5-1 ratios and rates course 2 warm up warm up problem of the day problem of the day lesson...

5-1 Ratios and Rates

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpWrite each fraction in lowest terms.

1.

Course 2


3640

2.

3. 1580

4. 2135

5. 4290

6. 5684

23

35

23

910

715

316

812

Problem of the Day

If June 1 falls on a Tuesday, on which day of the week does September 1 fall.

Wednesday

Course 2


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

Course 2


Vocabulary

ratiorateunit rate

Insert Lesson Title Here

Course 2


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.

1725

Kathlene can write her ratio of baskets madeto attempts in three different ways.

1725

17 to 25 17:25

Course 2


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


A. quarts of gasoline to quarts of motor oil801

, 80 to 1, 80:1 For every 80 quarts of gasolinethere is 1 quart of oil.

B. quarts of oil to quarts of fuel mixture

80 + 1 = 81

181

, 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.

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.


Course 2


A. quarts of water to quarts of fertilizer

201

, 20 to 1, 20:1 For every 20 quarts of waterthere is 1 quart of fertilizer.

B. quarts of fertilizer to quarts of fertilizer mixture

20 + 1 = 21

121

, 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.

Course 2


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


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 ÷ 33hr ÷ 3

= 25 mi1 hr

The unit rate 25 miles per hour expresses the average number of miles Ms. Latocki drove each hour.

Course 2


The unit rate is read as “twenty five

miles per hour.”

Reading Math

25miles 1 hour

Find the unit rates and write them in both fraction and word forms.

Additional Example 2A: Writing Rates and Unit Rates

Course 2


A. Gordon memorized 560 vocabulary words in 28 days.

560 words28 days

Rate in fraction form

560 ÷ 28 28 ÷ 28

= 20 words1 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


B. Pete added 12 ounces of chocolate chips to a recipe that yielded 48 cookies.

12 oz 48 cookies


12 ÷ 4848 ÷ 48

= 0.25 oz1 cookie


There is 0.25 ounce of chocolate chips per cookie.



Try This: Example 2A

Course 2


A. Harold could jog 1,000 meters in 5 minutes.

1,000 m5 min


1,000 ÷ 5 5 ÷ 5

= 200 m1 min


Harold jogged 200 meters per minute.



Try This: Example 2B

Course 2


B. Yvonne added 3 ounces of blueberries to a recipe that made 12 muffins.

3 oz 12 muffins


3 ÷ 1212 ÷ 12

= 0.25 oz1 muffin


There is 0.25 ounce of blueberries per muffin.


Course 2


It is often easy to compare ratioswhen they are written as fractionsin simplest form—especiallywhen they have a common denominator.

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


Honey-lemon Cherry

Ounces 10 6

Drops 30 24

Honey-lemon: dropsounces

= 3010

= 31

Cherry: dropsounces

= 246

= 41

41

is greater than 31

.

The ratio of drops to ounces is greater in the bag of cherry cough drops.

Simplify the ratio.

Simplify the ratio.

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


Large Small

Ounces 8 5

Jawbreaker 24 20

Large:jawbreaker ounces

= 248

= 31

Small: jawbreaker ounces

= 205

= 41

41

is greater than 31

.

The ratio of jawbreakers to ounces is greater in the small package.

Simplify the ratio.

Simplify the ratio.

Lesson Quiz: Part 1

A coin bank contains 16 quarters, 12 dimes, and 8 nickels. Write the given ratio in all three forms.


Course 2


1. nickels to quarters

2. dimes to nickels

3. nickels and dimes to quarters

816

, 8 to 16, 8:16 or 12

, 1 to 2, 1:2

128

, 12 to 8, 12:8 or 32

, 3 to 2, 3:2

2016

, 20 to 16, 20:16 or 54

, 5 to 4, 5:4

Lesson Quiz: Part 2


Course 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?

Kim

44 calories 1 cracker

, 44 calories per cracker

5-1 ratios and rates course 2 warm up warm up problem of the day problem of the day lesson...

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