1. 7-2 Ratio and Rate Problems Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 7-2 Ratio and Rate Problems Warm Up Find the unit rate. 1. 16 miles in 4 hours 2. 3 oranges for $2.40 3. 3 bottles for $0.93 4. 6 DVDs for $36.60 4 mi/h $0.80 per orange $0.31 per bottle $6.10 per DVD

3. 7-2 Ratio and Rate Problems Problem of the Day There are 4 ounces in a gill. There are 4 gills in a pint. There are 8 pints in a gallon. How many ounces are the same as the total of 3 gallons, 3 pints, 3 gills, and 3 ounces? 447

4. 7-2 Ratio and Rate Problems MA.6.A.2.1 Use reasoning about multiplication and division to solve ratio and rate problems. Also MA.6.A.2.2 Sunshine State Standards

5. 7-2 Ratio and Rate Problems Additional Example 1A: Finding Equivalent Ratios and Rates Use a table to find three equivalent ratios or rates. A. The ratio of girls to boys in a class is. 7 6 Original Ratio 6 26 36 4 7 27 37 4 Multiply the numerator and the denominator by 2, 3, and 4. The ratios,,, and are equivalent. 6 7 __ 12 14 ___ 18 21 ___ 24 28 ___ 1218 24 14 21 28 6 7 __

6. 7-2 Ratio and Rate Problems Multiplying by 2, 3, and 4 will give you three equivalent ratios, but there are many other equivalent ratios that are correct. Helpful Hint

7. 7-2 Ratio and Rate Problems Additional Example 1B: Finding Equivalent Ratios and Rates Use a table to find three equivalent ratios or rates. B. Samantha walks at a rate of. 60 3 Original Rate 3 23 3 4 60 260 360 4 Multiply the numerator and the denominator by 2 3, and 4. 6 9 12 120 180 240 3 miles 60 minutes _________ The ratios,,, and are equivalent. 3 60 ___ 9 120 ___ 180 ___ 240 ___ 6 12

8. 7-2 Ratio and Rate Problems Check It Out: Example 1A Find three equivalent ratios or rates. A. The ratio of apples to oranges in a fruit bowl is 10 6 ___ 15 9 ___ 20 12 ___ 5353 Possible answer : : ; ;.

9. 7-2 Ratio and Rate Problems Check It Out: Example 1B Find three equivalent ratios or rates. A. Angela drove at an average rate of. 210 6 ___ 140 4 ___ 70 2 ___ Possible answer : : ; ; 280 miles 8 hours ________

10. 7-2 Ratio and Rate Problems Additional Example 2: Comparing Rates The cost of each additional minute over 500 minutes on Jill's cell phone plan is. Which person's cell phone plan has the same rate for additional minutes over 500 minutes? NameRate Allison Juan Zach $6.50 24 min $3.25 12 min $12.00 48 min $0.25 1 min Find rates equivalent to. $0.25 1 min

11. 7-2 Ratio and Rate Problems Additional Example 2: Comparing Rates The cost of each additional minute over 500 minutes on Jill's cell phone plan is Which person's cell phone plan has the same rate for additional minutes over 500 minutes? Original Rate $0.25 12 $0.25 24 $0.25 48 1 121 241 48 Zach's rate of is equivalent to Jill's rate. Cost Minutes $0.25 $0.25 1 min 1 12 24 48 $3.00$6.00$12.00 $12.00 48 min

12. 7-2 Ratio and Rate Problems Check It Out Example 2 Plane W traveled at an average speed of. Which plane traveled at the same rate as plane W? PlaneRate X Y Z 750 miles 2 hours 750 miles 1 hour 2200 miles 3 hours 3250 miles 4 hours

13. 7-2 Ratio and Rate Problems Check It Out Example 2 continued 1 750 = 750. 2 _______ 1. 2 = 2 1500 _______ which is the same as plane X

14. 7-2 Ratio and Rate Problems Additional Example 3: Application Several groups of friends are going to take a shuttle bus to the park. It costs $24 for a group of 12 people to ride the bus. How much will a group of 15 friends pay? Find the unit rate. 24 ÷ 12 = 2 Divide the bus fare by the number in each group to find the amount paid per person. 2 15 = 30 Multiply the unit rate by 15 to find the rate for 15 people. A group of 15 friends will pay $30 in bus fare.

15. 7-2 Ratio and Rate Problems Check It Out: Additional Example 3A Several groups of friends are going to take a shuttle bus to the park. It costs $40 for a group of 10 people to ride the bus. How much will a group of 8 friends pay? $40 ÷ 10 $4 $4 10 ÷ 10 1 1 = 8 = $32

16. 7-2 Ratio and Rate Problems Check It Out: Additional Example 3B Groups of friends are going to ride the Ferris wheel at the county fair. It costs $6.00 for a group of 3 people to ride the Ferris wheel. How much will a group of 8 friends pay? $6 ÷ 3 $2 $2 3 ÷ 3 1 1 = 8 = $16