Warm Up

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Preview
Warm Up
California Standards
Lesson Presentation
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Warm Up Evaluate the following for x 16. 1.
3x 2. x Evaluate the following for x
. 3. 10x 4. x
48
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Vocabulary
scale drawing scale model scale scale factor
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A scale drawing is a two-dimensional drawing of
an object that is proportional to the object.
A scale model is a three-dimensional model that
is proportional to the object.
A scale gives the ratio of the dimensions in the
drawing to the dimensions of the object. All
dimensions are reduced or enlarged using the same
scale. Scales can use the same units or different
units.
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Additional Example 1 Finding Actual
Measurements
Under a 10001 microscope view, an amoeba appears
to have a length of 8 mm. What is its actual
length?
1000 ? x 1 ? 8
The cross products are equal.
Solve the proportion.
x 0.008
The actual length of the amoeba is 0.008 mm.
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Check It Out! Example 1
Under a 10,0001 microscope view, a fiber appears
to have length of 1 mm. What is its actual length?
10,000 ? x 1 ? 1
The cross products are equal.
x 0.0001
Solve the proportion.
The actual length of the fiber is 0.0001 mm.
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Additional Example 2 Using Proportions to Find
Unknown Scales
A. The length of an object on a scale drawing is
2 cm, and its actual length is 8 m. The scale is
1 cm __ m. What is the scale?

1 ? 8 x ? 2
Find the cross products.
8 2x
4 x
Divide both sides by 2.
The scale is 1 cm4 m.
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Check It Out! Example 2
The length of an object on a scale drawing is 4
cm, and its actual length is 12 m. The scale is 1
cm __ m. What is the scale?

1 ? 12 x ? 4
Find the cross products.
12 4x
Divide both sides by 4.
3 x
The scale is 1 cm3 m.
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The ratio of a length on a scale drawing or model
to the corresponding length on the actual object
is called the scale factor. When finding a scale
factor, you must use the same measurement units.
You can use a scale factor to find unknown
dimensions.
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Additional Example 3 Using Scale Factors to Find
Unknown Dimensions
A model of a 27 ft tall house was made using a
scale of 2 in.3 ft. What is the height of the
model?
Find the scale factor.

Convert 27 ft 324 in.
324 18h
Find the cross products.
18 h
Divide both sides by 18.
The height of the model is 18 in.
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Check It Out! Example 3
A model of a 24 ft tall bridge was made using a
scale of 4 in.2 ft. What is the height of the
model?
Find the scale factor.

Convert 24 ft 288 in.
288 6h
Find the cross products.
48 h
Divide both sides by 6.
The height of the model is 48 in.
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Additional Example 4 Life Science Application
A DNA model was built using the scale 5 cm
0.0000001 mm. If the model of the DNA chain is 20
cm long, what is the length of the actual chain?
Find the scale factor.
The scale factor for the model is 500,000,000.
This means the model is 500 million times larger
than the actual chain.
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Additional Example 4 Continued

Set up a proportion.
500,000,000x 1(20)
Find the cross products.
Divide both sides by 500,000,000.
x 0.00000004
The length of the DNA chain is 4 ? 10-8 cm.
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Check It Out! Example 4
A model was built using the scale 2 cm0.01 mm.
If the model is 30 cm long, what is the length of
the actual object?
Find the scale factor.
The scale factor for the model is 2,000. This
means the actual object is two thousand times
larger than the model.
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Check It Out! Example 4 Continued

Set up a proportion.
2,000x 1(30)
Find the cross products.
Divide both sides by 2,000.
x 0.015
The length of the actual object is 1.5 ? 10-2 cm.
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Lesson Quiz
1. Using a in. 1 ft scale, how long would a
drawing of a 22 ft car be? 2. What is the scale
of a drawing in which a 9 ft wall is 6 cm
long? 3. The height of a person on a scale
drawing is 4.5 in. The scale is 116. What is
the actual height of the person?
5.5 in.
1 cm 1.5 ft
72 in.