Week 17, Day Four
HW # 61 - Begin the Group Exam (Put this on a new TOC)
Warm up
Evaluate the following for x = 16.
1. 3x
48
2. x
3
4
12
Evaluate the following for x = 2 .
5
1
1
3. 10x
4.
x
4
10
4
Place your EXTRA CREDIT and your warm up page in the
center of your table.
Place your OLD HW TOC in the center of the table.
Warm Up Response
24
Homework Check
Practice 5-6
Check your answers ONLINE
Proportions Practice- see hard copy (use
document camera)
• Area Volume Ratios worksheet
• (we will work on this next week)
Vocabulary
scale drawing
scale model
scale
scale factor
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.
Additional Example 1: Finding Actual
Measurements
Under a 1000:1 microscope view, an amoeba appears to have a
length of 8 mm. What is its actual length?
1000 = 8 mm
1
x mm
1000  x = 1  8
x = 0.008
Write a proportion using the scale.
Let x be the actual length of the
amoeba.
The cross products are equal.
Solve the proportion.
The actual length of the amoeba is 0.008 mm.
Check It Out! Example 1
Under a 10,000:1 microscope view, a fiber appears to have
length of 1 mm. What is its actual length?
10,000 = 1 mm
1
x mm
10,000  x = 1  1
x = 0.0001
Write a proportion using the scale. Let
x be the actual length of the fiber.
The cross products are equal.
Solve the proportion.
The actual length of the fiber is 0.0001 mm.
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 cm = 2 cm
xm
8m
Set up proportion using
1  8 = x 2
8 = 2x
Find the cross products.
4=x
Divide both sides by 2.
The scale is 1 cm:4 m.
scale length .
actual length
Reading Math
The scale a:b is read “a to b.” For example, the scale 1
cm:4 m is read “one centimeter to four meters.”
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 cm = 4 cm
xm
12 m
1  12 = x  4
12 = 4x
3=x
Set up proportion using
Find the cross products.
Divide both sides by 4.
The scale is 1 cm:3 m.
scale length .
actual length
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.
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?
2 in. = 2 in. = 1 in. = 1
3 ft
36 in.
18 in.
18
The scale factor for the model is
1 = h in.
18 324 in.
Find the scale factor.
1
. Now set
18 up a proportion.
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.
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?
4 in. = 4 in. = 1 in.
= 1
Find the scale factor.
2 ft
24 in.
6 in.
6
1 up a proportion.
The scale factor for the model is . Now set
6
1
h in.
=
6
288 in.
288 = 6h
48 = h
Convert: 24 ft = 288 in.
Find the cross products.
Divide both sides by 6.
The height of the model is 48 in.
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.
5 cm
0.0000001 mm
50 mm
= 0.0000001
mm
= 500,000,000
The scale factor for the model is 500,000,000. This means the
model is 500 million times larger than the actual chain.
Additional Example 4 Continued
500,000,000
1
cm
= 20
x cm
500,000,000x = 1(20)
x = 0.00000004
Set up a proportion.
Find the cross products.
Divide both sides by
500,000,000.
The length of the DNA chain is 4  10-8 cm.
Check It Out! Example 4
A model was built using the scale 2 cm:0.01 mm. If the model is 30
cm long, what is the length of the actual object?
Find the scale factor.
2 cm
0.01 mm
=
20 mm
0.01 mm
= 2,000
The scale factor for the model is 2,000. This means the actual
object is two thousand times larger than the model.
Check It Out! Example 4 Continued
2,000
1
=
30 cm
x cm
2,000x = 1(30)
x = 0.015
Set up a proportion.
Find the cross products.
Divide both sides by 2,000.
The length of the actual object is 1.5  10-2 cm.
Lesson Quiz
1
1. Using a 4 in. = 1 ft scale, how long would a
drawing of a 22 ft car be? 5.5 in.
2. What is the scale of a drawing in which a 9 ft
wall is 6 cm long? 1 cm = 1.5 ft
3. The height of a person on a scale drawing is
4.5 in. The scale is 1:16. What is the actual
height of the person? 72 in.