7-2 Using Tables to Explore Equivalent Ratios and Rates Warm Up Course 1 Warm Up Problem of the Day Lesson Presentation

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 4mi/h $0.80 per orange $0.31 per bottle $6.10 per DVD

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

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

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

Use a table to find ratios equivalent to 3 to 2. Original Ratio 3 • 2 3 • 3 3 • 4 Pints of yellow 3 6 9 12 Pints of blue 2 4 8 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.

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

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

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. 3 5 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.

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

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

Use a table to find the equivalent ratios. 2 to 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. 2 9 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.

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

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. Number in Group 6 12 18 Bus Fare($) 24 36 12< 15 < 18; therefore, the group will pay between $24 and $36.

Additional Example 2 Continued Number in Group 6 12 18 Bus Fare($) 24 36 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.

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. Number in Group 4 6 8 Tickets($) 20 30 40 6 < 7 < 8; therefore, the group will pay between $30 and $40.

Check It Out: Example 2 Continued Number in Group 4 6 8 Tickets($) 20 30 40 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.

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

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 Weeks 4 8 12 Savings 50 100 150