Learn to understand ratios and proportions in scale drawings.

Learn to use ratios and proportions with scale.

What will I learn today?

This HO gauge model train is a scale model of a historic train. A scale model is a proportional model of a three-dimensional object. Its dimensions are related to the dimensions of the actual object by a ratio called the scale factor. The scale factor of an HO

gauge model train is . 1

87

This means that each dimension of the model is of the corresponding dimension of the actual train.

187

A scale is the ratio between two sets of measurements. Scales can use the same units or different units. The photograph shows a scale drawing of the model train.

A scale drawing is a proportional drawing of an object. Scale drawings and scale models can be smaller or larger than the objects they represent.

Steps to finding scale factor:

S1: Write a ratio with the model’s dimensions over the actual object’s dimensions.

S2: Reduce the ratio to the simplest form.

Identify the scale factor.

Example 1: Finding a Scale Factor

RoomBlueprint

Length (in.)

144 18

Width (in.) 108 13.5blueprint lengthroom length

= 18

18

The scale factor is .

Write a ratio using one of thedimensions.

Simplify.

18144

=

Example 2Insert Lesson Title Here

Identify the scale factor.

Model Aircraft

Blueprint

Length (in.) 12 2

Wing span (in.)

18 3blueprint length aircraft length =

212

= 16

Write a ratio using one of the dimensions.

Simplify.

On a road map, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities if the map scale is 1.5 inches = 60 miles?

Example 3:

Let d be the actual distance between the cities.

1.560

= 7.5d

1.5d = 450

1.5d1.5

= 4501.5

d = 300

The distance between the cities is 300 miles.

Write a proportion.

Find the cross products.

Divide both sides by 1.5.

Lesson Quiz: Part I

Identify the scale factor.

Statue of Liberty Model

Height (in.) 1,824 8

1.

2.

144 inches, or 12 feet

1228

On a scale drawing, a kitchen wall is 6 inches long.

The scale factor is . What is the length of the

actual wall?

124

Lesson Quiz: Part IIInsert Lesson Title Here

3. On a road map, the distance from Green Bay toChicago is 11 cm. What is the actual distance between the cities if the map scale is 3 cm = 90 km?

330 km