block 2 ~ ratios, rates and percents - oregon focus

30 Block 2 ~ Ratios, Rates And Percents ~ Rates

BLoCK 2 ~ rAtIos, rAtes And PerCentsrates

terminAte

word wAll

motion rAte

unit rAte

raTe

rePeAting decimAl

eQuiVAlent FrActions

rAte conVersion

Lesson 6 FracTions and deciMaLs ---------------------------------------------- 32 Explore! Back and Forth

Lesson 7 rePeaTing deciMaLs and roUnding ----------------------------------- 36 Explore! Calculators and Fractions

Lesson 8 raTes and UniT raTes ------------------------------------------------ 41Lesson 9 raTe ProBLeM soLving ------------------------------------------------ 45

Explore! Match the RatesLesson 10 coMParing raTes ----------------------------------------------------- 51

Explore! Shopping SalesLesson 11 MoTion raTes -------------------------------------------------------- 57review BLock 2 ~ raTes ------------------------------------------------------ 63

Block 2 ~ Rates ~ Tic - Tac - Toe 31

BLoCK 2 ~ rAtestic - tac - tOe

gAs mileAge

Find the gas mileage of your family car and what the manufacturer says the

gas mileage should be.

See page for details.

children’s story

Write a children’s story using three diff erent rates that need to be converted.


motion rAte

Find the time, in miles per hour, it takes you to walk

and run 0.25 miles. Use this rate to answer questions.


Food dilemmA

Take a trip to the grocery store. Find the best deal on cereal, peanut butter

and cheese.


does sPeeding helP?

Find the amount of time it takes a car to travel 2 miles in a construction zone at

diff erent speeds.


BAtting AVerAges

Calculate batting averages. Research batting averages in Major League Baseball.


tyPing

Time your typing to fi nd your rate of words typed

per minute.


FrActions And decimAls GaMe

Create a matching game with equivalent fractions

and decimals.


BAnking

Figure out how much banks earn by rounding up

or down on statements.


32 Lesson 6 ~ Fractions And Decimals

Jacob ran 1 _ 2 mile and Sam ran 2 _ 5 mile in four minutes. Who ran farther during the four minutes?

One method of comparing fractions is fi nding a common denominator and comparing the numerators of the equivalent fractions to determine which fraction is greater. Another method is rewriting each fraction as a decimal and comparing the decimals.

Th e fraction bar is a way of showing division. Th is means 1 _ 2 can also be written 1 ÷ 2. To write 1 _ 2 as a decimal fi nd the value of 1 ÷ 2. 0.5 2 |

___ 1.0 1 _ 2 = 0.5

To write 2 _ 5 as a decimal fi nd the value of 2 ÷ 5. 0.4 5 |

___ 2.0 2 _ 5 = 0.4

Since 0.5 is larger than 0.4 it can be written as 0.5 > 0.4. Th is means 1 _ 2 is larger than 2 _ 5 , or 1 _ 2 > 2 _ 5 . Since Jacob ran 1 _ 2 mile during the four minutes, Jacob ran farther than Sam.

Each tick mark between inches on a customary ruler represents one-sixteenth of an inch. Th ey can be simplifi ed to the following fractions:

1 __ 16 , 1 _ 8 , 3 __ 16 , 1 _ 4 , 5 __ 16 , 3 _ 8 , 7 __ 16 , 1 _ 2 , 9 __ 16 , 5 _ 8 , 11 __ 16 , 3 _ 4 , 13 __ 16 , 7 _ 8 , 15 __ 16 , 1

step 1: Copy the table. Use a calculator to fi nd the correct decimal value for each fraction. Complete the table.

Fraction 1 __ 16 1 _ 8 3 __ 16 1 _ 4 5 __ 16 3 _ 8 7 __ 16 1 _ 2 9 __ 16 5 _ 8 11 __ 16 3 _ 4 13 __ 16 7 _ 8 15 __ 16 1

decimal

step 2: Carla measured the length of a piece of wood. It was 8 1 _ 4 inches long. Rewrite this measurement as a decimal using the table. Explain how the table is useful.

step 3: Pam measured the length of a diff erent piece of wood. It was 10.625 inches long. Rewrite this measurement as a mixed number using the table.

exPlOre! Back and FOrth

FractiOns and decimals

Lesson 6

Lesson 6 ~ Fractions And Decimals 33

step 4: Use the table in step 1 to write each decimal as a fraction or mixed number. a. 0.625 b. 2.25 c. 5.8125 d. 3.5 e. 12.75 f. 9.1875

Sometimes it is helpful to write decimals as fractions. Th e place value of the last number in the decimal tells you which number to put in the denominator.

For example, the decimal in the place value chart above is read “sixteen hundredths.” It can be written as a fraction.

0.16 = 16 ____ 100 = 4 ___ 25

Convert each decimal to a fraction or mixed number in simplest form.

a. 0.7 b. 0.25 c. 6.2

a. Write 0.7 in words. 0.7 = seven tenths Use 10 as the denominator. 7 __ 10 b. Write 0.25 in words. 0.25 = twenty-fi ve hundredths Use 100 as the denominator. 25 ___ 100 Write in simplest form. 1 _

4

c. Write 6.2 in words. 6.2 = six and two tenths Use 10 as the denominator. 6 2 __ 10 Write in simplest form. 6 1 _ 5

examPle 1

solutions

exPlOre! cOntinued

1000 100 10 1 0.1 0.01 0.001

Th ou

sand

s

Hun

dred

s

Tens

One

s

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hs

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0 1 6

Whole Number Less Th an One

{ {

34 Lesson 6 ~ Fractions And Decimals

exercises

Convert each fraction or mixed number to a decimal.

1. 2 __ 5 2. 1 __ 8 3. 7 ___ 10

4. 1 ___ 16 5. 5 __ 8 6. 1 __ 4

7. 2 1 _ 2 8. 1 3 _ 4 9. 10 3 _ 5

10. Micaela measured the height of a candle in her room. It was 7 1 _ 4 inches tall. a. Write the height of the candle as a decimal.b. Micaela measured the candle again aft er burning it. It was 4 1 _ 8 inches tall. Write

the new height as a decimal.

11. Tricia and Natalia converted 5 _ 8 to decimal form. Which person did the problem correctly? Explain the mistake in the other person’s work.

determine which fraction is larger. rewrite each fraction as a decimal. Compare the decimals.

12. 5 __ 8 and 1 __ 2 13. 3 ___ 16 and 1 __ 4 14. 4 _ 5 and 7 _ 8

Write each decimal as a fraction or mixed number in simplest form.

15. 0.3 16. 0.6 17. 0.5

18. 0.25 19. 0.15 20. 1.25

21. 9.375 22. 10.2 23. 4.02

Tricia’s Work Natalia’s Work

5 _ 8 = 8 ÷ 5

1.6 5 |

___ 8.0

− 5 3 0

−3 0

0

5 _ 8 = 1.6

5 _ 8 = 5 ÷ 8 0.625 8 |

____ 5.000

−4.8 20 −16 40 − 40 0 5 _ 8 = 0.625

Lesson 6 ~ Fractions And Decimals 35

Write a fraction in simplest form that represents each model. Convert each fraction to a decimal.

24. 25. 26.

27. Each tick mark on a ruler between centimeters represents one millimeter or 0.1 centimeters. Th e table shows the value of each tick mark between 0 and 1 centimeters on a ruler in decimal form.

a. Copy and complete the table. Convert each decimal to a fraction in simplest form.b. Do you think it is easier to write parts of centimeters as decimals or fractions? Explain your answer.c. Pedro measured a piece of yarn. It was 7 4 _ 5 centimeters long. Write this measurement as a decimal.

review

Find the ratio of each geometric sequence. use the ratio to fi nd the next two terms of the geometric sequence. 28. 1, 3, 9, 27, 81, … 29. 4, 20, 100, 500, ... 30. 100, 10, 1, 0.1, …

Complete each conversion.

31. 10 yards = ________ feet

32. 18 inches = __________ feet

33. 2,000 meters = _________ kilometers

34. 14 meters = ________ centimeters

35. Patrick walked 2.5 kilometers to work today. Convert this distance to meters.

decimal 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Fraction

10 yards = ________ feet

2,000 meters = _________ kilometers

36 Lesson 7 ~ Repeating Decimals And Rounding

Marcus’ teacher asked him to write 1 _ 3 as a decimal.

0.3333...He began by fi nding 1 ÷ 3. 3 |

_______ 1.0000...

“Th is will keep going forever!” he realized. He wondered what to do.

Sometimes when you divide the numerator of a fraction by its denominator, the decimal does not terminate or stop. Instead it keeps going. If a decimal has one or more digits that repeat forever, it is a repeating decimal.

When a decimal is a repeating decimal write the repeating pattern once and draw a bar above the repeating part of the decimal. For example, Marcus would show that the 3 continues forever by writing: 1 __ 3 = 0.

_ 3

Convert each fraction to a decimal.

a. 2 __ 3 b. 1 __ 6 c. 1 ___ 11

0.6666...a. 2 __ 3 = 2 ÷ 3 = 3 |

_______ 2.0000... 2 __ 3 = 0.

_ 6

0.1666...b. 1 __ 6 = 1 ÷ 6 = 6 |

_______ 1.0000... 1 __ 6 = 0.1

_ 6

0.0909...c. 1 ___ 11 = 1 ÷ 11 = 11 |

_______ 1.0000... 1 ___ 11 = 0.

__ 09

examPle 1

solutions

rePeating decimals and rOunding

Lesson 7

Lesson 7 ~ Repeating Decimals And Rounding 37

step 1: Convert each fraction to a decimal. 1 __ 3 1 __ 9 8 __ 9 5 __ 6 step 2: Use a calculator to write each fraction in step 1 as a decimal. Divide the numerator of the fraction by its denominator. Write all numbers on the screen of the calculator as the answer.

step 3: Are the answers in step 2 diff erent than the answers in step 1? Explain why or why not. step 4: Samantha says 2 _ 3 = 0.666667. Pam says 2 _ 3 = 0.

_ 6 . Who is correct? Explain.

A calculator has limited space on the display screen. It cannot show all the numbers in a repeating decimal. It rounds the last digit on the screen.

You will oft en round decimal solutions. Use place value to round to the appropriate number.

round 2. _

4 to the nearest hundredth.

Underline the number in the hundredth place. 2.444...

Look at the digit one place to its right. 2.444...

Round down since 4 is less than 5. 2. _

4 ≈ 2.44

exPlOre! calculatOrs and FractiOns

examPle 2

solution

1000 100 10 1 0.1 0.01 0.001

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sand

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ths

Whole Number Less Th an One{ {


Convert 2 _ 3 to a decimal rounded to the nearest hundredth.

Convert 2 _ 3 to a decimal. 2 _ 3 = 0.666...Underline the number in the hundredths place. 0.6666….Look at the digit one place to its right. 0.6666….Round up since 6 is more than 5. 0.666... ≈ 0.67

2 _ 3 ≈ 0.67

exercises

Convert each fraction to a decimal. If it is a repeating decimal, use the bar to show which number(s) repeat. 1. 2 __ 3 2. 2 __ 9 3. 7 __ 9

4. 5 ___ 11 5. 3 __ 4 6. 1 __ 6

7. 1 ___ 11 8. 1 __ 3 9. 4 __ 9

10. Juan had a piece of fabric 1 _ 4 yard long. Lucinda had a piece of fabric 3 _ 4 yard long. Th ey wanted to know how much fabric they had combined.

a. Juan added the fractions together to fi nd the sum. Find the sum like Juan did.

b. Lucinda converted each fraction to a decimal. She added the decimals to fi nd the sum. Convert the fractions to decimals. Find the sum like Lucinda did.

c. Should Juan and Lucinda have the same answer? Do you have the same answer in part a as in part b? Explain.

11. Justin had a piece of wire 1 _ 3 meter long. Sherry had a piece of wire 2 _ 3 meter long. Th ey wanted to know how much wire they had altogether.

a. Justin added the fractions together to fi nd the sum. Find the sum like Justin did.b. Sherry converted each fraction to a decimal. She added the decimals to fi nd the sum. Convert the

fractions to decimals and fi nd the sum like Sherry did.c. Should Justin and Sherry have the same answer? Do you have the same answer in part a as in

part b? Explain.

examPle 3

solution

Lesson 7 ~ Repeating Decimals And Rounding 39

round each number to the nearest tenths place.

12. 0. __

17 13. 0. _

3

14. 4. __

48 15. 10. __

26

round each number to the nearest hundredths place.

16. 0. _

3 17. 5. __

07 18. 0.

_ 8 19. 11.2

__ 13

round each number to the nearest thousandths place.

20. 0.1 __

45 21. 23. _

4 22. 0.1

__ 09 23. 0.

______ 285714

Convert each fraction to a decimal. round the answer to the nearest hundredths place.

24. 2 __ 3 25. 7 __ 9

26. 2 ___ 11 27. 5 __ 6

28. The fraction 22 __ 7 is often used to find the area of a circle. a. Write 22 __ 7 as a decimal. b. Does the decimal for 22 __ 7 terminate or repeat? c. Round the decimal for 22 __ 7 to the nearest hundredth.

29. Marci and Adalya ran a 100 meter dash. Marci ran the distance in 12.025 seconds. It took Adalya 12.031 seconds. a. Which runner had the faster time? b. The timers’ stop watches rounded the times to the nearest hundredth. Would you be able to tell who won the race based on the stop watch times? Explain.

review

Convert each decimal to a fraction in simplest form.

30. 0.2 31. 0.75 32. 0.375 determine which fraction is larger. Convert each fraction to a decimal. Compare each decimal.

33. 1 __ 3 or 3 ___ 10 34. 2 __ 3 or 3 __ 4 35. 2 __ 5 or 1 __ 2


tic-tAc-toe ~ BAtti ng AV e r Age s

Batting averages for baseball and soft ball players are computed by fi nding the ratio of the number of hits a batter has to his/her number of times at bat.

Example: During the season Alex has batted 64 times. He has 19 hits. His batting average would be:

Batting Average = number of hits _____________ number of at bats = 19 ___ 64

Although 19 __ 64 is the ratio describing Alex’s batting average, batting averages are always expressed as decimals rounded to the nearest thousandths place. Alex’s batting average = 19 __ 64 = 0.296875 ≈ 0.297. Th is is read as, “Alex’s batting average is 297”.

1. Use a calculator to fi nd the batting average for each player on the school baseball team aft er 10 games.

Player Jones Field Gonzales Nguyen Huff Smith Kent Gwynn Raxter BradyHits 12 11 14 7 12 15 2 16 13 13

At Bats 40 36 42 35 38 40 12 40 34 41Batting Average

2. Which player had the highest batting average?

3. If Kent had 8 more at bats and 4 more hits, what would his new batting average be?

4. Ted Williams once had a batting average above 0.400 (read “400”) at the end of a Major League Baseball season. Since then, other players have tried to hit that high of an average but no one has. Baseball is said to be a sport with many failures; you fail to get a hit more oft en than you succeed. Find the players with the top batting averages in both the National League and the American League for the past three years. Record the information. What is the highest batting average any player had in the last three years?

Lesson 8 ~ Rates And Unit Rates 41

Dea found two diff erent deals online for downloading songs onto her computer. Songs Now charges $4.60 for 20 songs. Let’s Sing charges $0.25 per song. She wanted to fi gure out which company charges less money per song.

Dea will compare rates. A rate is a comparison of two numbers with diff erent units. In this case, she will compare the units of dollars and songs. Songs Now charges a rate of $4.60 _______ 20 songs . Let’s Sing charges a rate of $0.25 _____ 1 song .

Let’s Sing’s rate is a special rate called a unit rate. A unit rate is a rate that can be written as a fraction with a denominator of 1. Th ese rates can also be written as a single number using the word per or using a fraction bar to explain the units. $0.25 ______ 1 song = $0.25 per song = 25 cents/song

Write the rate at Songs Now as a unit rate to compare the cost per song. To compare the prices of the two companies, the rates should be written as unit rates.

Rewrite the rate $4.60 _______ 20 songs so it has a denominator of 1. $4.60 ________ 20 songs = $0.23 ______ 1 song

Th is means Songs Now charges $0.23 per song or 23 cents/song.

Songs Now charges less per song than Let’s Sing since $0.23 per song is less than $0.25 per song. Dea chose to buy songs from Songs Now.

Find each unit rate.

a. 50 miles ________ 2 hours b. $2.40 ___________ 3 candy bars

a. Rewrite the fraction with a 50 miles _______ 2 hours = 25 miles _______ 1 hour denominator of 1. Th e unit rate is 25 miles per hour.

b. Rewrite the fraction with a $2.40 ___________ 3 candy bars = $0.80 __________ 1 candy bar denominator of 1. Th e unit rate is $0.80 per candy bar.

examPle 1

solutions

÷ 20

÷ 20

÷ 2

÷ 2

÷ 3

÷ 3

rates and unit rates

Lesson 8

42 Lesson 8 ~ Rates And Unit Rates

Finding a unit rate is similar to rewriting a fraction as a decimal. One thing is diff erent. A unit rate includes the words for the units.

Th e united states Mint in Philadelphia produces 2,250 coins every 30 minutes. Find how many coins per minute the Mint produces.

Write the ratio of the number of coins 2250 coins _________ 30 minutes per 30 minutes as a rate.

Rewrite the fraction so it has a denominator of 1. 2250 coins _________ 30 minutes = 75 coins ________ 1 minute

Th e Mint produces 75 coins per minute.

exercises


1. 60 miles _______ 2 hours 2. 96 words ________ 4 minutes 3. 300 miles _________ 15 gallons

4. 12 days

_______ 2 jobs 5. $3.30 ______ 3 pens 6. 24 ounces __________ 1.5 servings

7. 32 pounds

_________ 8 inches 8. 30 feet ________ 3 seconds 9. 15 kilometers ___________ 5 hours

10. Jaden and Jaxen knew they could skateboard 3 miles in 30 minutes. Th ey fi gured out their speed in miles per minute. Th eir work is below.

a. Explain how Jaden solved the problem.b. Explain how Jaxen solved the problem.c. What number did both boys divide by to get their answers?d. Th eir friend, Max, wanted to fi nd their rate in miles per hour. His

calculations are shown below. He said Jaden and Jaxen skateboarded 6 miles per hour. Is this correct? Explain.

3 miles ÷ 0.5 ____________ 0.5 hour ÷ 0.5 = 6 miles ______ 1 hour

examPle 2

solution

Jaden Jaxen

3 miles ÷ 30 ____________ 30 minutes ÷ 30 = 0.1 miles _______ 1 minute

0.1 miles per minute

0.1 3 miles ________ 30 minutes = 30 |

___ 3.0

0.1 miles per minute

÷ 30

÷ 30

Lesson 8 ~ Rates And Unit Rates 43

11. José spent $36 for 4 movie tickets. Find the price per ticket.

12. Rob spent $3.30 for 6 large cookies. Find the price per cookie.

13. Polly used 10 gallons of gas to drive 235 miles on a trip. Find how many miles per gallon Polly’s car got on the trip.

14. Tran rode his scooter 10 miles in 1.5 hours. Find how many miles per hour he rode.

15. Maria could buy 6 songs online for $3.00 at Songs-R-Us, or she could pay $0.45 per song at Music Hooray. a. Find the unit rate of dollars per song for Songs-R-Us. b. Which company charges less per song?

16. Luke walked 2 miles in 40 minutes. He determined his unit rate was 20 minutes per mile. Sally informed him his rate was 0.05 miles per minute. Are these both accurate unit rates? Explain.

review

Convert each fraction to a decimal. If it is a repeating decimal, use the bar to show which number(s) repeat.

17. 1 __ 3 18. 1 __ 2 19. 3 __ 8 20. 2 __ 3

Convert each decimal to a fraction. Write in simplest form.

21. 0.25 22. 0.06

23. 1.3 24. 0.8

round each decimal to the nearest tenth.

25. 0. _

3 26. 2. __

09

27. 5.8 _

3 28. 0. _

7

44 Lesson 8 ~ Rates And Unit Rates

tic-tAc-toe ~ BA n k i ng

A bank oft en rounds interest added to a savings account by rounding the value down to the nearest cent. Th is is called truncating the number.

Example: Th e interest added to Jim’s savings account is $2.34976. Rather than rounding the number to the nearest penny ($2.35), the bank rounds down to $2.34 because they truncate the number 2.34|976. Th is means they ignore the digits aft er the hundredths place.

step 1: Why would a bank round interest this way? Explain using complete sentences.

step 2: If 10,000 people save money in the bank and half of them have interest that should round up, about how much money will the bank save by rounding down to the nearest cent?

step 3: If 100,000 people save money in the bank and half of them have interest that should round up, about how much money will the bank save by rounding down to the nearest cent?

A credit card company charges interest on items purchased using a credit card. Th e credit card company oft en rounds interest by rounding the value up to the nearest cent rather than truncating the number.

Example: Th e interest added to the credt card bill is $10.9813. Th e credit card company adds $10.99 to the bill even though the interest rounds to $10.98.

step 4: Why would a credit card company round interest this way? Explain using complete sentences.

step 5: If 20,000 people use the credit card company and half of them have interest that should round down, about how much extra money will the credit card company get by rounding up to the nearest cent?

step 6: If 1,000,000 people use the credit card company and half of them have interest that should round down, about how much extra money will the credit card company get by rounding up to the nearest cent?

step 7: Most banks loan money and provide savings accounts for their customers. A national banking company had 10,000,000 customers with both a savings account and a credit account one month. Half of their customers had interest rounded up on their credit statements and down on their savings statements. How much money did the bank make that month?

Lesson 9 ~ Rate Problem Solving 45

The fractions 2 _ 4 , 3 _ 6 , 4 _ 8 , and 5 __ 10 can be written in simplest form as 1 _ 2 . Th ese are examples of equivalent fractions. Equivalent fractions are fractions with the same value. Since ratios and rates can be written as fractions, they also can be written in many equivalent forms.

Below are 10 rates.

step 1: Each rate has the same units. Write the units for the rates. (______ per ______)

step 2: Which of the above rates are already written as unit rates?

step 3: Th ere are fi ve pairs of equivalent rates. One is given below. Find the four other pairs. Write the pairs next to one another with an equals sign between the two rates.

1. 12.00 ______ 4 tickets = .00 ______ 3 tickets 2. 3. 4. 5.

step 4: Explain how you fi gured out which rates were equivalent.

step 5: Th e price for a ticket to a jazz concert was $14. Write 5 equivalent rates using the unit rate of $14 per ticket.

exPlOre! match the rates

rate PrOBlem sOlving

Lesson 9

$12.00 ______ 4 tickets

$8.00 ______ 4 tickets

$10.00 ______ 2 tickets $16.00 ______ 2 tickets

$5.00 ______ 1 ticket

$24.00 ______ 4 tickets

$24.00 _________ 3 tickets

$9.00 ______ 3 tickets $6.00 ______ 1 ticket

$12.00 ______ 6 tickets

46 Lesson 9 ~ Rate Problem Solving

Problems involving rates can be solved using two diff erent methods. You can use equivalent fractions or unit rates.

Complete each equivalent rate.

a. 24 miles _______ 1 gallon = miles _______ 6 gallons b. $ 6.00 _____ 4 liters = $ ______ 32 liters

a. Find the factor from one denominator 24 miles ______ 1 gallon = miles _______ 6 gallons to the other.

Multiply the numerator by the same 24 miles _______ 1 gallon = 144 miles _______ 6 gallons factor to complete the equivalent rate.

b. Find the factor from one denominator $ 6.00 _____ 4 liters = $ ______ 32 liters to the other.

Multiply the numerator by the same $ 6.00 ______ 4 liters = $ 48.00 ______ 32 liters factor to complete the equivalent rate.

nigel paid $3.60 to send 30 text messages. use a unit rate to determine the cost to send 80 text messages.

Write the rate as a fraction. $3.60 ______ 30 texts

Find the unit rate. $3.60 _______ 30 texts = $0.12 ____ 1 text

Multiply the cost per text messageby the number of texts. $0.12 × 80 = $9.60

Nigel will pay $9.60 to send 80 text messages.

examPle 1

solutions× 6× 6

× 8× 8

examPle 2

solution

÷ 30

÷ 30


tom buys some hood river apples. A local fruit stand charges $3.00 for every 2 pounds. Find the price tom pays for 12 pounds of apples.

METHOD 1 ~ Equivalent FractionsWrite the rate as a fraction. $3.00 ____ 2 lbs

Write a second fraction with a denominator $3.00 _____ 2 lbs = $ ____ 12 lbs of 12 pounds.

Th e new denominator is 6 times the original denominator. Multiply the $3.00 _____ 2 lbs = $18.00 ______ 12 lbs numerator by 6.

Tom pays $18 for 12 pounds of apples.

METHOD 2 ~ Unit RatesWrite the rate as a fraction. $3.00 _____ 2 lbs

Find the unit rate. $3.00 _____ 2 lbs = $1.50 ____ 1 lb

Multiply the cost per pound ($1.50)by the number of pounds. $1.50 × 12 = $18.00

Tom pays $18 for 12 pounds of apples.

exercises


1. $3.00 ______ 1 gallon = $ _______ 10 gallons 2. 3 miles _____ 1 hour = miles ______ 8 hours 3. 60 words _______ 2 minutes = words ________ 14 minutes

4. 3 kilometers _________ 1 hour = kilometers __________ 3 hours 5. 25 miles ______ 1 gallon = 200 miles ________ gallons 6. 12 jobs

_____ 5 days = 48 jobs

______ days

use equivalent rates to complete each problem.

7. Felicia drove 120 miles in 3 hours. At this rate, how far will she drive in 6 hours?

8. Marcus burns 9 calories per minute when running. How many calories will he burn if he runs for 30 minutes?

examPle 3

solution

× 6

× 6

÷ 2

÷ 2


9. Henry paid $60 for 5 people to attend a play at the Shakespeare Festival in Ashland. Next year, 15 people in his class would like to go. If the cost is the same per ticket, how much will Henry pay for 15 people to attend next year?

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

10. 8 feet _______ 2 minutes 11. $4.00 _______ 10 pencils

12. 70 miles _______ 3 gallons 13. 12 meters ________ 48 seconds

14. 105 words ________ 2 minutes 15. $8.00 _______ 12 books

use a unit rate to complete each problem.

16. Jimmy’s new car went 204 miles on 12 gallons of gas. At this rate, how many miles can he travel using 5 gallons of gas?

17. Patrick went to the store to buy a seedless watermelon from Hermiston. It was on sale for $0.44 for every 2 pounds. He bought an 11 pound watermelon. How much did Patrick pay for the watermelon?

18. Denise filled her wading pool using her garden hose. The pool filled at a rate of 7 gallons every 2 minutes. She left the water on for 9 minutes. How many gallons of water were in the wading pool?

use equivalent fractions or unit rates to solve each problem.

19. Aaron walked 4 miles in 1 hour. At this rate, how far would he walk in 3 hours?

20. Josh spent $4.40 for 4 candy bars at the student store. How much would he pay for 7 candy bars at the student store?

21. Miranda’s mom sent her to the grocery store with $20.00. She bought 2 pounds of roast beef, 3 pounds of apples, 1 loaf of bread and 1 gallon of milk. She could buy anything else at the store she wanted with the remaining money. Use the prices below to answer the following questions.

Roast beef: $5.00 per pound Juice Box: $0.50 per box Apples: $2.50 for 2 pounds Cookie: $1.50 for 2 cookies Bread: $2.00 per loaf Candy bar: $1.00 per candy bar Milk: $2.50 per gallon Popcorn: $1.25 per bag

a. What was the total amount Miranda spent on the items her mom asked her to buy? b. How much money did she have left over? c. Could she purchase one cookie and one bag of popcorn with the remaining money?


review

Complete each conversion.

22. 3 kilometers = __________ meters 23. 35 millimeters = ___________ centimeters

24. 42 inches = ___________ feet 25. 5 yards = _________ feet

26. Lonnie spent $9.30 on 3 small cakes. Find the price per cake.

27. Jeff walked 27 miles in 6 hours. Find his speed in miles per hour.

tic-tAc-toe ~ gAs mile Age

Th e gas mileage a car gets is the ratio of the miles a car has driven to the number of gallons of gas used.

Gas Mileage = miles driven _____________ gallons of gas used

Example: A car traveled 235 miles on 12 gallons of gas. Its gas mileage is 235 miles _______ 12 gallons . Th e rate for gas mileage is usually written as a decimal rounded to the nearest tenth.

In this case, 235 miles _______ 12 gallons = 19.58 _

3 ≈ 19.6 miles per gallon.

step 1: Record the gas mileage of your family car. Write the number of miles driven. Write the amount of gas needed to fi ll up the tank at the gas station.

step 2: Record the gas mileage of your family car one more time to compare the two rates.

step 3: What is the estimated gas mileage for your family car based on your data?

step 4: Research your car to fi nd out what the manufacturer says the gas mileage should be.

step 5: Research to fi nd which car has the best gas mileage (most miles per gallon). Create a list of the top fi ve cars.


tic-tAc-toe ~ ty Pi ng

How many words per minute can you type? Use a timer or ask a friend to time you as you type the following story.

step 1: Type the entire 115 word paragraph and time yourself. Record the number of seconds it took you to type the passage. Also record the number of errors you made. Keep typing the passage until you make fewer than 5 errors. If this happens on your fi rst try, type faster and see how many errors you make. Type the passage and record the information at least three times.

Attempts Time (sec) Number of Errors

123

step 2: Convert the time it took you to type the passage from seconds to minutes. Round to the nearest hundredth.

step 3: What was your fastest typing rate as a unit rate of words per minute?

step 4: What was your fastest typing rate with fewer than 5 errors?

step 5: How long would it take you to type a 1-page paper with 460 words at your fastest rate?

Sally went to the store with her mother and brother and bought some milk, carrots, onions, salad dressing and tomatoes. Next, Sally’s mom took her to the dentist and the dry cleaners. Sally wanted to go home and play with her friends. Finally, Sally’s mom was done with errands for the day. She took Sally to the park to play with her friends. Sally’s friend, Tom, asked her what she had done that day. She told Tom she went to the store, the dentist and the dry cleaners. Tom reminded her that they had soccer practice in the evening. Sally told him she would see him at practice. She left for home to get ready.

Lesson 10 ~ Comparing Rates 51

step 1: Kay went to the department store to buy new t-shirts for the 12 girls on her soccer team. She found a sale and could buy 3 shirts for $9.00. a. Write the rate as a fraction: $ _______ shirts b. Rewrite the rate as a unit rate. What is the price per shirt?

c. How much will it cost Kay to buy 12 shirts at this price per shirt?

d. Another way to fi nd the cost is to use equivalent rates. Complete the equivalent rate to fi nd Kay’s cost for 12 shirts. $9.00 ______ 3 shirts = $ ______ 12 shirts

step 2: Trudy and Cathy went to a diff erent department store. Th ey could buy 4 shirts for $12.00. a. Write the rate as a fraction: $ ________ shirts

b. Rewrite the rate as a unit rate. What is the price per shirt?

c. How much will it cost Trudy to buy 12 shirts at this price per shirt?

d. Another way to fi nd the cost is to use equivalent rates. Complete the equivalent rate to fi nd Trudy’s cost for 12 shirts. $12.00 ______ 4 shirts = $ ______ 12 shirts

step 3: Mark can buy 2 pairs of jeans for $48.00 at Bob’s or 3 pairs of jeans for $66.00 at Joe’s. At which store will Mark pay less per pair of jeans? Explain your answer.

exPlOre! shOPPing sales

cOmParing rates

Lesson 10

52 Lesson 10 ~ Comparing Rates

Is it a better deal to buy a 20 ounce box of cereal for $3.50 or a 16 ounce box of cereal for $3.00?

To fi nd the best deal, write each rate as a unit rate by fi nding dollars per ounce.

20 ounce box for $3.50 $3.50 ____ 20 oz = $0.175 _____ 1 oz $0.175 per ounce

16 ounce box for $3.00 $3.00 ____ 16 oz = $0.1875 ______ 1 oz $0.1875 per ounce

Th e 20 ounce box is the better deal because it costs less per ounce.

Which vehicle gets better gas mileage: a car that travels 408 miles using 12 gallons of gas or a truck that travels 448 miles using 14 gallons of gas?

To fi nd the better gas mileage write each rate as a unit rate by fi nding miles per gallon to compare the gas mileage.

Car: 408 miles _______ 12 gallons = 34 miles ______ 1 gallon 34 miles per gallon

Truck: 448 miles _______ 14 gallons = 32 miles ______ 1 gallon 32 miles per gallon

Th e car gets better gas mileage because it travels more miles per gallon.

examPle 1

solution

examPle 2

solution

÷ 20

÷ 20

÷ 16

÷ 16

÷ 12

÷ 12

÷ 14

÷ 14


Paul went to the grocery store to buy potatoes. A 10 pound bag of potatoes cost $4.00. A 6 pound bag of potatoes cost $2.70. a. Which size of bag is the best deal?b. What is the lowest total cost Paul will pay for 20 pounds of potatoes?

a. Compare the unit rates. $4.00 for 10 lbs: $4.00 ____ 10 lbs = $0.40 ____ 1 lb $0.40 per pound

$2.70 for 6 lbs: $2.70 ____ 6 lbs = $0.45 ____ 1 lb $0.45 per pound

It is cheaper per pound to buy the 10 pound bag.

b. Use equivalent rates. $4.00 for 10 lbs: $4.00 ____ 10 lbs = $ ____ 20 lbs

$4.00 _____ 10 lbs = $8.00 ____ 20 lbs

Twenty pounds of potatoes cost $8.00.

exercises

use unit rates to determine which of the two rates is smaller. 1. $5.00 __________ 2 sandwiches or $6.75 __________ 3 sandwiches 2. 10 miles ______ 1 hour or 35 miles ______ 4 hours

3. 162 miles _______ 6 gallons or 150 miles _______ 5 gallons 4. 16 jobs

_____ 4 days or 10 jobs

_____ 2 days

5. Kyle types at a rate of 55 words per minute. Christine types at a rate of 120 words in 2 minutes. Which person types more words per minute? 6. Marta runs a race against her best friend Markesha. Marta runs at a rate of 7 miles in 1 hour. Markesha runs at a rate of 4 miles in 0.5 hours. Which person runs at a faster rate?

7. Ivan needs new highlighters. He can buy a package of 6 highlighters for $7.50 or a package of 4 highlighters for $6.00. Which package of highlighters has the best price per highlighter?

examPle 3

solutions

÷ 10

÷ 10

× 2

× 2

÷ 6

÷ 6


8. Lyuba needs to buy dog food for her dog. She can buy a 20 pound bag of dog food for $15.00 or a 40 pound bag for $28.00. Which bag of dog food is cheaper per pound?

9. Mark drove 150 miles in 3 hours. Jamal drove 220 miles in 4 hours. a. Find the unit rate of speed for both trips. b. Who was driving faster? c. Both men traveled at these rates for a total of 6 hours. How far did each one travel?

use equivalent rates to determine the total cost for 24 pounds of marionberries from three local farms given the price each farm charges.

10. $1.50 per pound 11. $5.00 for 3 pounds 12.$4.00 for 2 pounds 13. Ryan needs to buy 60 notebooks. At the store he found he could buy a package of 20 notebooks for $20.00 or a package of 15 notebooks for $10.00. a. How many 20 notebook packages would Ryan need to buy? b. How much will Ryan pay if he chooses to buy packages of 20? c. How many 15 notebook packages would Ryan need to buy? d. How much will Ryan pay if he chooses to buy packages of 15? e. Which packages should Ryan buy if he wants the cheaper cost?

f. Check your answer. Find the unit rate (price per notebook) for the 20 notebook package and the 15 notebook package.

14. Shelly rides her 10-speed bike at a rate of 16 miles per hour. She rides her mountain bike 24 miles in 2 hours. She needs to ride 48 miles. Which bike should she ride to get there most quickly? a. Find the unit rate of speed (miles per hour) for the 10-speed. b. How long would it take Shelly to ride the 10-speed 48 miles? c. Find the unit rate of speed (miles per hour) for the mountain bike. d. How long would it take Shelly to ride the mountain bike 48 miles? e. On which bike will Shelly ride the 48 miles faster?

15. Zane needs to buy 20 balloons for a birthday party. He can buy a package of 5 balloons for $4.00 or a package of 4 balloons for $3.60. a. Determine which package of balloons is a better price per balloon. b. How much will it cost him to buy 20 of the cheaper balloons?

review

Convert each fraction or mixed number to a decimal. If it is a repeating decimal, use the bar to show which number(s) repeat. 16. 3 _ 4 17. 2 _ 3

18. 2 4 _ 5 19. 1 1 _ 2


20. Th ree pigs and 9 goats live at a local farm. a. Write the ratio of pigs to goats.

b. Write the ratio of pigs to animals at the farm.c. Write the ratio of goats to animals at the farm.

21. Six out of 9 boys surveyed like soccer. a. Write the ratio of boys who like soccer to boys surveyed.

b. Write the ratio of boys who like soccer to boys who do not like soccer.

tic-tAc-toe ~ Food dile m m A Grocery stores sell the same type of cereal in diff erent sized boxes. Th ere is one price for a 14 ounce box and another price for a 20 ounce box of the same brand. Which one is the best deal?

Take a trip to a grocery store to fi nd the items listed in the chart. Remember you DO NOT have to buy the items, just fi nd the prices.

step 1: Copy the following table and take it to a local grocery store.step 2: Record the brand name of the item you have selected for cereal, cheese, and peanut butter.step 3: Record the size of the item and its price. If it is on sale, put a * next to the price.step 4: Find the unit price for each item (the price per ounce or price per pound).step 5: Determine which size item is the best deal (cheapest price per ounce or pound).

Size Price Unit Price Best Deal?

CerealBrand: _____

1.

2.

3.

1.

2.

3.

1.

2.

3.

CheeseBrand: _____

1.

2.

3.

1.

2.

3.

1.

2.

3.

Peanut ButterBrand: _____

1.

2.

3.

1.

2.

3.

1.

2.

3.


tic-tAc-toe ~ doe s sPe e di ng he l P?

Th ere is a two-mile stretch of highway under construction. Th e speed limit in the construction zone is 20 miles per hour. Th e fi nes for speeding on that section of the road begin at $280 and increase according to the speed of the driver. If a person chooses to speed in the construction zone, how much time will they really save?

step 1: Find the amount of time it takes to drive two miles at 20 miles per hour. You need to know the time it takes to drive 1 mile to fi nd the time for 2 miles.

Change the ratio from 20 miles per hour to 1 hour for 20 miles and fi nd the unit rate.

1 hour ______ 20 miles = ? hour _____ 1 mile

Convert the decimal for the number of hours to minutes → ______ minutes How many minutes does it take a driver to drive the 2 miles at 20 miles per hour?

step 2: Use the steps above to fi nd the number of minutes it takes a driver to drive the 2 mile section of road at each of the speeds in the chart. Copy and complete the chart.

Miles per hour 15 20 25 30 40 50Minutes to travel 2 miles

step 3: Explain why it is not better to drive 50 miles per hour than 20 miles per hour in the construction zone. Use complete sentences and include information from your table in your explanation.

tic-tAc-toe ~ ch il dr e n’s story

step 1: Create a children’s book that incorporates three diff erent rates that need to be converted. For example, convert miles per hour to feet per hour or jobs per week to jobs per day.

step 2: Th e story may also involve comparison of rates. Look through this textbook to get more ideas about the three diff erent rates to use in your story.

step 3: Your book should have a cover, illustrations and an appropriate story line for children.

Lesson 11 ~ Motion Rates 57

Rates that compare distance to time are called motion rates. Meters per hour, feet per hour and inches per minute are examples of motion rates. Distance can be measured using customary or metric units. Time is most oft en written as seconds, minutes, hours, days, weeks, months or years.

If you know the unit rate someone is traveling and the amount of time they travel, you can use motion rates to determine how far they traveled.

oksana’s family traveled on a highway through central oregon at a rate of 60 miles per hour. her family traveled at this rate for 2.5 hours. how far did they drive?

Locate the unit rate. 60 miles per hourMultiply by 2.5 hours. 60 × 2.5 = 150

Oksana’s family traveled 150 miles in 2.5 hours.

You can use unit rates to compare two motion rates.

Wayne and Marla each left home on their bikes. Th ey were meeting at the library, which is exactly the same distance from each of their homes. Wayne traveled at a rate of 20 miles every 2 hours. Marla traveled at a rate of 6 miles every 0.5 hour. Th ey left home at the same time. Who arrived at the library fi rst?

Find Wayne’s unit rate of speed. 20 miles ______ 2 hours = 10 miles ______ 1 hour

Wayne traveled 10 miles per hour.

Find Marla’s unit rate of speed. 6 miles ______ 0.5 hour = 12 miles ______ 1 hour

Marla traveled 12 miles per hour.

Marla rode faster, so she arrived at the library fi rst.

examPle 1

solution

examPle 2

solution

÷ 2

÷ 2

÷ 0.5

÷ 0.5

mOtiOn rates

Lesson 11

58 Lesson 11 ~ Motion Rates

Martin traveled at a rate of 3 kilometers per hour on his tricycle. What is this unit rate when converted to meters per hour?

Karla walked at a rate of 4 miles per hour. What is this unit rate when converted to feet per hour?

Justin watched a bug travel at a rate of 3 feet per minute. How fast was the bug traveling when measured in feet per hour?

Each of these situations requires a rate conversion. A rate conversion is performed by changing at least one of the units in the rate. Th ree kilometers per hour can be changed to meters per hour by converting kilometers to meters.

Look at Martin’s rate on his tricycle. Find an equivalent measurement relating kilometers and meters. Since 1 kilometer = 1000 meters, this will be used to make the conversion rate. Multiply the original rate by a conversion rate so unwanted units will cancel.

3 kilometers _________ 1 hour × 1000 meters _________ 1 kilometer = 3000 meters _________ 1 hour

original rate conversion rate new equivalent rate

Convert 4 miles per hour to feet per hour.

Write the rate as a fraction. 4 miles _____ 1 hour

Identify the units in the answer. 4 miles _____ 1 hour × ____ = feet ______ hour

Fill in the conversion rate using 4 miles _____ 1 hour × 5280 feet _______ 1 mile = 21120 feet ________ 1 hour equivalent measurements. 1 mile = 5280 ft

4 miles per hour = 21,120 feet per hour

examPle 3

solution


Convert 3 feet per minute to feet per hour.

Write the rate as a fraction. 3 feet _______ 1 minute

Identify the units in the answer. 3 feet _______ 1 minute × ______ = feet ______ hour

Fill in the conversion rate using equivalent 3 feet ________ 1 minute × 60 minutes _________ 1 hour = 180 feet _______ 1 hour measurements. 1 hour = 60 minutes

3 feet per minute = 180 feet per hour

exercises

1. Efran can ride his skateboard at a rate of 6 miles per hour. Copy the table and fill in the total miles he skateboards after each hour.

2. Olivia rode her bike at a rate of 12 miles per hour. She rode at this rate for 2 hours. How far did she ride?

3. Jean walked to her friend’s house at a rate of 4.5 miles per hour. She walked for 0.5 hours. How far did she walk?

4. Janette watched a woolly caterpillar crawl across the playground at a rate of 6 inches per minute. It crawled at that rate for 10 minutes. How far across the playground did it crawl? 5. Maricela watched a race car go around a track at a speed of 120 miles per hour. Maricela watched the race car travel 180 miles. How many hours did Maricela watch the race car?

6. A turtle walks 2 feet per minute. How long will it take the turtle to walk 15 feet?

7. Hector ran 15 miles in 3 hours. How far could he run at that speed in 4 hours?

8. Ben drove 25 miles in 0.5 hours. How far could he drive at that speed in 3 hours?

examPle 4

solution

hours 1 2 3 4 5 6 total miles traveled


Compare the two rates by fi nding the unit rate of each. Identify the faster rate.

9. 9 miles _____ 1 hour or 16 miles ______ 2 hours 10. 32 centimeters ___________ 2 minutes or 120 centimeters ___________ 4 minutes

11. 14 yards

______ 2 days or 18 yards

______ 3 days 12. 5 kilometers _________ 1 week or 24 kilometers __________ 4 weeks

13. Ryan walked at a rate of 5 miles per hour. His sister, Hillary, walked 9 miles in 1.6 hours. Who walked at a faster rate?

14. Carmen and Gabriella each live 2 miles from the ice rink. Carmen ran to the rink at a rate of 4.2 miles per hour. Gabriella ran to the rink in 0.4 hours. Th ey left their homes at the same time. Who arrived at the ice rink fi rst?

15. Two work crews in the Columbia Gorge were trying to fi x potholes on the Historic Highway. Th e red crew repaired 3 kilometers of highway in 0.5 days. Th e blue crew repaired 5 kilometers of highway in 1 day. Which crew repaired a longer length of road per day?

Complete each conversion rate. 16. 1 kilometer ________ ? meters 17. 1 foot ________ ? inches

18. ? minutes _________ 1 hour 19. 1 meter ____________ ? centimeters

20. Which of the following rate(s) are not conversion rate(s)? Explain your choice(s).

1 ft ____ 12 in 1 m ______ 100 cm

2 yds ____ 9 ft 1 minute ________ 60 seconds 1 mi ______ 5280 ft 24 hours _______ 1 day

determine which rate should be used to complete each conversion.

21. 8 miles _____ 1 hour to feet ____ hour A. 1 mile _______ 5280 feet or B. 5280 feet _______ 1 mile

22. 5 meters _______ 1 minute to meters ______ seconds A. 1 minute ________ 60 seconds or B. 60 seconds ________ 1 minute

23. 2 yards per day to feet per day A. 1 yard

_____ 3 feet or B. 3 feet _____ 1 yard

24. A worm travels at a rate of 1 inch per second. Find this rate in inches per minute.


25. A deer runs at a rate of 7 miles per hour. Convert this rate to feet per hour.

Write the equivalent rate by converting the rate on the left to the rate on the right. 26. 2 miles _____ 1 hour = ? feet _____ 1 hour 27. 9 kilometers _________ 1 year = ? meters ______ 1 year

28. 24 inches _______ 1 second = ? feet _______ 1 second 29. 5 meters _______ 1 minute = ? meters ______ 1 hour

review

Convert each fraction or mixed number to a decimal. If it is a repeating decimal, use the bar to show which number(s) repeat.

30. 2 _ 9 31. 3 1 _ 4 32. 1 2 _ 3 33. 1 _ 8


34. Kirk walked 0.75 miles on the track every morning. Write the distance he walked as a fraction in simplest form.

35. Sierra bought 3. _

3 pounds of pears at the local farmer’s market. Write the weight of her pears as a fraction in simplest form.

36. Jules grew 0.125 inches last month. Write the amount of Jules’ growth as a fraction in simplest form. 37. Erin rides her bike 1.6 miles to school everyday. Write the distance she travels as a fraction in simplest form.


tic-tAc-toe ~ motion r Ate

Find a 1 _ 4 mile track or fi nd a 1 _ 4 mile length near your home where you can run and walk to answer the questions below.

step 1: Run 1 _ 4 mile. Record your time in minutes and seconds. Convert your time to minutes rounded to the nearest hundredth.

step 2: Find your rate in miles per hour for running 1 _ 4 mile. Your initial rate will be 0.25 miles ________ ? minutes . Convert this rate to miles per hour as a unit rate.

step 3: Walk 1 _ 4 mile. Record your time in minutes and seconds. Convert your time to minutes rounded to the nearest hundredth.

step 4: Find your rate in miles per hour for walking 1 _ 4 mile. Your initial rate will be 0.25 miles ________ ? minutes . Convert this rate to miles per hour as a unit rate.

step 5: Determine how long it will take you to walk and run each of the lengths below. Assume you keep your calculated rate. Copy and complete the chart.

1 mile 5 miles 10 miles 26 miles (marathon)

Run timeWalk time

tic-tAc-toe ~ Fr Actions A n d deci m A l s gA me

Create a memory card game using common equivalent fractions and decimals. Common fractions are fractions with denominators of 2, 3, 4, 5, 6, 8 and 10. Use at least four diff erent denominators to create pairs of cards so one card has a fraction and the matching card has the equivalent decimal. Th e cards should be made on thick paper, such as card stock, construction paper, index cards or poster board. Th e game must have a minimum of 24 cards.

Block 2 ~ Review 63

review

equivalent fractions rate terminate motion rates rate conversion unit rate repeating decimal

vocabulary

BLoCK 2

Lesson 6 ~ Fractions and Decimals

Convert each fraction or mixed number to a decimal. 1. 1 _ 5 2. 5 _ 8 3. 2 3 __ 10

determine which fraction is larger by fi rst rewriting the fractions as decimals to compare them.

4. 3 _ 8 and 1 _ 2 5. 3 __ 12 and 1 _ 5 6. 4 _ 5 and 3 _ 4


7. 0.6 8. 0.5 9. 0.125

10. Petra’s mom bought 0.375 pounds of cashews. What is the weight of the cashews as a fraction in simplest form?

Lesson ~ Repeating Decimals and Rounding

Convert each fraction to a decimal. use the bar to show which number(s) repeat.

11. 2 _ 3 12. 1 _ 3 13. 5 _ 9

64 Block 2 ~ Review

round each number to the nearest tenths place.

14. 0. _

6 15. 0. __

45 16. 1 _ 3 17. 1 _ 6 18. 6.

_ 9 19. 5 _ 7

round each number to the nearest hundredths place.

20. 0. __

09 21. 1 _ 8 22. 2 _ 3

Lesson ~ Rates and Unit Rates


23. 450 miles _______ 15 gallons 24. 14 days

______ 2 jobs 25. 40 miles ______ 4 hours

26. 36 meters _______ 9 minutes 27. $5.50 ________ 11 pictures 28. 18 ounces _________ 1.5 servings

29. Darlene spent $52 for 13 notebooks. Find the price per notebook.

30. Tim bought a box of 36 marbles for $12.00. Find the price per marble. Round your answer to the nearest hundredth.

31. Rebecca used 8 gallons of gas to drive 204 miles. Find how many miles per gallon Rebecca’s car got.

32. Anna skipped at a rate of 2 miles per hour. Her friend, Jenna, skipped at a rate of 0.5 miles in 0.2 hours. Which one skipped at a faster rate?

Lesson 9 ~ Rate Problem Solving


33. 80 words _______ 1 minute = words _______ 5 minutes 34. 12 kilometers __________ 1 hour = kilometers _________ 3 hours

35. $2.80 ______ 1 gallon = $ _______ 10 gallons 36. $5.50 ______ 1 ticket = $27.50 ______ tickets

Block 2 ~ Review 65

use equivalent rates to complete each problem.

37. Holly drove 110 miles in 2 hours. At this rate, how far will she drive in 6 hours?

38. Ari paid $48.33 for 3 concert tickets for herself and two friends. How much money will each friend pay Ari for her ticket? Find each unit rate. round to the nearest hundredth if necessary.

39. $10.00 _______ 3 toy cars 40. 25 millimeters __________ 5 seconds 41. 154 miles _______ 7 gallons

use a unit rate to complete each problem.

42. Isabella loves eating apples. She eats apples at the rate of 45 apples every 30 days. At this rate, how many apples does Isabella eat in 10 days?

43. Lisa bought pears at a Mt. Hood fruit stand. They were on sale for $2.50 for 2 pounds. Lisa bought 9 pounds. How much did Lisa pay for the pears?

Lesson 10 ~ Comparing Rates

use unit rates to determine which of the two rates is smaller. 44. $16.00 _____ 5 toys or $9.75 _____ 3 toys 45. 11 miles _______ 1 hour or 42 miles _______ 4 hours 46. 10 calories ________ 30 ounces or 20 calories ________ 50 counces

47. Quinn spent $31.00 for 5 comic books. His friend, Casey, spent $18.00 for 3 comic books. Which person got a better deal? 48. Janelle paints at a rate of 5 pictures every 8 days. Her teacher paints at a rate of 3 pictures every 6 days. Which person paints more pictures per day?

use equivalent rates to determine the total cost for 12 pounds of tomatoes from two local farms given the price each farm charges. 49. $1.50 per pound of tomatoes 50. $4.00 for 3 pounds of tomatoes

51. Tyler needs to buy 24 pens. He could buy packages of 6 pens for $12.00 or packages of 8 pens for $14.00. a. How many packages of the 6 pens would Tyler need to buy? b. How much will Tyler pay if he chooses to buy packages of 6 pens? c. How many packages of the 8 pens would Tyler need to buy? d. How much will Tyler pay if he chooses to buy packages of 8 pens? e. Which packages should Tyler buy if he wants the cheaper cost? f. Check your answer. Find the unit rate (price per pen) for the 6-pack and the 8-pack of pens.

66 Block 2 ~ Review

Lesson 11 ~ Motion Rates

52. Ellen rode her bike at a rate of 15 miles per hour. She rode at this rate for 3 hours. How far did she ride?

53. Stacie walked to school from home at a rate of 3.5 miles per hour. She walked for 0.2 hours. How far is the school from her house?

54. Manuel ran 16 miles in 2 hours. How many hours does it take him to run 24 miles?

55. One frog hopped at a rate of 3 meters for every 15 minutes. A second frog hopped at a rate of 1 meter every 4 minutes. The two frogs entered a frog hopping contest. Which frog won?

Complete each conversion rate. 56. 1 meter __________ ? centimeters 57.

1 yard _____ ? feet 58. ? seconds _______ 1 minute

Which conversion rate should be used to convert:

59. 45 miles ______ 1 hour to feet ____ hour ? A. 1 mile _______ 5280 feet or B. 5280 feet _______ 1 mile

60. 9 meters _______ 1 minute to meters _____ second ? A. 1 minute ________ 60 seconds or B. 60 seconds ________ 1 minute

61. A dog runs at a rate of 5 miles per hour. Convert this rate to feet per hour.

Write each equivalent rate by converting the rate on the left to the rate on the right. 62. 2 feet _____ 1 hour = inches _______ 1 hour 63. 8 kilometers _________ 1 minute = meters _______ 1 minute

Block 2 ~ Review 67

ana middle school PrinciPAl

PortlAnd, oregon

I am a middle school principal. My job has lots of different duties. One thing I do is make sure that my school is a safe and positive place for students and staff. I work with parents, students and teachers to make sure our students are achieving as highly as they can. My job includes managing our school budget and making sure we are doing everything the state and federal governments require.

Math is an important part of running any school. We must account for and keep track of money grants we receive. Teachers and other staff are paid salaries for which I must budget. Textbooks and supplies must be purchased. My school has to manage the budget in a way that best helps students learn. Student achievement is tracked using percentages. I regularly use math to see if students are making good progress toward our learning goals.

I completed a college program and got a master’s degree to become a middle school principal. I also had to pass tests to make sure that I knew everything that would be required of a principal. Principals are licensed by the state. I have to renew my license every few years and keep current on what is happening in education. I am always learning new things about education as a principal.

A principal’s salary can range from $65,000 - $90,000 per year. Principals also get other benefits like health insurance. Salaries depend on where in the state you work, what level of school you are the principal of and how many years experience you have.

I enjoy my profession because it allows me to have an impact on student learning and student success.

CAreer FoCus

block 2 ~ ratios, rates and percents - oregon focus

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