01/18/11 Unit Rates Today’s Plan: -Warm-Up & Test Results -Unit Rates Lesson -Unit Rates Assignment Learning Target: I will calculate and compare unit

01/18/11 Unit Rates

Today’s Plan:-Warm-Up & Test Results-Unit Rates Lesson-Unit Rates Assignment

Learning Target: I will calculate and compare unit rates.

A shopping cart contains 35 cans of soda, 16 oranges, 17 carrots, and 29 cookies. Write ratios for each of the following.

1. Carrots to oranges

2. Cookies to cans of soda

3. Oranges to carrots

4. Cookies to oranges and soda

Warm Up

01/18/11 Unit Rates



Test Results

01/18/11 Unit Rates



Divide. Round answers to the nearest tenth.

1. 2.

3. 4.

23.3 3.5

23.8 23.9

420 18

73 21

380 16

430 18

Now arrange the original ratios from least to greatest.

Compare and Order Ratios

01/18/11 Unit Rates



Unit Rates

If the measure of the second quantity in a rate or ratio is one unit, then the rate is a unit rate.

01/18/11 Unit Rates



An aspect ratio describes a screen by comparing its width to its height.

Movie and television screens range in shape from almost perfect squares to wide rectangles.

Common aspect ratios are 4:3, 37:20, 16:9, and 47:20.

Additional Example 1A: Ordering Ratios

A. Order the ratios 4:3, 23:10, 13:9, and 47:20 from the least to greatest.

4:3 =

23:10 =

13:9 =

47:20 =

4 3

4 3

Divide. = 1.3 1

= 1.3

23 10

13 947 20

= 1.4

= 2.3

= 2.35

The ratios in order from least to greatest are 4:3, 13:9, 23:10, and 47:20.

The decimals in order are 1.3, 1.4, 2.3, and 2.35.

A. Order the ratios 2:3, 35:14, 5:3, and 49:20 from the least to greatest.

Try This: Example 1A

2:3 =

35:14 =

5:3 =

49:20 =

2 3

2 3

Divide. = 0.6 1

= 0.6

35 14

5

3 49 20

= 1.6

= 2.5

= 2.45

The ratios in order from least to greatest are 2:3, 5:3, 49:20, 35:14.

The decimals in order are 0.6, 1.6, 2.45, and 2.5.

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


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.




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.


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.

Insert Lesson Title Here

Course 2


Find the unit rate and write it in both

fraction and word form. There are 220 calories in 5 crackers.

44 calories 1 cracker

, 44 calories per cracker

01/18/11 Unit Rates



Unit price is a unit rate used to compare costs per item. With unit price, $ go on the top of the ratio.

$3 2 bags goldfish = $1.50 per bag goldfish

Pens can be purchased in a 5-pack for $1.95 or a 15-pack for $6.20. Which is the better buy?

Additional Example 3A: Finding Unit Prices to Compare Costs

Divide the price by the number of pens.

price for packagenumber of pens

$1.955

= $0.39

price for packagenumber of pens

= $6.2015

$0.41

The better buy is the 5-pack for $1.95.

Golf balls can be purchased in a 3-pack for $4.95 or a 12-pack for $18.95. Which is the better buy?


Divide the price by the number of balls.

price for packagenumber of balls

$4.953

= $1.65

price for packagenumber of balls

= $18.9512

$1.58

The better buy is the 12-pack for $18.95.

Jamie can buy a 15oz jar peanut butter for $2.19 or a 20 oz jar for $2.78. Which is the better buy?

Additional Example 3B: Finding Unit Prices to Compare Costs

$2.1915

= $0.15

= $2.7820

$0.14

The better buy is the 20-oz jar for $2.78.

price for jarnumber of ounces

price for jarnumber of ounces

Divide the price by the number of ounces.

Try This: Example 3B

John can buy a 24 oz bottle of ketchup for $2.19 or a 36 oz bottle for $3.79. Which is the better buy?

$2.1924

= $0.09

= $3.7936

$0.11

The better buy is the 24-oz jar for $2.19.

price for bottlenumber of ounces

price for bottlesnumber of ounces

Divide the price by the number of ounces.

01/18/11 Unit Rates



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01/18/11 Unit Rates Today’s Plan: -Warm-Up & Test Results -Unit Rates Lesson -Unit Rates Assignment Learning Target: I will calculate and compare unit