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
5-1 Ratios and Rates
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
5-1 Ratios and Rates
Learn to identify, write, and compare ratios and rates.
Course 2
5-1 Ratios and Rates
Vocabulary
ratiorateunit rate
Insert Lesson Title Here
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.
1725
Kathlene can write her ratio of baskets madeto attempts in three different ways.
1725
17 to 25 17:25
Course 2
5-1 Ratios and Rates
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 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.
Insert Lesson Title Here
Course 2
5-1 Ratios and Rates
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
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 ÷ 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
5-1 Ratios and Rates
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
5-1 Ratios and Rates
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
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 ÷ 4848 ÷ 48
= 0.25 oz1 cookie
Unit rate in fraction form
There is 0.25 ounce of chocolate chips per cookie.
Unit rate in word form
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 m5 min
Rate in fraction form
1,000 ÷ 5 5 ÷ 5
= 200 m1 min
Unit rate in fraction form
Harold jogged 200 meters per minute.
Unit rate in word form
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 ÷ 1212 ÷ 12
= 0.25 oz1 muffin
Unit rate in fraction form
There is 0.25 ounce of blueberries per muffin.
Unit rate in word form
Course 2
5-1 Ratios and Rates
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
5-1 Ratios and Rates
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
5-1 Ratios and Rates
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.
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
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
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