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section 5-7
 

Maps and Scale Drawings

 

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What You'll Learn

  1. To use proportions to solve problems involving scale

… And Why

To use maps, as in Example 2


Solving Problems Involving Scale

A scale drawing is an enlarged or reduced drawing of an object that is similar to an actual object. Maps and floor plans are smaller than the actual size. A scale drawing of a human cell is larger than the actual size.

Reading Math

On a map, the equal sign in 1 in. = 30 mi does not mean that the two quantities are equal, as it would in an equation.

A scale is the ratio that compares a length in a drawing to the corresponding length in the actual object. If a 30-mile road is 1 in. long on a map, you can write the scale of the map in these three ways:

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Example 1 Using a Scale Drawing Algebra logo

You have a scale drawing of a boat. The length of the boat on the drawing is 3 cm. What is the actual length of the boat?

Image of a scale drawing of a boat with scale 1 centimeter = 1.5 meters.Write the scale of the drawing, 1 cm = 1.5 m, as 1 centimeter over 1.5  meters. Then write a proportion in which each ratio compares centimeters to meters.

Let n represent the actual length of the boat.

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The actual length of the boat is 4.5 m.



You can use proportions and a map's scale to find actual distances.

Video Math
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Making Models

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Example 2 Real-World globe Problem Solving

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GeographyFind the actual distance from Charlotte to Winston-Salem.

  1. Use a centimeter ruler to find the map distance from Charlotte to Winston-Salem. The map distance is about 1.6 cm.
  2. Use a proportion to find the actual distance. Let n represent the actual distance.

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The actual distance from Charlotte to Winston-Salem is about 120 km.



You can use the GCF of two numbers to find the scale of a drawing or a model.

Example 3 Finding the Scale Real-World logo

Image of a model boxcar with a length of 7 inches.ModelsRefer to the model boxcar shown at the right. The actual length of a boxcar is 609 in. What is the scale of the model?

Start with the proportion scale length over  actual length  which is 7 over 609.  Divide each measure by the GCF, 7, to get 1 over 87.

The scale is 1 in. : 87 in.



  

Investigation:Making a Scale Drawing

Make a scale drawing of your classroom.

  1. Using a meter stick or yardstick, measure the classroom. Measure the length and width of the room and anything else you think you need.
  2. Choose a scale large enough to produce a good drawing, but small enough to fit on your paper.
  3. Complete your drawing. Include the scale.

PDF icon Exercises Click here to view the Exercises for this lesson.

PDF icon Investigation Click here to view the Investigation: Plan a Trip.

Course 2 iText

Page

Chapter 5
Ratios, Rates, and Proportions