1. Student will learn…. to find units and compare unit rates, such as average speed and unit price. Course 2 Rates M7 Workbook Volume 2 Chapter 5 Lesson 1 – Unit Rates (pgs. 349-356) Lesson 2 – Complex fractions & unit rates (pgs. 357-364 Lesson 3 – Covert unit rates (pgs. 365-372) Unit Rates

2. Course 2 Rates A rate is a ratio that compares two quantities measured in different units. A unit rate is a rate whose denominator is 1. To change a rate to a unit rate, divide both the numerator and denominator by the denominator. Unit rates vocabulary:

3. Find the rate. Example # 2 A Ferris wheel revolves 35 times in 105 minutes. How many minutes does 1 revolution take? 105 minutes 35 revolutions Write a rate that compares minutes and revolutions. Simplify. Divide the numerator and denominator by 35. Course 2 Rates 105 minutes ÷ 35 35 revolutions ÷ 35 3 minutes 1 revolution The Ferris wheel revolves 1 time in 3 minutes. Unit Rates: Finding the rate

4. Find the rate. Example 2 Sue walks 6 yards and passes 24 security lights set along the sidewalk. How many security lights does she pass in 1 yard? 24 lights 6 yards Write a rate that compares security lights and yards. Simplify. Divide the numerator and denominator by 6. Course 2 Rates 24 lights ÷ 6 6 yards ÷ 6 4 lights 1 yard Sue passes 4 security lights in 1 yard. Unit Rates: Finding the rate

5. Find the rate. Example 3 A dog walks 696 steps in 12 minutes. How many steps does the dog take in 1 minute? 696 steps 12 minutes Write a rate that compares steps and minutes. Simplify. Divide the numerator and denominator by 12. Course 2 Rates 696 steps ÷ 12 12 minutes ÷ 12 58 steps 1 minute The dog walks 58 steps per minute. Unit Rates: Finding the rate

6. Find the rate. Example 4 To make 12 smoothies, Henry needs 30 cups of ice. How many cups of ice does he need for one smoothie? 30 cups of ice 12 smoothies Write a rate that compares cups of ice and smoothies. Simplify. Divide the numerator and denominator by 12. Course 2 Rates 30 cups of ice ÷ 12 12 smoothies ÷ 12 2.5 cups of ice 1 smoothie Henry needs 2.5 cups of ice per smoothie. Unit Rates: Finding the rate

7. An average rate of speed is the ratio of distance traveled to time. The ratio is a rate because the units in the numerator and denominator are different. Unit Rates: Finding average speed

8. 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? Example 1 68 miles 4 hours Write the rate as a fraction. 68 miles ÷ 4 4 hours ÷ 4 = 17 miles 1 hour Divide the numerator and denominator by the denominator Danielle’s average speed should be 17 miles per hour. Course 2 Unit Rates: Finding average speed

9. 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? Example 2 1191 miles 3 hours Write the rate as a fraction. 1191 miles ÷ 3 3 hours ÷ 3 = 397 miles 1 hour Divide the numerator and denominator by the denominator Rhett’s average speed should be 397 miles per hour. Course 2 Rates Unit Rates: Finding average speed

10. 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. Course 2 Type of ItemExample of Units LiquidOunces, quarts, gallons, liters SolidOunces, pounds, grams, kilograms Any itemBottle, container, carton Unit Rates: Finding average speed

11. A 12-ounce sports drink costs $0.99, and a 16- ounce sports drink costs $1.19. Which size is the best buy? Example 3: Real world Application SizePrice 12 ounces$0.99 16 ounces$1.19 Divide the price by the number of ounces (oz) to find the unit price of each size. $0.99 12 oz ≈ $0.08 oz Since $0.07 < $0.08, the 16 oz sports drink is the best buy. Course 2 $1.19 16 oz ≈ $0.07 oz Unit Rates: Finding average speed

12. 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? Example 4 SizePrice 1.5 gal$4.02 3.5 gal$8.75 Divide the price by the number of grams (g) to find the unit price of each size. $4.02 1.5 gal = $2.68 gal Since $2.50 < $2.68, the 3.5 gallon container is the best buy. Course 2 $8.75 3.5 gal = $2.50 g Unit Rates: Finding average speed

13. Guided Practice 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? Insert Lesson Title Here $8 3.5 minutes 55 Guided practice

14. Insert Lesson Title Here 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 Course 2 Guided practice Guided practice continued