
  4. The model length is 7 centimeters.
  5. 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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