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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. Warm Up Divide. 1. 14 ÷ 1.75 2. 34 ÷ 0.17 3. 5.25 ÷ 1.5 4. 8.1 ÷ 2.7. Evaluate. 5. (4 + 1) 2 – 8 ÷ 2. 8. 21. 200. 3.5. 3. California Standards.

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. Warm Up Divide. 1. 14 ÷ 1.75 2. 34 ÷ 0.17 3. 5.25 ÷ 1.5 4. 8.1 ÷ 2.7 Evaluate. 5. (4 + 1)2 – 8 ÷ 2 8 21 200 3.5 3

  3. California Standards Algebra & Functions (AF2.2) - Demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity. Also covered: NS1.2, AF2.3

  4. Vocabulary rate unit rate

  5. A rate is a special type of 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. Dividing the numerator and denominator of a rate by the same number does not change the value of the rate.

  6. 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 to get an equivalent rate. 105 minutes ÷ 35 35 revolutions ÷ 35 3 minutes 1 revolution Simplify. The Ferris wheel revolves 1 time in 3 minutes.

  7. 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 to get an equivalent rate. 24 lights ÷ 6 6 yards ÷ 6 4 lights 1 yard Simplify. Sue passes 4 security lights in 1 yard.

  8. 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 to get an equivalent rate. 696 steps ÷ 12 12 minutes ÷ 12 58 steps 1 minute Simplify. The dog walks 58 steps per minute.

  9. 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 to get an equivalent rate. 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.

  10. 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. Speed is usually expressed as a unit rate.

  11. 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. Divide the numerator and denominator by 4 to get an equivalent rate. 68 miles ÷ 4 4 hours ÷ 4 17 miles 1 hour = Danielle’s average speed should be 17 miles per hour.

  12. Check It Out! Example 2 Rhett is a pilot and needs to fly 1,191 miles to the next city. He wants to complete his flight in 3 hours. What should be his average speed in miles per hour? 1,191 miles 3 hours Write the rate. Divide the numerator and denominator by 3 to get an equivalent rate. 1,191 miles ÷ 3 3 hours ÷ 3 397 miles 1 hour = Rhett’s average speed should be 397 miles per hour.

  13. 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.

  14. 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 each unit price. Item #1 Item #2 $0.99 12 oz $1.19 16 oz $0.08 oz $0.07 oz ≈ ≈ Since $0.07 < $0.08, the 16-ounce sports drink is the best buy.

  15. Check It Out! Example 3 A 1.5 gallon container costs $4.02, and a 3.5 gallon container costs $8.75. Which size is the best buy? Divide the price by the number of gallons to find the unit price of each size. Item #1 Item #2 $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.

  16. Lesson Quiz 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 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

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