Warm Up - Divide Problems and Finding Unit Rates

1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

2. Warm Up Divide. 1. 14 ÷ 1.75 2. 34 ÷ 0.17 3. 5.25 ÷ 1.5 4. 8.1 ÷ 2.7 8 200 3.5 3

3. Problem of the Day A number rounded to the nearest tenth is 5.3. Round to the nearest hundredth, it is 5.28. What could the number be? Possible answer: 5.279

4. Learn to find and compare unit rates, such as average speed and unit price.

5. Vocabulary rate unit rate

6. A rate is a ratio that compares two quantities measured in different units. A unit rate is a rate whose denominator is 1 when it is written as a fraction. To change a rate to a unit rate, first write the rate as a fraction and then divide both the numerator and denominator by the denominator.

7. Additional Example 1A: Finding Unit Rates Find the rate. A Ferris wheel revolves 35 times in 105 minutes. How many minutes does 1 revolution take? Write a rate that compares minutes and revolutions. 105 minutes 35 revolutions Divide the numerator and denominator by 35. 105 minutes ÷ 35 35 revolutions ÷ 35 3 minutes 1 revolution Simplify. The Ferris wheel revolves 1 time in 3 minutes.

8. Additional Example 1B: Finding Unit Rates Find the rate. Sue walks 6 yards and passes 24 security lights set along the sidewalk. How many security lights does she pass in 1 yard? Write a rate that compares security lights and yards. 24 lights 6 yards Divide the numerator and denominator by 6. 24 lights ÷ 6 6 yards ÷ 6 4 lights 1 yard Simplify. Sue passes 4 security lights in 1 yard.

9. Check It Out: Example 1A Find the rate. A dog walks 696 steps in 12 minutes. How many steps does the dog take in 1 minute? Write a rate that compares steps and minutes. 696 steps 12 minutes Divide the numerator and denominator by 12. 696 steps ÷ 12 12 minutes ÷ 12 58 steps 1 minute Simplify. The dog walks 58 steps per minute.

10. Check It Out: Example 1B Find the rate. To make 12 smoothies, Henry needs 30 cups of ice. How many cups of ice does he need for one smoothie? Write a rate that compares cups of ice and smoothies. 30 cups of ice 12 smoothies Divide the numerator and denominator by 12. 30 cups of ice ÷ 12 12 smoothies ÷ 12 2.5 cups of ice 1 smoothie Simplify. Henry needs 2.5 cups of ice per smoothie.

11. An average rate of speed is the ratio of distance traveled to time. The ratio is a rate because the units being compared are different.

12. Additional Example 2: Finding Average Speed Danielle is cycling 68 miles as a fundraising commitment. She wants to complete her ride in 4 hours. What should be her average speed in miles per hour? 68 miles 4 hours Write the rate as a fraction. 68 miles ÷ 4 4 hours ÷ 4 Divide the numerator and denominator by the denominator 17 miles 1 hour = Danielle’s average speed should be 17 miles per hour.

13. Check It Out: Example 2 Rhett is a pilot and needs to fly 1191 miles to the next city. He wants to complete his flight in 3 hours. What should be his average speed in miles per hour? 1191 miles 3 hours Write the rate as a fraction. Divide the numerator and denominator by the denominator 1191 miles ÷ 3 3 hours ÷ 3 397 miles 1 hour = Rhett’s average speed should be 397 miles per hour.

14. Type of Item Example of Units Liquid Ounces, quarts, gallons, liters Solid Ounces, pounds, grams, kilograms Any item Bottle, container, carton A unit price is the price of one unit of an item. The unit used depends on how the item is sold. The table shows some examples.

15. Size Price 12 ounces $0.99 16 ounces $1.19 Additional Example 3: Consumer Math Application A 12-ounce sports drink costs $0.99, and a 16-ounce sports drink costs $1.19. Which size is the best buy? Divide the price by the number of ounces (oz) to find the unit price of each size. $0.99 12 oz $1.19 16 oz $0.08 oz $0.07 oz ≈ ≈ Since $0.07 < $0.08, the 16 oz sports drink is the best buy.

16. Size Price 1.5 gal $4.02 3.5 gal $8.75 Check It Out: Example 3 A 1.5 gallon container of milk costs $4.02, and a 3.5 gallon container of milk costs $8.75. Which size is the best buy? Divide the price by the number of gallons (g) to find the unit price of each size. $4.02 1.5 gal $8.75 3.5 gal $2.68 gal $2.50 gal = = Since $2.50 < $2.68, the 3.5 gallon container is the best buy.

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

18. Lesson Quiz: Part I 1. Ian earned $96 babysitting for 12 hours. How much did he earn each hour? 2. It takes Mia 49 minutes to complete 14 homework problems. On average, how long did it take to solve each problem? 3. Seth’s family plans to drive 220 miles to their vacation spot. They would like to complete the drive in 4 hours. What should their average speed be in miles per hour? $8 3.5 minutes 55

19. Lesson Quiz: Part II 4. Abby can buy a 7-pound bag of dry cat food for $7.40, or she can purchase a 3-pound bag for $5.38. Which size is the best buy? 7 lb bag

20. Lesson Quiz for Student Response Systems 1. Kay earned $126 for 18 hours in a part-time job. How much did she earn each hour? A. $6 B. $7 C. $8 D. $9

21. Lesson Quiz for Student Response Systems 2. It takes John 54 minutes to paint a fence with a length of 12 meters. On average, how long did he take to paint 1 meter of the fence? A. 3.5 minutes B. 4.5 minutes C. 4.8 minutes D. 5.4 minutes

22. Lesson Quiz for Student Response Systems 3. Helen plans to drive 130 miles to a relative’s house. She would like to complete the drive in 2 hours. What should be her average speed in miles per hour? A. 55 miles per hour B. 60 miles per hour C. 65 miles per hour D. 70 miles per hour

23. Lesson Quiz for Student Response Systems 4. Frank can purchase bags of apples in four sizes. Which size is the best buy? A. 2-lb bag for $3.33 B. 3-lb bag for $4.70 C. 4-lb bag for $5.14 D. 5-lb bag for $6.20