7-1 Ratios and Proportions
You solved problems by writing and solving
equations.
• Write ratios.
• Write and solve proportions.
Ratio
• A ratio is a comparison of two quantities using
division.
• The ratio of quantities 𝑎 and 𝑏 can be expresses
𝑎
as 𝑎 to 𝑏, 𝑎: 𝑏, or where 𝑏 ≠ 0.
𝑏
• Ratios are usually expressed in simplest form.
• 32:18 = 16:9
𝑤𝑖𝑑𝑡ℎ 𝑜𝑓 𝑠𝑐𝑟𝑒𝑒𝑛
ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑠𝑐𝑟𝑒𝑒𝑛
=
32 𝑖𝑛
18 𝑖𝑛
=
32÷2
18÷2
=
16
9
SCHOOL The number of students who participate in
sports programs at Central High School is 520. The
total number of students in the school is 1850. Find
the athlete-to-student ratio to the nearest tenth.
To find this ratio, divide the number of athletes
by the total number of students.
0.3 can be written as
Answer: The athlete-to-student ratio is 0.3.
The country with the longest school year is China,
with 251 days. Find the ratio of school days to total
days in a year for China to the nearest tenth. (Use
365 as the number of days in a year.)
A. 0.3
B. 0.5
C. 0.7
D. 0.8
Extended Ratios
Extended ratios can be used to compare three or
more quantities.
The expression 𝑎: 𝑏: 𝑐 means
•
the ratio of the first two quantities is 𝑎: 𝑏,
•
the ratio of the last two quantities is 𝑏: 𝑐,
•
the ratio of the first and last quantities is 𝑎: 𝑐.
In ΔEFG, the ratio of the measures of the angles is
5:12:13. Find the measures of the angles.
5 or 5:12 is equivalent to ______
5x
Just as the ratio___
12x
12
or 5x:12x, the extended ratio 5:12:13 can be
written as 5x:12x:13x. Write and solve an
equation to find the value of x.
5x + 12x + 13x = 180
30x = 180
x =6
Triangle Sum Theorem
Combine like terms.
Divide each side by 30.
Answer: So, the measures of the angles are 5(6) or
30, 12(6) or 72, and 13(6) or 78.
The ratios of the angles in ΔABC is 3:5:7. Find the
measure of the angles.
A. 30, 50, 70
B. 36, 60, 84
C. 45, 60, 75
D. 54, 90, 126
Definition
• Proportion--an equation stating that
two ratios are equal.
8 2

12 3
300mi x mi

10gal 1gal
Properties of Proportions
Proportion – an equation stating that two ratios
are equal.
𝒂
𝒄
In the proportion = ,
𝒃
𝒅
the numbers 𝑎 and 𝑑 are called the extremes of
the proportion.
the numbers 𝒃 and 𝒄 are called the means of the
proportion.
𝒂 𝒄
mean
=
extreme
mean
𝒃 𝒅
Cross products - the products of the extremes
𝒂𝒅 and the product of the means 𝒃𝒄
extreme
Page 462
A.
Original proportion
Cross Products Property
Multiply.
Divide each side by 6.
y = 27.3
Answer:
y = 27.3
B.
Original proportion
Cross Products Property
Simplify.
Add 30 to each side.
Divide each side by 24.
Answer:
x = –2
A.
A. b = 0.65
B. b = 4.5
C. b = –14.5
D. b = 147
Use Proportions to Make Predictions
PETS Monique randomly surveyed 30 students from her class and
found that 18 had a dog or a cat for a pet. If there are 870 students
in Monique’s school, predict the total number of students with a
dog or a cat.
Write and solve a proportion that compares the number of students
who have a pet to the number of students in the school.
18 ● 870 = 30x
15,660 = 30x
←
Students who have a pet
←
total number of students
Cross Products Property
Simplify.
522 = x
Divide each side by 30.
Answer: Based on Monique's survey, about 522 students at
her school have a dog or a cat for a pet.
Brittany randomly surveyed 50 students and found
that 20 had a part-time job. If there are 810
students in Brittany's school, predict the total
number of students with a part-time job.
A. 324 students
B. 344 students
C. 405 students
D. 486 students
Page 463
When setting up proportions, the trick is to have all
of the same information in the numerators and all of
the same information in the denominators.
miles
gallon
or
gallons
mile
7-1 Assignment
Page 464, 10-28 even,
29-30
Show your work…