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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. 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

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.
  4. Connect the calculation back to Scale Drawings and Unit Conversions so the method, not just the arithmetic, is clear.

Answer: 87.5

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.

Practice problems

1. How many inches are in 5 feet?

Show solution
  1. There are 12 inches in 1 foot.
  2. 5 x 12 = 60.

Answer: 60

2. How many centimeters are in 3 meters?

Show solution
  1. There are 100 centimeters in 1 meter.
  2. 3 x 100 = 300.

Answer: 300

3. A map uses 1 inch for 10 miles. How many miles are shown by 6 inches?

Show solution
  1. Multiply 6 by 10.
  2. 6 inches represents 60 miles.

Answer: 60

4. A drawing scale is 2 inches = 5 feet. How many feet are represented by 8 inches?

Show solution
  1. 8 inches is 4 times 2 inches.
  2. 5 feet x 4 = 20 feet.

Answer: 20

5. A model uses 1 centimeter for every 4 meters. How many centimeters are needed for 28 meters?

Show solution
  1. Divide 28 by 4.
  2. The model length is 7 centimeters.

Answer: 7

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