Module # 1 of 15 Ratios & Proportions 11th Grade - Southwest ISD

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Module # 1 of 15
Ratios & Proportions
11 th Grade
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ooked
11th
Objective 7, 8, 9
Module # 5 of 15
O
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assing TAKS

POP
VOCABULARY ALERT
Ratio - a comparison of two quantities by division
Example: boys to girls;
apples
oranges
; baseballs:footballs
Proportion – two ratios that are equal
boys
girls
males
females
Example: ;
5
10
1
2
3

LOCK
Write a ratio for each situation.
1) 5 homework assignments to 3 tests
2) 6 wins to 8 losses
3) 15 free throw shots to 10 three
point shots
4
Check →

LOCK
Write a ratio for each situation.
1) 5 homework assignments to 3 tests
2) 6 wins to 8 losses
3) 15 free throw shots to 10 three
point shots
6
8
15
10
5
3
5

To solve proportions, just cross multiple and divide
13 x
7 x
52
104
14
34
x
(13)(104)
52
x
(7)(34)
14
x
26
x
17
6

LOCK
Solve each proportion for x
1)
12 x 2)
16
48
18
36
2
x
7
Check →

LOCK
Solve each proportion for x
1)
12 x 2)
18 36
16
2
48
x
x
(12)(36)
18
x
(2)(48)
16
x
24
x
6
8

POP
Proportions can be used to solve
a variety different problems -
questions about scale drawings,
percents, surveys, similar
figures, and many more.
9

A watch loses 3 minutes every 24 hours. How
much time will it lose in 2 hours?
This problem is comparing minutes to hours.
minutes
hours
3
24
x
2
(3)(2)
6
x
24
24
.25minutes per hour
10

LOCK
If a wheel spins at a rate of 36 revolutions per
minute, how many revolutions per hour does the
wheel spin? (Hint: how many minutes in an hour)
What is this problem comparing?
x
(
)(
)
revolutions per hour
11
Check →

LOCK
If a wheel spins at a rate of 36 revolutions per
minute, how many revolutions per hour does the
wheel spin? (Hint: how many minutes in an hour)
revolution s
minutes
36
1
x
60
x
(36)(60)
1
2160 , revolutions per hour
12

LOCK
The athletic budget of $65,000 at Central East High School is allocated proportionally to
male and female athletic teams according to the student population by gender. If there
are 400 female and 475 male students enrolled at Central East High School, what is the
amount allocated to female athletics? (Hint: how total students are there?)
What is this problem comparing?
x
(
)(
)
13
Check →

LOCK
The athletic budget of $65,000 at Central East High School is allocated proportionally to
male and female athletic teams according to the student population by gender. If there
are 400 female and 475 male students enrolled at Central East High School, what is the
amount allocated to female athletics?
How many total students are
there? 400 + 475 = 875
female students
totalstudents
400
875
x
$65,000
x
(400)(65000)
875
$29,714.29
14
Check →

VOCABULARY ALERT
POP
Percent - a special ratio that compares a number to
100. The word percent means per hundred or out of
100.
Proportions involving percents will most often have
100% in the denominator of one of the ratios.
15

A couple bought a house and calculated that they would pay 30%
of their combined monthly income of $5,569.75 toward the
monthly mortgage payment on the house. Approximately how
much will the couple pay for their monthly mortgage payment?
mortgage
payment
totalincome
x
5,569.75
30%
100%
Remember with
percents to put 100%
on the bottom of one
the ratios.
16

A couple bought a house and calculated that they would pay 30%
of their combined monthly income of $5,569.75 toward the
monthly mortgage payment on the house. Approximately how
much will the couple pay for their monthly mortgage payment?
mortgage
payment
x
30%
totalincome
5,569.75
100%
(30)(5,569.75)
16,7092
x
$1,670.93
100
100
17

LOCK
Mr. Salinas, a real estate agent, received a 5% commission on the
selling price of a house. If his commission was $6,975, what was
the selling price of the house?
commission
total cost
What needs to go at
the bottom of this
percent problem?
x
(
)(
)
$
18
Check →

LOCK
Mr. Salinas, a real estate agent, received a 5% commission on the
selling price of a house. If his commission was $6,975, what was
the selling price of the house?
commission
total cost
$6,975
x
5%
100%
x
(6,975)(100)
5
$139,500
19

POP
VOCABULARY ALERT
Similar - two figures that are the same shape but not
the same size; the side lengths are proportional
Example:
20

Kate has 2 similar triangular pieces of paper, as shown below.
Using the dimensions given, find the approximate length of the
side labeled p.
18cm 12cm
11cm
p
(12)(11)
p 7. 3cm
18
21

LOCK
If ΔTSR is similar to ΔTNM, what is the length of x?
x
x
(
)(
)
22
Check →

LOCK
If ΔTSR is similar to ΔTNM, what is the length of x?
120
240
70
x
x
(240)(70)
120
140
23

POP
Proportions can also be used to
solve problems involving scale
drawings, maps, or blueprints.
24

Olga plans to take a trip from her house in San Marcos, Texas, to a friend’s house in
Zapata, Texas. She measured the distance between the two places on a map and
found it to be 8 inches. If the scale on the map is ½ inch represents 14 miles, what is
the actual distance in miles between the two places?
This problem is comparing inches to miles.
inches
miles
.5in 8in
14mi
x
(8)(14)
x 224mi
.5
25

LOCK
A blueprint of a house plan uses a scale in which ¼ inch equals 1 foot. If the
length of one side of the house is 65 feet, how many inches will the length be
on the blueprint?
What is this problem comparing?
x
x
(
)(
)
26
Check →

LOCK
A blueprint of a house plan uses a scale in which ¼ inch equals 1 foot. If the
length of one side of the house is 65 feet, how many inches will the length be
on the blueprint?
inches
feet
.25in
1ft
x
65
ft
(65)(.25)
x 16. 25in
1
27

POP
You can solve problems involving
predictions or surveys using
proportions.
28

VOCABULARY ALERT
POP
Prediction: : foretell on the basis of observation,
experience, or scientific reason; a statement made
about the future
Sample: a small part of something intended as
representative of the whole
Survey: results from a questionaire
29

The student council at Southwest High School is planning a school-wide trip.
Skateland West will provide a discounted rate if at least 250 of the school’s
3000 students sign up for the trip. The student council surveyed a random
sample of students and asked which of the following activities the students
would prefer as a school trip. Based on the data in the survey, how many
students are likely to choose skating?
This problem is comparing the students
who were surveyed to the entire school to
make a prediction.
20 + 30 +110 +40 = 200
skating
totalstudents
20
200
x
3000
30

The student council at Southwest High School is planning a school-wide trip.
Skateland West will provide a discounted rate if at least 250 of the school’s
3000 students sign up for the trip. The student council surveyed a random
sample of students and asked which of the following activities the students
would prefer as a school trip. Based on the data in the survey, how many
students are likely to choose skating?
skating
totalstudents
20
200
x
3000
x
(20)(3000)
200
300
31

LOCK
A high school is changing its school colors. Melanie surveyed 50 students, and each
student voted for one color combination. Some of the results are shown in the table
below.
According to the table, which is the best
prediction of the number of students who will
choose blue and gold if there are 1250
students enrolled at the high school?
A 350 B 900
C 486 D 98
Check →

LOCK
A high school is changing its school colors. Melanie surveyed 50 students, and each
student voted for one color combination. Some of the results are shown in the table
below.
According to the table, which is the best
prediction of the number of students who will
choose blue and gold if there are 1250
students enrolled at the high school?
How many of those surveyed want blue and
gold.
50-12-6-8-10 = 14 students surveyed want blue
and gold

LOCK
A high school is changing its school colors. Melanie surveyed 50 students, and each
student voted for one color combination. Some of the results are shown in the table
below.
14
According to the table, which is the best
prediction of the number of students who will
choose blue and gold if there are 1250
students enrolled at the high school?
14 x
50 1250
(14)(1250)
50
350

POP
LOCK
AND
DROP
Answer the following questions and your
math teacher will check them for you.
35

The ratio of juniors to seniors enrolled in
technology classes is 9 to 8. If the total
number of juniors and seniors enrolled in
these classes is 51, which of these best
represents the percent of students enrolled in
technology classes who are seniors?
What is the length of OP?
A. 27%
B. 24%
C. 53%
D. 47%
36

Harry wants to buy two new tires for his car. The Tire Shop has the
tires Harry wants. They are advertised as follows: “Buy 1 tire at full
price, $45, and get the second for 25% off.” Another store, Tires
Unlimited, has the same tires listed for $42.50 each but is having a
10%-off sale this week.
At which of these two tire stores should Harry buy his tires to save
money?
How much money will he save?
37

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