Transcript 7.1 Notes Ratios and Proportions

Warm-Up
With your new neighbor, find:
1) The ratio of people wearing glasses to those not wearing glasses in our
class (not counting teachers)
2) The ratio students wearing shoes with laces to students wearing shoes
without laces
3) The ratio of students wearing short sleeves (above elbow) to those
wearing long sleeves (below elbow)
7.1 Notes
Ratios and Proportions
Today’s Objectives:
1. Students will be able to write ratios.
2. Students will be able to write and
solve proportions.
Vocab
•
Ratio
a comparison of two quantities using
division
𝑎
• ratio of a and b: a to b, a : b, or (𝑏 ≠ 0)
𝑏
• simplest form (reduce fractions)
Example 1
a) 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.
b) 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.)
Vocab
Extended
Ratios
• used to compare three or more quantities
• a : b : c means 3 ratios:
• a : b, b : c, a : c
Example 2
a) In ΔEFG, the ratio of the measures of the angles is 5:12:13.
Find the measures of the angles.
b) The ratios of the angles in ΔABC is 3:5:7. Find the measure of
the angles.
Example 3
a. The ratio of the measures of the sides of a triangle is 4:5:7, and its
perimeter is 160 centimeters. Find the measures of each side of the triangle.
b. The ratio of the measures of the sides of a triangle is 4:7:11, and its
perimeter is 3300 meters. What are the measures of the sides of the triangle?
c. The ratio of the measures of the sides of a triangle is 5:6:9, and its
perimeter is 280 feet. What are the measures of the sides of the triangle?
Vocab
Proportion
equation stating that two ratios are equal
𝑥
4
Ex: =
3
Cross
Product
Property
To solve a proportion, cross multiply and set
products equal to each other
𝑥
4
Ex: =  𝑥 𝑐 = (4)(3)
3
Converse of
the Cross
Products
Property
𝑐
𝑐
𝑎
𝑏
If ad = bc and 𝑏 ≠ 0 and 𝑑 ≠ 0, then =
𝑐
𝑑
Example 4
Solve the following proportions.
a) 6  9
b) 4 x  5  26
18.2
y
3
6
c) 7n  1  15.5
8
2
Example 5
a) 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.
b) 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.
Summary
1. You jog 3.6 miles in 30 minutes. At that rate, how long will it
take you to jog 4.8 miles?
2. You earn $33 in 8 hours. At that rate, how much would you
earn in 5 hours?
Summary
3. An airplane flies 105 miles in ½ hour. How far can it fly in 1 ¼ hours at the
same rate of speed?
4. What is the cost of six filters if eight filters cost $39.92?
5. If one gallon of paint covers 825 sq. ft., how much paint is needed to cover
2640 sq. ft.?
Summary
6.
A map scale designates 1” = 50 miles. If the distance between two towns
on the map is 2.75 inches, how many miles must you drive to go from the
first town to the second?
7.
Bob is taking his son to look at colleges. The first college they plan to visit
is 150 miles from their home. In the first hour they drive at a rate of 60
mph. If they want to reach their destination in 2 ½ hours, what speed
must they average for the remainder of their trip?
Summary
8. Four employees can wash 20 service vehicles in 5 hours. How long would
it take 5 employees to wash the same number of vehicles?
Exit Slip
9
2
1) Solve the proportion =
27
2𝑦
2) In a triangle, the ratio of the measures of the sides is 2:3:4
and the perimeter is 72. Find the measures of the sides of the
triangle.