1. Section 7-1 Ratios and Proportions

2. Then
Now
Objectives
You solved problems by writing and solving equations.
Write ratios.
Write and solve proportions.

3. Common Core State Standards
Content Standards
G.MG.3 – Apply geometric methods to solve problems.
Mathematical Practices
7) Look for and make use of structure.
8) Look for and express regularity in repeated reasoning.
Common Core State Standards

4. Ratio: a comparison of two quantities using division.
Vocabulary

5. In Logan’s high school, there are 190 teachers and 2650 students
In Logan’s high school, there are 190 teachers and students. What is the approximate student- teacher ratio at his school?
Example 1

6. The number of students that participate in sports programs at Central High School is The total number of students in the school is Find the athlete-to-student ratio to the nearest tenth.
Example 1

7. Extended Ratio: used to compare three or more quantities.
Vocabulary

8. The ratio of the measures of the three angles in a triangles is 4:5:6
The ratio of the measures of the three angles in a triangles is 4:5:6. Find the measure of each angle.
Example 2

9. The ratio of the measures of the sides of a triangle is 3:4:6, and its perimeter is 104 feet. Find the measure of each side of the triangle.
Example 2

10. The ratio of the measures of the three angles of a triangle is 5:7:8
The ratio of the measures of the three angles of a triangle is 5:7:8. Find the measure of the smallest angle. The ratio of the measures of the sides of a triangle is 6:7:9, and its perimeter is 77 cm. Find the length of the largest side of the triangle.
Example 2

11. Proportion: An equation stating two ratios are equal
Proportion: An equation stating two ratios are equal. a and d are called the extremes of the proportion, while b and c are called the means.
Vocabulary

13. Solve each proportion.
Example 3

14. In an experiment, students netted butterflies, recorded the number with tags on their wings, and then released them. The students netted 48 butterflies and 3 of those had tagged wings. Predict the number of butterflies that would have tagged wings out of 100 netted.
Example 4

15. Monique randomly surveyed 30 students from her class and found that 18 had a dog or cat for a pet. If there are 870 students in Monique’s school, predict the total number of students with a dog or cat.
Example 4

17. p.464 #1 – 4, 9, 13, 14, 17, 19, 25 – 29, 44
Homework