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7-2Using Tables to Explore Equivalent Ratios and Rates7-2 Using Tables to Explore

Equivalent Ratios and Rates

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Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

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7-2Using Tables to Explore Equivalent Ratios and Rates

Warm UpFind 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

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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

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

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

Reading Math

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Use a table to find ratios equivalent to 3 to 2.

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.

Pints of yellow 3 6 9 12

Pints of blue 2 4 6 8

Original Ratio

3 • 2 3 • 3 3 • 4

2 • 2 2 • 3 2 • 4

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Additional Example 1A: Making a Table to Find Equivalent Ratios

Use a table to find the equivalent ratios.

67__

6

7

Original Ratio

6 • 2 6 • 3 6 • 4

7 • 2 7 • 3 7 • 4

Multiply the numerator and the denominator by 2, 3, and 4.

The ratios , , , and are equivalent.67__ 12

14___ 18

21___ 24

28___

12 18 24

14 21 28

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

Helpful Hint

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Additional Example 1B: Making a Table to Find Equivalent Ratios


3 to 5

3

5

Original Ratio

3 • 2 3 • 3 3 • 4

5 • 2 5 • 3 5 • 4


The ratios 3 to 5, 6 to 10, 9 to 15, and 12 to 20 are equivalent.

6 9 12

10 15 20

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Additional Example 1C: Making a Table to Find Equivalent Ratios


48:36

48

36

Original Ratio

48 ÷ 2 48 ÷ 3 48 ÷ 4

36 ÷ 2 36 ÷ 3 36 ÷ 4

Divide the numerator and the denominator by 2, 3, and 4.

The ratios 48:36, 24:18, 16:12, and 12:9 are equivalent.

24 16 12

18 12 9

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Check It Out: Example 1A


38__

3

8

Original Ratio

3 • 2 3 • 3 3 • 4

8 • 2 8 • 3 8 • 4


The ratios , , , and are equivalent.38__ 6

16___ 9

24___ 12

32___

6 9 12

16 24 32

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Check It Out: Example 1B


2 to 9

2

9

Original Ratio

2 • 2 2 • 3 2 • 4

9 • 2 9 • 3 9 • 4


The ratios 2 to 9, 4 to 18, 6 to 27, and 8 to 36 are equivalent.

4 6 8

18 27 36

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Check It Out: Example 1C


36:12

36

12

Original Ratio

36 ÷ 2 36 ÷ 3 36 ÷ 4

12 ÷ 2 12 ÷ 3 12 ÷ 4

Divide the numerator and the denominator by 2, 3, and 4.

The ratios 36:12, 18:6, 12:4, and 9:3 are equivalent.

18 12 9

6 4 3

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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($) 12 24 36

12< 15 < 18; therefore, the group will pay between $24 and $36.

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Additional Example 2 Continued


Bus Fare($) 12 24 36

Use the amount paid by the group of 6.

12 ÷ 6 = 2 Divide the bus fare by the number in each group to find the amount paid per person.

2 • 15 = 30 Multiply.

A group of 15 friends will pay $30 in bus fare.

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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.


Tickets($) 20 30 40

6 < 7 < 8; therefore, the group will pay between $30 and $40.

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Check It Out: Example 2 Continued

Use the amount paid by the group of 8.

40 ÷ 8 = 5 Divide the ticket prices by the number of people in each group to find the amount paid per person.

5 • 7 = 35 Multiply.

A group of 7 friends will pay $35 for amusement park tickets.


Tickets($) 20 30 40

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Lesson Quiz: Part IUse a table to find three equivalent ratios.

Possible Answers:

1. 2.

3.

1 3

__

12 60

__

9 4

__ 2 6

__ 3 9

__ 412

__ , ,18 8

__ 2712

__ 3616

__ , ,

630

__ 210

__ 1 5

__ , ,

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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

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