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

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

5-1 Ratios and Rates Problem of the Day Course 2 5-1 Ratios and Rates 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 Learn to identify, write, and compare ratios and rates.

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

Course 2 5-1 Ratios and Rates 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 25 17:25

Additional Example 1: Writing Ratios Course 2 5-1 Ratios and Rates Additional Example 1: Writing Ratios 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. 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 Find the total number of quarts in the mixture. 1 81 , 1 to 81, 1:81 For each quart of oil there are 81 quarts of mixture.

Insert Lesson Title Here Course 2 5-1 Ratios and Rates Insert Lesson Title Here 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. A. quarts of water to quarts of fertilizer 20 1 For every 20 quarts of water there is 1 quart of fertilizer. , 20 to 1, 20:1 B. quarts of fertilizer to quarts of fertilizer mixture Find the total number of quarts in the mixture. 20 + 1 = 21 1 21 , 1 to 21, 1:21 For each quart of fertilizer there are 21 quarts of mixture.

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

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.

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

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

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

5-1 Ratios and Rates 1,000 m Rate in fraction form 5 min 1,000 ÷ 5 Course 2 5-1 Ratios and Rates Try This: Example 2A Find the unit rates and write them in both fraction and word forms. 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

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

It is often easy to compare ratios when they are written as fractions 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.

Additional Example 3: Simplifying Ratios to Make Comparisons Course 2 5-1 Ratios and Rates Additional Example 3: Simplifying Ratios to Make Comparisons 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. Honey-lemon Cherry Ounces 10 6 Drops 30 24 drops ounces 30 10 3 1 = Honey-lemon: = Simplify the ratio. drops ounces 24 6 4 1 Cherry: = = Simplify the ratio. 4 1 3 1 is greater than . The ratio of drops to ounces is greater in the bag of cherry cough drops.

5-1 Ratios and Rates Try This: Example 3 Large Small Ounces 8 5 Course 2 5-1 Ratios and Rates Try This: Example 3 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. Large Small Ounces 8 5 Jawbreaker 24 20 jawbreaker ounces 24 8 3 1 = Large: = Simplify the ratio. jawbreaker ounces 20 5 4 1 Small: = = Simplify the ratio. 4 1 3 1 is greater than . The ratio of jawbreakers to ounces is greater in the small package.

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

Insert Lesson Title Here Course 2 5-1 Ratios and Rates Insert Lesson Title Here Lesson Quiz: Part 2 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? 44 calories 1 cracker , 44 calories per cracker Kim