11

MathMath

RatesRates

22

VocabularyVocabulary

RateRate—Ratio that compares quantities with —Ratio that compares quantities with different kinds of units.different kinds of units.

Ex.: Ex.: 100 words100 words

2 minutes2 minutes

Unit RateUnit Rate— a Rate that has been simplified that — a Rate that has been simplified that has a denominator of 1.has a denominator of 1.

Ex.: Ex.: 50 words50 words

1 minute1 minute

The units WORDS and MINUTES are

different.

The denominator is 1 unit.

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RatioRatio Unit RateUnit Rate AbbreviationAbbreviation NameName

# of # of miles/1hour miles/1hour

Miles per Miles per hour hour

Mi/h or mph Mi/h or mph SpeedSpeed

# of miles/1 # of miles/1 gallon gallon

Miles per Miles per gallongallon

Mi/gal or Mi/gal or mpg mpg

Gas Gas MileageMileage

# of # of dollars/1 dollars/1 pound pound

Price per Price per PoundPound

Dollars/lb Dollars/lb Unit PriceUnit Price

# of # of dollars/1 dollars/1 hour hour

Dollars per Dollars per hourhour

Dollars/hDollars/h Hourly Hourly WageWage

COMMON UNIT RATES

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NotesNotesTo find unit rate, you divide by the To find unit rate, you divide by the denominator.denominator.

Ex.: Allie ran 24 miles in 3 hours. What is her Ex.: Allie ran 24 miles in 3 hours. What is her average speed in miles per hour?average speed in miles per hour?

11stst write the rate as a fraction. write the rate as a fraction.

24 mi24 mi

3 hr3 hr

Then divide the numerator by the Then divide the numerator by the denominator. denominator.

The answer is 8 miles per hour.The answer is 8 miles per hour.

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Example #1Example #1

Gavin traveled 300 miles and used 15 Gavin traveled 300 miles and used 15 gallons of gas. How many miles did he gallons of gas. How many miles did he travel per gallon?travel per gallon?

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Example #2Example #2

Julia biked 40 miles in 5 hours. What Julia biked 40 miles in 5 hours. What should her average speed be in miles per should her average speed be in miles per hour?hour?

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ReadingReading

Julia read 52 pages in 2 Julia read 52 pages in 2 hours. hours.

What is the average number What is the average number of pages she read per hour?of pages she read per hour?

88

ExampleExample

Natalie swam 16 laps in 4 minutes. What Natalie swam 16 laps in 4 minutes. What is the average number of laps she swam is the average number of laps she swam per minute?per minute?

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RunningRunning

Alice ran 24 miles in 3 hours. Alice ran 24 miles in 3 hours.

What is her average speed in What is her average speed in miles per hour?miles per hour?

1010

How Much Does It Cost?How Much Does It Cost?

Find the unit price per orange if it costs $2 for 6 Find the unit price per orange if it costs $2 for 6 oranges. Round to the nearest tenth if oranges. Round to the nearest tenth if necessary.necessary.

Find the unit price per can if it costs $3 for 6 Find the unit price per can if it costs $3 for 6 cans of soda. Round to the nearest tenth if cans of soda. Round to the nearest tenth if necessary.necessary.

Find the unit price per cookie if it costs $3 for 12 Find the unit price per cookie if it costs $3 for 12 cookies. Round to the nearest tenth if cookies. Round to the nearest tenth if necessary.necessary.

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ExampleExample

Claire is a member of a book club at a Claire is a member of a book club at a book store. The store offers 3 book deals book store. The store offers 3 book deals for members. Which deal is the best buyfor members. Which deal is the best buy

DealDeal PricePrice

3 books3 books $19.35$19.35

5 books5 books $32.25$32.25

7 books7 books $38.50$38.50

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Dish Detergent PricesDish Detergent Prices

The table shows the The table shows the various sizes and various sizes and prices of dish prices of dish detergent.detergent.

Which size is the Which size is the better buy?better buy?

Size Size VolumeVolume (fl oz) (fl oz)

Price Price

MiniMini 1212 $1.20 $1.20

FamilyFamily 2828 $2.24 $2.24

EconomyEconomy 4040 $3.60 $3.60

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Let’s Go Shopping!Let’s Go Shopping!

The costs of different The costs of different sizes of peanut butter sizes of peanut butter are shown below. are shown below.

Which jar costs the Which jar costs the least per ounce?least per ounce?

Size Size PricePrice

12 oz12 oz $2.49 $2.49

40 oz40 oz $5.30 $5.30

80 oz80 oz $10.89 $10.89

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Let’s Go Shopping!Let’s Go Shopping!

The costs of different The costs of different sizes of orange juice sizes of orange juice are shown below. are shown below.

Which container costs Which container costs the least per ounce?the least per ounce?

Size Size VolumeVolume (fl (fl oz) oz)

16 oz16 oz $1.28 $1.28

32 oz32 oz $1.92 $1.92

64 oz64 oz $2.56 $2.56

96 oz96 oz $3.36 $3.36

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Find each unit rate. Round to the Find each unit rate. Round to the nearest hundredth if necessary.nearest hundredth if necessary.

a.a. 300 tickets in 6 days300 tickets in 6 days

b.b. 220 miles in 8 gallons220 miles in 8 gallons

c.c. 228 feet in 24 seconds228 feet in 24 seconds

d.d. 440 miles in 8 hours440 miles in 8 hours