What will I learn today?
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Transcript of What will I learn today?
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
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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