Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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

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

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

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.

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: 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

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 : : ; ;

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 : : ; ;

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? $0.25 1 min Name Rate Allison Juan Zach $0.25 1 min Find rates equivalent to . $3.25 12 min $6.50 24 min $12.00 48 min

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? $0.25 1 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 $12.00 48 min Zach's rate of is equivalent to Jill's rate.

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 2 hours 2200 miles 3 hours 3250 miles 4 hours

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

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.

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 ÷ 10 $4 = 1 10 ÷ 10 $4 • 8 = $32 1

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 ÷ 3 $2 = 1 3 ÷ 3 $2 • 8 = $16 1

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Use a table to find three equivalent ratios. Lesson Quiz: Part I Use a table to find three equivalent ratios. 1. 2. 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 , ,

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

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

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

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

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. $3.25 D. $3.50