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

Transcription

1 Learn to identify, write, and compare ratios and rates.

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

3 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. Kathlene can write her ratio of baskets made to attempts in three different ways to 25 17:25

4 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, 80 to 1, 80:1 For every 80 quarts of gasoline 1 there is 1 quart of oil. B. quarts of oil to quarts of fuel mixture = 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.

5 A ratio that compares two quantities measured in different units is a rate, which the units must ALWAYS be labeled. Suppose Ms. Latocki drove 75 miles in 3 hours. Her rate of travel was 75 miles in 3 hours, or 75 mi. 3 hr

6 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.

7 Reading Math The unit rate miles per hour. 25miles 1 hour is read as twenty five

8 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. 560 words 28 days Rate in fraction form = 20 words 1 day Unit rate in fraction form Gordon memorized 20 words per day. Unit rate in word form

9 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. 12 oz 48 cookies Rate in fraction form = 0.25 oz 1 cookie Unit rate in fraction form There is 0.25 ounce of Unit rate in chocolate chips per cookie. word form

10 It is often easy to compare ratios when they are written as fractions in simplest form especially when they have a common denominator.

11 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 Honey-lemon: drops ounces = = 3 1 Cherry: drops ounces = 24 6 = is greater than 3 1. Simplify the ratio. Simplify the ratio. The ratio of drops to ounces is greater in the bag of cherry cough drops.

12 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 jawbreaker Large: ounces Small: jawbreaker ounces 4 is greater than = 24 8 = 3 1 = 20 5 = 4 1 Simplify the ratio. Simplify the ratio. The ratio of jawbreakers to ounces is greater in the small package.

13 5-1 Ratios Insert Lesson and Rates 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 dimes to nickels 12 8, 8 to 16, 8:16 or 1, 1 to 2, 1:2 2, 12 to 8, 12:8 or 3, 3 to 2, 3: nickels and dimes to quarters 20 16, 20 to 16, 20:16 or 5, 5 to 4, 5:4 4

14 5-1 Ratios Insert Lesson and Rates 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. 44 calories 1 cracker 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 per cracker

15 5-1 Ratios Insert Lesson and Rates Title Here Orange Juice 1. Count off by A, B, C, D. 2. Get into A, B, C, D groups in the science room. 3. With a Sharpie, label 26 Dixie cups with your group letter. 4. OJ people, measure out the OJ from the can according to the recipe. 5. Water people, take the OJ container and bowl with OJ and go to one of the water fountains in the hall (there are 4) and fill the cup measure with the correct amount of water and put into bowl. 6. Stirrers, stir the water and OJ together. 7. Pourers, using another cup, ladle out the same amount of OJ (without spilling) into all 26 cups. 8. Passer Outers- Pass out your cup to everyone. 9. At the end, everyone should have 4 cups, unless you said pass. 10. DO NOT DRINK until Mrs. Staudohar says to drink!