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. Sunshine State Standards
MA.6.A.2.1 Use reasoning about multiplication and division to solve ratio and rate problems.
Also MA.6.A.2.2

5. 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 6 7 __
Original Ratio
6 • 2
6 • 3
6 • 4
Multiply the numerator and the denominator by 2, 3, and 4. 7 6 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.

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

7. 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
3 miles
60 minutes
_________
Original Rate
3 • 2
3 • 3
3 • 4
Multiply the numerator and the denominator by 2 3, and 4. 60 3 6 9 12
120
180
240
60 • 2
60 • 3
60 • 4
The ratios , , , and are equivalent. 3 60
___ 9
120
180
240 6 12

8. Find three equivalent ratios or rates.
Check It Out: Example 1A
Find three equivalent ratios or rates.
A. The ratio of apples to oranges in a fruit bowl is
5 3 . 10 6
___ 15 9
___ 20 12
___
Possible answer : : ; ;

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

10. 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?
$ min
Name
Rate
Allison
Juan
Zach
$ min
Find rates equivalent to
$ min
$ min
$ min

11. 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?
$ min
$0.25 • 12
$0.25 • 24
$0.25 • 48
Original Rate
Cost
Minutes
$0.25
$3.00
$6.00
$12.00 1 12 24 48
1 • 12
1 • 24
1 • 48
$ min
Zach's rate of is equivalent to Jill's rate.

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

13. Check It Out Example 2 continued
750
1500
_______
_______
_______ = = 1
1 . 2 2
which is the same as plane X

14. 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.
Divide the bus fare by the number in each group to find the amount paid per person.
24 ÷ 12 = 2
Multiply the unit rate by 15 to find the rate for 15 people.
2 • 15 = 30
A group of 15 friends will pay $30 in bus fare.

15. 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 ÷ $4 = 1
10 ÷ 10 $4
• 8 = $32 1

16. 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 ÷ $2 = 1
3 ÷ 3 $2
• 8 = $16 1

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

18. Use a table to find three equivalent ratios.
Lesson Quiz: Part I
Use a table to find three equivalent ratios. 3.
Possible Answers: 9 4 __ 18 8 __ 27 12 36 16
, , 1 3 __ 2 6 __ 3 9 4 12
, , 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
150
100 50
Savings 12 8 4
Weeks

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

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

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

23. 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. $ B. $3.00
C. $ D. $3.50