Understanding Unit Rates and Equivalent Ratios Explained with Examples

1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

2. 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. 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. Learn to use a table to find equivalent ratios and rates.

5. Reading Math Finding equivalent ratios is sometimes referred to as “scaling up” or “scaling down.”

6. Pints of yellow 3 6 9 12 Pints of blue 2 4 6 8 Use a table to find ratios equivalent to 3 to 2. Original Ratio 3 • 2 3 • 3 3 • 4 2 • 2 2 • 3 2 • 4 You can increase amounts but keep them in the same ratio by multiplying both the numerator and denominator of the ratio by the same number. The ratios 3 to 2, 6 to 4, 9 to 6, and 12 to 8 are equivalent. You can also decrease amounts in the same ratio by dividing the numerator and denominator by the same number.

7. 6 __ 7 6 7 6 12 18 24 __ ___ ___ ___ 7 14 21 28 Additional Example 1A: Making a Table to Find Equivalent Ratios Use a table to find the equivalent ratios. Original Ratio 6 • 2 6 • 3 6 • 4 Multiply the numerator and the denominator by 2, 3, and 4. 12 18 24 14 21 28 7 • 2 7 • 3 7 • 4 The ratios , , , and are equivalent.

8. Helpful Hint Multiplying by 2, 3, and 4 will give you three equivalent ratios, but there are many other equivalent ratios that are correct.

9. 3 5 Additional Example 1B: Making a Table to Find Equivalent Ratios Use a table to find the equivalent ratios. 3 to 5 Original Ratio 3 • 2 3 • 3 3 • 4 Multiply the numerator and the denominator by 2, 3, and 4. 6 9 12 10 15 20 5 • 2 5 • 3 5 • 4 The ratios 3 to 5, 6 to 10, 9 to 15, and 12 to 20 are equivalent.

10. 48 36 Additional Example 1C: Making a Table to Find Equivalent Ratios Use a table to find the equivalent ratios. 48:36 Original Ratio 48 ÷ 4 48 ÷ 2 48 ÷ 3 Divide the numerator and the denominator by 2, 3, and 4. 24 16 12 9 18 12 36 ÷ 4 36 ÷ 2 36 ÷ 3 The ratios 48:36, 24:18, 16:12, and 12:9 are equivalent.

11. 3 __ 8 3 8 3 6 9 12 __ ___ ___ ___ 8 16 24 32 Check It Out: Example 1A Use a table to find the equivalent ratios. Original Ratio 3 • 2 3 • 3 3 • 4 Multiply the numerator and the denominator by 2, 3, and 4. 6 9 12 16 24 32 8 • 2 8 • 3 8 • 4 The ratios , , , and are equivalent.

12. 2 9 Check It Out: Example 1B Use a table to find the equivalent ratios. 2 to 9 Original Ratio 2 • 2 2 • 3 2 • 4 Multiply the numerator and the denominator by 2, 3, and 4. 4 6 8 18 27 36 9 • 2 9 • 3 9 • 4 The ratios 2 to 9, 4 to 18, 6 to 27, and 8 to 36 are equivalent.

13. 36 12 Check It Out: Example 1C Use a table to find the equivalent ratios. 36:12 Original Ratio 36 ÷ 4 36 ÷ 2 36 ÷ 3 Divide the numerator and the denominator by 2, 3, and 4. 18 12 9 3 6 4 12 ÷ 4 12 ÷ 2 12 ÷ 3 The ratios 36:12, 18:6, 12:4, and 9:3 are equivalent.

14. Number in Group 6 12 18 Bus Fare($)‏ 12 24 36 Additional Example 2: Application Several groups of friends are going to take a shuttle bus to the park. The table shows how much the different groups will pay in all. Predict how much a group of 15 friends will pay. 12< 15 < 18; therefore, the group will pay between $24 and $36.

15. Number in Group 6 12 18 Bus Fare($)‏ 12 24 36 Additional Example 2 Continued Use the amount paid by the group of 6. Divide the bus fare by the number in each group to find the amount paid per person. 12 ÷ 6 = 2 2 • 15 = 30 Multiply. A group of 15 friends will pay $30 in bus fare.

16. Number in Group 4 6 8 Tickets($)‏ 20 30 40 Check It Out: Example 2 Several groups of friends are purchasing tickets to an amusement park. The table shows how much the different groups will pay in all. Predict how much a group of 7 friends will pay. 6 < 7 < 8; therefore, the group will pay between $30 and $40.

17. Number in Group 4 6 8 Tickets($)‏ 20 30 40 Check It Out: Example 2 Continued Use the amount paid by the group of 8. Divide the ticket prices by the number of people in each group to find the amount paid per person. 40 ÷ 8 = 5 5 • 7 = 35 Multiply. A group of 7 friends will pay $35 for amusement park tickets.

18. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

19. 1 2 3 4 9 18 27 36 __ __ __ __ __ __ __ __ , , , , 3 6 9 12 4 8 12 16 12 6 2 1 __ __ __ __ , , 60 30 10 5 Lesson Quiz: Part I Use a table to find three equivalent ratios. 1. 2. 3. Possible Answers:

20. Weeks 4 8 12 Savings 50 100 150 Lesson Quiz: Part II 4.Fred is saving for a new sound system. The table shows some amounts he could save in different numbers of weeks. Predict the amount of his savings after 10 weeks. $125

21. Lesson Quiz for Student Response Systems 1. Use a table identify three equivalent ratios of . A. B. C. D.

22. Lesson Quiz for Student Response Systems 2. Use a table identify three equivalent ratios of . A. B. C. D.

23. Lesson Quiz for Student Response Systems 3. Use a table identify three equivalent ratios of . A. B. C. D.

24. Lesson Quiz for Student Response Systems 4. A grocery store sells eggs in crates. The following table shows the prices of some crates. Predict how much Lee will pay for a crate of 18 eggs at the rate shown in the table. A. $2.75 B. $3.00 C. $3.25D. $3.50