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

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
4mi/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. 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.

7. 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.

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. 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 are equivalent.

10. 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.

11. 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.

12. 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 are equivalent.

13. 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.

14. 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.

15. 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.

16. 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.

17. 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.

18. Use a table to find three equivalent ratios.
Lesson Quiz: Part I
Use a table to find three equivalent ratios.
Possible Answers: 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
, ,

19. 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