Learn to understand ratios and proportions in scale drawings. Learn to use ratios and proportions with scale.

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Learn to understand ratios and proportions in
scale drawings. Learn to use ratios and
proportions with scale.
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Insert Lesson Title Here
Vocabulary
scale model scale factor scale scale drawing
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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. Both scale drawings and scale models can
be smaller or larger than the objects they
represent.
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Additional Example 1 Finding a Scale Factor
Identify the scale factor.
Room Blueprint
Length (in.) 144 18
Width (in.) 108 13.5
blueprint length room length
Write a ratio using one of the dimensions.

1 8

Simplify.
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Insert Lesson Title Here
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
Write a ratio using one of the dimensions.

1 6

Simplify.
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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
photograph.
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.
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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.
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Check It Out Example 2
Marys 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
Write a proportion to find the length l.
Find the cross products.
l 45 1.5
l 67.5
Multiply.
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Check It Out 2 Continued
Marys 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
Write a proportion to find the width w.
1.5 1

w 24 1.5
Find the cross products.
w 36
Multiply.
The dollhouse is 67.5 inches long and 36 inches
wide.
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Additional Example 3 Measurement Application
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?
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 products.
1.5d 450
Multiply.
450 1.5
1.5d 1.5

Divide both sides by 1.5.
d 300
The distance between the cities is 300 miles.
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Check It Out Example 3
On a road map, the distance between Dallas and
Houston is 7 inches. What is the actual distance
between the cities if the map scale is 1 inch
50 kilometers?
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.