So far, we've explored how ratios and proportions are used in architecture, interior design, and cartography. Without ratios and proportions, these jobs would be much more difficult to do. Even if you do not choose a career in one of these fields, you are likely to need knowledge of ratios and proportions at some point in your life, for some type of job.
Review the steps below for solving problems of proportion. Then see if you can solve the problems on the flash cards at the bottom of this page.
| Read the question carefully and identify what the problem is asking you to find. |
| Identify the important ratios in the problem. |
| Write the proportion that will help you solve the problem. |
| Solve the proportion using cross multiplication. |
In your notebook, solve the problem on each of these cards. After solving each problem, click the card to check your work. Look back at the steps at the top of this page if you need a reminder.
An architect is drawing up plans for a building. She is working with a 2.25:1 inch to foot ratio. If a room is twelve feet wide, how many inches does the architect need to draw in her plan for the room?
Let x equal the width of the room in inches.
\(\small\mathsf{ \frac{2.25}{1} = \frac{x}{12} }\)
\(\small\mathsf{ x = 27 }\)
The architect will need to draw the width of the room to be 27 inches.
A roof has a rise to span ratio of 1:3. If the span is 6.6 m, how high is the roof? (What is the rise?)
Let x equal the rise of the roof in meters.
\(\small\mathsf{ \frac{1}{3} = \frac{x}{6.6} }\)
\(\small\mathsf{ 3x = 6.6 }\)
\(\small\mathsf{ x = 2.2 }\)
The roof will be 2.2 meters high.
A cartographer is creating a road map of a city. He has made a key that says that each inch on his map equals ten miles of real road. If the city measures 35 miles from north to south, how many inches is that on the map?
Let x equal the number of inches on the map.
\(\small\mathsf{ \frac{1}{10} = \frac{x}{35} }\)
Cross multiply: \(\small\mathsf{ 10x = 35 }\)
Solve for x: \(\small\mathsf{ x = 3.5\text{ inches} }\)
Cards remaining:
