1. 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.

2. Vocab
Ratio
The relation between two amounts. Can be expressed as a ration 𝑎 𝑏 .

3. 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 Find the athlete-to-student ratio to the nearest tenth.
520 : 1850 or ≈ 3.6 1

4. Vocab
Extended Ratios
 The relation between more than 2 quantities

5. 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.
5x: 12x: 13x
72° 5x
5x + 12x + 13x = 180
30x = 180
x = 6
30°
13x
12x
78°
3x: 5x: 7x
60° 5x
3x + 5x + 7x = 180
15x = 180
x = 12
84° 3x 7x
36°

6. 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?
4x + 5x + 7x = 160
16x= 160
x = 10
4x: 5x: 7x
Measures: 40, 50, 70
4x + 7x + 11x = 3300
22x= 3300
x = 150
4x: 7x: 11x
Measures: 600, 1050, 1650
5x + 6x + 9x = 280
20x= 280
x = 14
5x: 6x: 9x
Measures: 84, 70, 126

7. Vocab Proportion An equation stating two ratios are equal
Proportion
 An equation stating two ratios are equal
Cross Product Property
The product of the extremes (ad) and the products of the means (bc)
 Converse of the Cross Products Property
 If ad=bc, and b ≠ 0, then 𝑎 𝑏 = 𝑐 𝑑

8. Example 4 Solve the following proportions. a) b) c) 6∗𝑦=9∗18.2
6𝑦=163.8
𝑦=27.3
4𝑥−5 ∗6=3∗−26
24𝑥−30=−78
24𝑥=−48
𝑥=−2
(7𝑛−1)∗2=8∗15.5
24𝑥−30=−78
24𝑥=−48
𝑥=−2

9. You try!
7𝑛−1 8 =
7𝑛−1 ∗2=8∗15.5
14𝑛−2=124
𝑛=9

10. 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.
18 30 = 𝑥 870
𝑥=522
Students with cat or dog
# of total students
20 50 = 𝑥 810
𝑥=324
Students part-time job
# of total students

11. You Try!
A twinjet airplane has a length of 78 meters and a wingspan of 90 meters. A toy model is made in proportion to the real airplane. If the wingspan of the toy is 36 centimeters, find the length of the toy.
**Convert cm to m**
36 cm = .36 m
78 90 = 𝑥 .36
𝑥=.312 𝑚 𝑜𝑟 31.2 𝑐𝑚
Length
Wingspan