1. Preview
Warm Up
California Standards
Lesson Presentation

2. Warm Up Write each fraction in simplest form. 4 48 1 12 9 135 1 15 2.1.
Convert the following measurements.
inches = feet 16
feet = inches
222
inches = feet 27

3. California
Standards
NS Use proportions to solve problems (e.g., determine the value of N if T = , find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse.
4 7
N 21

4. Vocabulary
scale model
scale factor
scale
scale drawing

5. This HO gauge model train is a scale model of a historic train
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. 1 87

6. A scale is the ratio between two sets of measurements
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 two-dimensional drawing of an object. Both scale drawings and scale models can be smaller or larger than the objects they represent.

7. Additional Example 1: Finding a Scale Factor
Identify the scale factor.
You can use the lengths or widths to find the scale factor.
Room
Blueprint
Length (in.)
144 18
Width (in.)
108
13.5
blueprint length
room length 18
144 1 8 = =
Write a ratio. Then simplify.
blueprint width
room width
13.5
108 1 8 = =
Write a ratio. Then simplify. 1 8
The scale factor is .

8. Identify the scale factor.
Check It Out! Example 1
Identify the scale factor.
Model Aircraft
Blueprint
Length (in.) 12 2
Wing span (in.) 18 3
blueprint length
aircraft length 2 12 1 6 = =
Write a ratio. Then simplify.
blueprint wing span
aircraft wing span 3 18 1 6 = =
Write a ratio. Then simplify.
The scale factor is . 1 6

9. Additional Example 2: Using Scale Factors to Find Unknown Lengths
A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches.
The scale factor is . Find the size of the original photograph to the nearest tenth of an inch. 5 1
poster
photo 5 1
Think: = 36 l 5 1 =
Write a proportion to find the length l.
5l = 36
Find the cross products.
l = 7.2
Divide.

10. Additional Example 2 Continued
A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches.
The scale factor is . Find the size of the photograph. 5 1
poster
photo 5 1
Think: =
20.5 w 5 1
Write a proportion to find the width w. =
5w = 20.5
Find the cross products.
w = 4.1
Divide.
The photo is 7.2 in. long and 4.1 in. wide.

11. factor is . Find the size of the dollhouse. 1.5 1
Check It Out! Example 2
Mary’s father made her a dollhouse which was modeled after the blueprint of their home. The blueprint is 24 inches by 45 inches. The scale
factor is Find the size of the dollhouse.
1.5 1
dollhouse
blueprint
1.5 1
Think: = l 45 =
1.5 1
Write a proportion to find the length l.
Find the cross products.
l = 45 · 1.5
l = 67.5
Multiply.

12. Check It Out! 2 Continued
Mary’s father made her a dollhouse which was modeled after the blueprint of their home. The blueprint is 24 inches by 45 inches. The scale
factor is Find the size of the dollhouse.
1.5 1
dollhouse
blueprint
1.5 1
Think: = w 24
1.5 1
Write a proportion to find the width w. =
w = 24 · 1.5
Find the cross products.
w = 36
Multiply.
The dollhouse is 67.5 inches long and 36 inches wide.

13. Additional Example 3: Measurement Application
On a road map with a scale of 1.5 inches = 60 miles, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities?
Let d be the actual distance between the cities.
1.5 60
7.5 d =
Write a proportion.
1.5 · d = 60 · 7.5
Find the cross product.
1.5d = 450
Multiply.
1.5d
1.5
450
1.5 =
Divide both sides by 1.5.
d = 300
The distance between the cities is 300 miles.

14. Check It Out! Example 3
On a road map with a scale of 1 inch = 50 kilometers, the distance between Dallas and Houston is 7 inches. What is the actual distance between the two cities?
Let d be the actual distance between the cities. 1 50 7 d =
Write a proportion.
1 · d = 50 · 7
Find the cross products.
1d = 350
Multiply.
d = 350
The distance between the cities is 350 kilometers.