1. Lesson 6-1 Proportions

2. Objectives Write ratios Use properties of proportions

3. Vocabulary Ratio: a comparison of two quantities (a:b) Proportion: an equation stating that two ratios are equal Extremes of the proportion: the outer numbers in the proportion Means of the proportion: the inner numbers in the proportion Cross product of means = to cross product of extremes

4. The total 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. Answer: The athlete-to-student ratio is 0.3. To find this ratio, divide the number of athletes by the total number of students. Example 1 or 3:10

5. 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.) Answer: 0.7 Example 1b How many days does the state of Virginia require you to be in school? Answer: 180 or 0.5 (to nearest tenth)

6. In a triangle, the ratio of the measures of three sides is 5:12:13, and the perimeter is 90 centimeters. Find the measure of the shortest side of the triangle. A 15 cm B 18 cm C 36 cm D 39 cm We can rewrite 5:12:13 as 5x:12x:13x and use those measures for the sides of the triangle. Write an equation to represent the perimeter of the triangle as the sum of the measures of its sides. Multiple-Choice Test Item Perimeter Combine like terms.

7. In a triangle, the ratio of the measures of three sides is 3:4:5, and the perimeter is 42 feet. Find the measure of the longest side of the triangle. A 10.5 ft B 14 ft C 17.5 ft D 37 ft Answer: C Multiple- Choice Test Item

8. Original proportion Cross products Multiply. Answer: 27.3 Solve Divide each side by 6. Example 3

9. Answer: 4.5 Answer: 9 Solve each proportion. a. b. Example 3b & c

10. A boxcar on a train has a length of 40 feet and a width of 9 feet. A scale model is made with a length of 16 inches. Find the width of the model. Because the scale model of the boxcar and the boxcar are in proportion, you can write a proportion to show the relationship between their measures. Since both ratios compare feet to inches, you need not convert all the lengths to the same unit of measure. Example 4a Substitution Cross products Multiply. Divide each side by 40. Answer: The width of the model is 3.6 inches.

11. Two large cylindrical containers are in proportion. The height of the larger container is 25 meters with a diameter of 8 meters. The height of the smaller container is 7 meters. Find the diameter of the smaller container. Answer: 2.24 m Example 4b

12. Summary & Homework Summary: –A ratio is a comparison of two quantities –A proportion is an equation stating that two ratios are equal –Recipes are “scaled up” or “scaled down” to fit the amount required Homework: –pg 285-6: 4, 10, 13, 14, 18, 21, 28-31