Exercise
Write in fraction form:
2 : 7 as 6 : 21. 2 = 6
7
21
What are the extremes? 2; 21
What are the means? 7; 6
Does the product of the
extremes equal the product of
the means? What is the
product? yes; 42
Exercise
Use the rule for dividing
rational numbers to find the
quotient.
2
2 × 1 = 1
3
3 50 75
50
Scale
The scale for a drawing or
map is the ratio of the
drawing’s length to the
actual length.
Scale Drawing
A scale drawing is a
drawing in which all of the
lengths are at the same
scale, or ratio, to the actual
lengths of the object.
A scale is a ratio.
1 in.
1 in.
1
=
=
10 ft.
120 in. 120
1
of
actual
size
120
Example 1
Find the length of a bridge in
a drawing if the scale is
1 cm : 5 m and the actual
length is 27 m.
Let b = the length of the
bridge in the drawing.
1 = b
5b = 27 b = 5.4 cm
5
27
5
5
Example 2
The distance between two
towns on a map is 3.6 cm.
The scale on the map is
2 cm : 15 km. What is the
actual distance between the
towns?
Let n = the actual distance
between the two towns.
The distance between two
towns on a map is 3.6 cm.
The scale on the map is
2 cm : 15 km. What is the
actual distance between the
towns?
2n = 54
2 = 3.6
15
n
2
2
n = 27 km
Example 3
Find the distance from
Carville to Danville.
5 cm
Carville
Danville
scale – 2 cm : 25 km
2 = 5
25 n
2n = 125 n = 62.5 km
2
2
Example
If a model airplane is
constructed on a 1 in. : 25 ft.
scale, what is the actual
length of the airplane if the
length of the model is 9 in.?
225 ft.
Example
If a map is drawn on a
1 in. : 50 mi. scale, what is the
distance between towns if the
distance on the map is 2.5 in.?
125 mi.
Example
How far apart on a map with a
scale of 1 in. : 50 mi. should
two towns be drawn if they
are actually 275 mi. apart?
5.5 in.
Example 4
A map is to be made with a
scale of 1 in. to 40 mi. How far
apart will two cities appear on
the map if they are actually 55
mi. from each other?
Let n = the map distance.
1 = n 40n = 55 n = 1 3 in.
40 55 40
8
40
Example 5
Find the scale used if two
cities that are 60 mi. apart
3
appear on a map in. apart.
4
3
13
3
1
1
4
x
÷ 60 =
=
4
4
80
60
20
60 mi.
The scale is 1 in. : 80 mi.
Example
If the circumference of the
earth is about 25,000 mi.,
what should be the scale of a
globe if it is to have a
circumference of 2.5 ft.?
30 in. : 25,000 mi.
1 in. : 833.33 mi.
Example
If that same globe has relief
(e.g. it is raised where there
are mountains), then how
high should Mt. Everest be
raised on the globe if it is
29,000 ft. high? 0.006 in.
Example
A blueprint of a house is
drawn to a scale of 1 in. : 5 ft.
If a bedroom is 10 ft. by 12 ft.,
what are its dimensions on
the blueprint? 2 in. by 2.4 in.
Example
In the science classroom, which
measures 20 ft. by 20 ft., the
teacher wishes to hang a scale
model of the solar system from
the ceiling. She plans to hang the
sun in the center of the room and
Neptune, which is 2.8 billion mi.
from the sun, in a corner 14 ft.
away. Determine the scale of the
model.
1 ft : 0.2 billion mi.
Example
How far from the center of the
room should Earth be placed
if it is about 93 million mi.
from the sun? 0.465 ft.
Example 6
If a 2.5 in. x 3.5 in. photo is to
be enlarged to 5 in. x 7 in.,
what enlargement setting
would be used?
Let p = the % enlargement.
2.5p = 5
200%
2.5 2.5
enlargement
p=2
Example 7
A 10 cm x 16 cm table of data
is reduced using a copier
setting of 67%. What are the
dimensions of the new table?
10(0.67) = 6.7 cm
16(0.67) = 10.7 cm
6.7 cm x 10.7 cm
Example 8
If a picture in a book is
1
labeled
and an object in
30
the photo is 5 in. wide, how
wide is the real object?
30 x 5 in. = 150 in.
150 ft. = 12.5 ft. wide
12
Example
Find the size of a 3 in. by 5 in.
photo if it is enlarged 250%.
7.5 in. by 12.5 in.
Example
What should the enlargement
of a 3 in. by 4 in. photograph
be if you wish to place in on
9 in. by 12 in. paper? 300%