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Proportions
Using Equivalent Ratios
What is a proportion?
 A proportion is an equation with a ratio on
each side. It is a statement that two ratios
are equal.
 3
4
6
= 8 is an example of a proportion.
Read each proportion.
Why is each one a proportion?
 a) 5





10
1 = 2
"5 is to 1 as 10 is to 2."
5 is five times 1, as 10 is five times 2.
b) 2
6
8 = 24
"2 is to 8 as 6 is to 24."
2 is a fourth of 8, as 6 is a fourth of 24.
c) 75
3
100 = 4
"75 is to 100 as 3 is to 4."
75 is three fourths of 100, as 3 is three fourths of 4.
Proportion problem
from the 2003 TAKS
If the ratio of boys to girls in the sixth-grade is 2 to 3,
which of these show the possible numbers of the boys
and girls in the chorus?
A. 20 boys, 35 girls
B. 24 boys, 36 girls
C. 35 boys, 20 girls
D. 36 boys, 24 girls
Solving a Proportion.
 When one of the four numbers in a proportion is
unknown, setting up equivalent ratios may be
used to find the unknown number.
 This is called solving the proportion. Question
marks or letters are frequently used in place of
the unknown number.
Example:
1
n
 Solve for n: 2 = 4
Solve each proportion.
4
n
=
3
5
9
.
9
=
2
7
10
9
n
12
=
=
8
9
n
2
12
18
n
4
=
=
18
n
n
2
Conversion Ratios
 A conversion ratio is a fraction where the
numerator and denominator express the
same quantity using different units.
 1 hr
1 yd
1T
60 min
3 ft
2000 lb
 Note that since each of these examples
has the same quantity in both the
numerator and the denominator.
 We can use conversion ratios in a
proportion to solve conversion problems.
Use Proportions to Solve
Conversion Problems

Setting up a proportion to solve a conversion
problem needs to be written carefully.
 Example:
12yd = ____ft
1. Write a conversion ratio for the units given in the
problem.
2. Then write the information in the problem as a ratio.
3. Solve the proportion
(Hint: Label both ratios in your proportion)
12 yd
1 yd
3 ft
=
n ft
Rate
A rate is a ratio that expresses how long it takes to
do something, such as traveling a certain
distance. To walk 3 kilometers in one hour is to
walk at the rate of 3 km/h.
The fraction expressing a rate has units of
distance in the numerator and units of time in
the denominator.
Problems involving rates typically involve setting
two ratios equal to each other and solving for an
unknown quantity, that is, solving a proportion.
Use Proportions to Solve Rate Problems
Juan runs 4 km in 30 minutes. At that rate, how far
could he run in 45 minutes?
 Give the unknown quantity the name n. In this
case, n is the number of km Juan could run in 45
minutes at the given rate.
 We know that running 4 km in 30 minutes is the
same as running n km in 45 minutes; that is, the
rates are the same.
 So we have the proportion
4km = n km
30min
45min
Two Rate Problems
 The Browns averaged 55 miles per hour
on their vacation. How many miles did
they travel in four days?
 Sharon rode her bicycle a total of 36 km at
a rate of 9 km per hour. Hour long did she
ride?
Proportion problem
from the 2003 TAKS
Corinne’s group was responsible for painting
windows on the set of the school play. The
group painted 18 windows in 90 minutes. If they
continued painting at this rate, how many
windows would they paint in 3 hours?