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Scale drawings, proportions and unit changes

Set up a proportion, read a map or floor-plan scale, see why a scale factor changes area more than length, and change units step by step. Includes six original questions with worked answers.

By FinishHigh · Published 2026-11-02 · Updated 2026-11-02

A proportion is two equal ratios

A car uses 4 gallons of gas to go 126 miles. How many gallons for 315 miles at the same rate? Write gallons over miles twice and set them equal: 4/126 = x/315.

Cross-multiply: 126 × x = 4 × 315, so 126x = 1,260 and x = 10 gallons. The rule that keeps you safe: the same kind of quantity goes in the same place in both ratios. Gallons on top both times, miles on the bottom both times.

Map and floor-plan scales

A scale is a ratio between the drawing and real life. On a map where 1 inch stands for 20 miles, two towns 3.5 inches apart are 3.5 × 20 = 70 miles apart.

On a floor plan drawn at ¼ inch = 1 foot, every inch on paper is 4 feet. A room drawn 3 inches by 2.5 inches is 12 feet by 10 feet. To go the other way, from real life to the drawing, divide by the scale instead of multiplying.

A scale factor changes area more than length

A 4-inch by 6-inch photo is enlarged by a scale factor of 2.5. Each side is multiplied by 2.5: the new photo is 10 inches by 15 inches.

The area does not grow by 2.5. It goes from 4 × 6 = 24 square inches to 10 × 15 = 150 square inches, which is 6.25 times as much. That is 2.5 × 2.5, because both the length and the width were stretched. When a question asks about area after a size change, multiply by the scale factor twice.

Change units with a fraction worth 1

Since 12 inches = 1 foot, the fraction (1 foot ÷ 12 inches) equals 1. Multiplying by it changes the units without changing the amount. 90 inches × (1 foot ÷ 12 inches) = 7.5 feet. The inches cancel, and feet is left.

Pick the fraction that puts the unit you want to get rid of on the bottom. With 1 mile = 5,280 feet, a 1.5-mile walk is 1.5 × 5,280 = 7,920 feet. With 1 hour = 60 minutes, 2.5 hours is 150 minutes. If a test question gives you the conversion, use the number it gives.

Check that the answer makes sense

Before you choose an answer, ask whether it should be bigger or smaller than the number you started with. Feet to inches should give a bigger number; inches to feet a smaller one. A longer trip should take more gas, not less.

Write the units next to every number. If the units do not cancel to the one the question asks for, the setup is upside down.

Where this comes from

Where this comes from: GED Testing Service’s Assessment Guide for Educators: Mathematical Reasoning lists indicators Q.3.b, using scale factors and converting between scale drawings and real sizes, and Q.3.c, solving real-world problems with ratios or proportions, including ones that need a change of units. The GED math study booklet lists multi-step ratio and proportion problems as a skill. We checked both on November 2, 2026.

These sources set the topic. The explanations, numbers and questions here are original FinishHigh practice with invented situations, not GED® test questions. GED® is a registered trademark of the American Council on Education. FinishHigh is independent and not affiliated with or endorsed by it. This lesson teaches one skill. It is not a full course or a readiness result.

For unit prices and simple ratios first, see Ratios and unit prices, linked below.

Try this next: 6 questions ↓

ORIGINAL PRACTICE

Your turn.

Try each question before opening the explanation. These are FinishHigh practice examples, not GED® test questions.

A recipe uses 3 cups of flour for 24 cookies. How much flour for 40 cookies?
Show the answer and why
5 cups. 3/24 = x/40, so 24x = 120 and x = 5.
On a map, 1 inch stands for 15 miles. Two towns are 4.2 inches apart on the map. How far apart are they?
Show the answer and why
63 miles. 4.2 × 15 = 63.
A floor plan uses ½ inch = 1 foot. A wall is drawn 7 inches long. How long is the real wall?
Show the answer and why
14 feet. Each inch on paper is 2 feet, so 7 × 2 = 14.
A square tile with 8-inch sides is copied at a scale factor of 3. What are the new side length and the new area? How many times larger is the area?
Show the answer and why
Side: 8 × 3 = 24 inches. Area: 24 × 24 = 576 square inches, compared with 8 × 8 = 64 before. That is 9 times larger, because 3 × 3 = 9.
How many minutes are in 2.75 hours?
Show the answer and why
165 minutes. 2.75 × 60 = 165.
A worker earns $84 for 6 hours. At the same rate, how much for 15 hours?
Show the answer and why
$210. The rate is 84 ÷ 6 = $14 an hour, and 14 × 15 = 210. A proportion gives the same answer: 84/6 = x/15.