1. 5-1 Ratios and Rates Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Warm Up Write each fraction in lowest terms. 1. Course 2 5-1 Ratios and Rates 36 40 2. 3. 15 80 4. 21 35 5. 42 90 6. 56 84 2323 3535 2323 9 10 7 15 3 16 8 12

3. Problem of the Day If June 1 falls on a Tuesday, on which day of the week does September 1 fall. Wednesday Course 2 5-1 Ratios and Rates

4. Learn to identify, write, and compare ratios and rates. Course 2 5-1 Ratios and Rates

5. Vocabulary ratio rate unit rate Insert Lesson Title Here Course 2 5-1 Ratios and Rates

6. In basketball practice. Kathlene made 17 baskets in 25 attempts. She compared the number of baskets she made to the total number of attempts she made by using the ratio. A ratio is a comparison of two quantities by division. 17 25 Kathlene can write her ratio of baskets made to attempts in three different ways. 17 25 17 to 2517:25 Course 2 5-1 Ratios and Rates

7. The recommended fuel for Suzanne’s snowblower is made from 80 quarts of gasoline and 1 quart of motor oil. Write each ratio in all three forms. Additional Example 1: Writing Ratios Course 2 5-1 Ratios and Rates A. quarts of gasoline to quarts of motor oil 80 1, 80 to 1, 80:1 For every 80 quarts of gasoline there is 1 quart of oil. B. quarts of oil to quarts of fuel mixture 80 + 1 = 81 1 81, 1 to 81, 1:81 For each quart of oil there are 81 quarts of mixture. Find the total number of quarts in the mixture.

8. Try This: Example 1 The label on a bag of plant fertilizer suggests that the fertilizer be diluted in 20 quarts of water for each quart of fertilizer. Write each ratio in all three forms. Insert Lesson Title Here Course 2 5-1 Ratios and Rates A. quarts of water to quarts of fertilizer 20 1, 20 to 1, 20:1 For every 20 quarts of water there is 1 quart of fertilizer. B. quarts of fertilizer to quarts of fertilizer mixture 20 + 1 = 21 1 21, 1 to 21, 1:21 For each quart of fertilizer there are 21 quarts of mixture. Find the total number of quarts in the mixture.

9. Course 2 5-1 Ratios and Rates A ratio that compares two quantities measured in different units is a rate. Suppose Ms. Latocki drove 75 miles in 3 hours. Her rate of travel was 75 miles in 3 hours, or. 75 mi 3 hr

10. Course 2 5-1 Ratios and Rates If the measure of the second quantity in a rate is one unit, then the rate is a unit rate. To change a rate to a unit rate, divide both the numerator and denominator by the number in the denominator. 75 mi 3 hr = 75 mi ÷ 3 3hr ÷ 3 = 25 mi 1 hr The unit rate 25 miles per hour expresses the average number of miles Ms. Latocki drove each hour.

11. Course 2 5-1 Ratios and Rates The unit rate is read as “twenty five miles per hour.” Reading Math 25miles 1 hour

12. Find the unit rates and write them in both fraction and word forms. Additional Example 2A: Writing Rates and Unit Rates Course 2 5-1 Ratios and Rates A. Gordon memorized 560 vocabulary words in 28 days. 560 words 28 days Rate in fraction form 560 ÷ 28 28 ÷ 28 = 20 words 1 day Unit rate in fraction form Gordon memorized 20 words per day. Unit rate in word form

13. Find the unit rates and write them in both fraction and word forms. Additional Example 2B: Writing Rates and Unit Rates Course 2 5-1 Ratios and Rates B. Pete added 12 ounces of chocolate chips to a recipe that yielded 48 cookies. 12 oz 48 cookies Rate in fraction form 12 ÷ 48 48 ÷ 48 = 0.25 oz 1 cookie Unit rate in fraction form There is 0.25 ounce of chocolate chips per cookie. Unit rate in word form

14. Find the unit rates and write them in both fraction and word forms. Try This: Example 2A Course 2 5-1 Ratios and Rates A. Harold could jog 1,000 meters in 5 minutes. 1,000 m 5 min Rate in fraction form 1,000 ÷ 5 5 ÷ 5 = 200 m 1 min Unit rate in fraction form Harold jogged 200 meters per minute. Unit rate in word form

15. Find the unit rates and write them in both fraction and word forms. Try This: Example 2B Course 2 5-1 Ratios and Rates B. Yvonne added 3 ounces of blueberries to a recipe that made 12 muffins. 3 oz 12 muffins Rate in fraction form 3 ÷ 12 12 ÷ 12 = 0.25 oz 1 muffin Unit rate in fraction form There is 0.25 ounce of blueberries per muffin. Unit rate in word form

16. Course 2 5-1 Ratios and Rates It is often easy to compare ratios when they are written as fractions in simplest form—especially when they have a common denominator.

17. Honey-lemon cough drops come in packages of 30 drops per 10-ounce bag. Cherry cough drops come in packages of 24 drops per 6-ounce bag. Compare the ratio of drops per ounces for each bag of cough drops. Additional Example 3: Simplifying Ratios to Make Comparisons Course 2 5-1 Ratios and Rates Honey-lemonCherry Ounces106 Drops3024 Honey-lemon: drops ounces = 30 10 = 3131 Cherry: drops ounces = 24 6 = 4141 4141 is greater than 3131. The ratio of drops to ounces is greater in the bag of cherry cough drops. Simplify the ratio.

18. Jawbreakers come in small packages of 20 per 5 ounce package and large packages of 24 per 8 ounce package. Compare the ratio of jawbreakers per ounce for each of the packages. Try This: Example 3 Course 2 5-1 Ratios and Rates LargeSmall Ounces85 Jawbreaker2420 Large: jawbreaker ounces = 24 8 = 3131 Small: jawbreaker ounces = 20 5 = 4141 4141 is greater than 3131. The ratio of jawbreakers to ounces is greater in the small package. Simplify the ratio.

19. Lesson Quiz: Part 1 A coin bank contains 16 quarters, 12 dimes, and 8 nickels. Write the given ratio in all three forms. Insert Lesson Title Here Course 2 5-1 Ratios and Rates 1. nickels to quarters 2. dimes to nickels 3. nickels and dimes to quarters 8 16, 8 to 16, 8:16 or 1212, 1 to 2, 1:212 8, 12 to 8, 12:8 or 3232, 3 to 2, 3:220 16, 20 to 16, 20:16 or 5454, 5 to 4, 5:4

20. Lesson Quiz: Part 2 Insert Lesson Title Here Course 2 5-1 Ratios and Rates 4. Find the unit rate and write it in both fraction and word form. There are 220 calories in 5 crackers. 5. Kim and Ted work out on treadmills together at the gym. Kim walked 3.0 miles in 21 minutes, while Ted walked 4.5 miles in 42 minutes. Who walked at the faster rate? Kim 44 calories 1 cracker, 44 calories per cracker