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2 Chapter 1

1A Whole Numbers andExponents

1-1 Comparing and OrderingWhole Numbers

1-2 Estimating with Whole Numbers

1-3 Exponents

1B Using WholeNumbers

LAB Explore the Orderof Operations

1-4 Order of Operations

1-5 Mental Math

1-6 Choose the Methodof Computation

1-7 Patterns and Sequences

LAB Find a Pattern inSequences

2 Chapter 1

Whole Numbers and PatternsWhole Numbers and Patterns

Veterinary TechnicianDo you like caring for animals? Veterinary

technicians perform many of the same tasks forveterinarians as nurses do for doctors. Veterinarytechnicians also do research that can help animals. To care for animals, technicians must know what the animals need to eat and how they behave with other types of animals.Large plant-eating animals, many of which live in Africa, need to eat specific kinds of grasses and trees. The table above shows the approximate weight of some animals and the approximate amount of food the animals eat each day.

African Plant-Eating Animals

Animal Weight (lb) Daily FoodIntake (lb)

Buffalo 1,500 45

Elephant 11,000 660

Giraffe 2,500 75

Hippopotamus 5,500 90

Zebra 950 30

KEYWORD: MR7 Ch1

Whole Numbers and Patterns 3

VocabularyChoose the best term from the list to complete each sentence.

1. The answer in a multiplication problem is called the .

2. 5,000 � 400 � 70 � 5 is a number written in form.

3. A(n) tells about how many.

4. The number 70,562 is written in form.

5. Ten thousands is the of the 4 in 42,801.

Complete these exercises to review skills you will need for this chapter.

Compare Whole NumbersCompare. Write � , �, or �.

6. 245 219 7. 5,320 5,128

8. 64 67 9. 784 792

Round Whole NumbersRound each number to the nearest hundred.

10. 567 11. 827 12. 1,642 13. 12,852

14. 1,237 15. 135 16. 15,561 17. 452,801

Round each number to the nearest thousand.

18. 4,709 19. 3,399 20. 9,825 21. 26,419

22. 12,434 23. 4,561 24. 11,784 25. 468,201

Whole Number OperationsAdd, subtract, multiply, or divide.

26. 18 � 22 27. 135 � 3 28. 247 � 96 29. 358 � 29

Evaluate Whole Number ExpressionsEvaluate each expression.

30. 3 � 4 � 2 31. 20 � 100 � 40

32. 5 � 20 � 4 33. 6 � 12 � 5

?

?

?

?

?

place value

estimate

product

expanded

standard

period

Vocabulary ConnectionsTo become familiar with some of thevocabulary terms in the chapter, consider thefollowing. You may refer to the chapter, theglossary, or a dictionary if you like.

1. The word evaluate means “to determinethe value of something.” What do you thinkyou will in this chapter?

2. An order is the way things are arranged oneafter the other. How do you think an

will help you solvemath problems?

3. The word numerical means “of numbers.”The word expression can refer to amathematical symbol or combination ofsymbols. What do you think a

is?

4. A sequence is a list or arrangement that isin a particular order. What kind of

do you expect to see in thischapter?sequence

numerical expression

order of operations

evaluate

Key Vocabulary/VocabularioAssociative Property propiedad asociativa

base base (en numeración)

Commutative Property propiedad conmutativa

Distributive Property propiedad distributiva

evaluate evaluar

exponent exponente

numerical expression expresión numérica

order of operations orden de las operaciones

sequence sucesión

term término (en una sucesión)

Previously, you

• compared and ordered wholenumbers to the hundredthousands.

• used the order of operationswithout exponents.

• looked for patterns.

You will study

• comparing and ordering wholenumbers to the billions.

• using the order of operations,including exponents.

• how to recognize and extendsequences.

• using properties to computewhole-number operationsmentally.

• representing whole numbers byusing exponents.

You can use the skillslearned in this chapter

• to express numbers in scientificand standard notation in scienceclasses.

• to recognize and extendgeometric sequences.

4 Chapter 1

Stu

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ide:

Pre

view

Reading Strategy: Use Your Book for SuccessUnderstanding how your textbook is organized will help you locate and use helpful information.

Use your textbook.

1. Use the glossary to find the definitions of bisect and factor tree.

2. Where in the Skills Bank can you review how to round whole numbersand decimals?

3. Use the Problem Solving Handbook to list the four steps of the problem-solving plan and two different problem-solving strategies.

4. Use the index to find the pages where angles and histogram appear.

Try This

Read

ing

and

Writin

g M

ath

Whole Numbers and Patterns 5

A group of four talmarks with a linethrough it means f

To write a repeatindecimal, you canshow three dots odraw a bar over th

Estimating beforeyou add or subtrawill help you checwhether your answ

When you write anexpression for dataa table, check that expression works f

As you read through an example problem, pay attention to the margin notes,such as Reading Math notes, Writing Math notes, Helpful Hints, and Caution notes.

These notes will help you understand concepts and avoid common mistakes.

Place Value—Trillions

You can use a place-value chart to read and write numbers.

Skills BankSkills Bank ReGlossary/GlosarioGlossary/Glosario

ENGLISHabsolute value The distance of anumber from zero on a numberline; shown by⏐⏐.

valor abestá un nnuméricabsoluto

Aaron, Hank, 36Abacus, 9Absolute value, 762Accuracy, 767A t It O t

in scale374–

in simisolving

tiles, 634variables

Algebra tileAlgebraic e

writing, 6Alternate exAlternate inAlvin submAngle meas

IndexIndex

The Glossary is foundin the back of yourtextbook. Use it as a resource when youneed the definition ofan unfamiliar word or property.

The Index is locatedat the end of yourtextbook. Use it tolocate the page wherea particular concept istaught.

The Skills Bank is found in the back ofyour textbook. Thesepages review conceptsfrom previous mathcourses, includinggeometry skills.

6 Chapter 1 Whole Numbers and Patterns

Learn to compare andorder whole numbersusing place value or anumber line.

The midyear world population in 1995 was 5,694,418,460 people. The world population by midyear 2015 is projected to be 7,202,516,136people.

You can use place value to read and understand large numbers. In the place value chart below, 1 has a value of 1 ten thousand or 1 hundred, dependingon its position in thenumber.

Place Value

Billions Millions Thousands Ones

6

One

s

Tens

Hun

dred

s

One

s

Tens

Hun

dred

s

One

s

Tens

Hun

dred

s

One

s

Tens

Hun

dred

s

316152027 , , ,

Standard form: 7,202,516,136

Expanded form: 7,000,000,000 � 200,000,000 � 2,000,000 � 500,000 �10,000 � 6,000 � 100 � 30 � 6

Word form: seven billion, two hundred two million, five hundred sixteen thousand, one hundred thirty-six

1-1 Comparing and OrderingWhole Numbers

World Population

1995

1998

2000

2010

2015

Year

Population (billions)Source: U.S. Bureau of the Census, International Data Base, 2005

0 4.5 4.8 5.1 5.4 5.7 6.0 6.3 6.6 6.9 7.2 7.5

5,929,735,977

6,081,527,896

6,825,750,456

7,202,516,136

5,694,418,460

Think and Discuss

1. Give the place value of the digit 3 in each of the following numbers: 2,037,912; 2,370,912; 2,703,912.

2. Read each of the following numbers: 937,052; 3,012,480;8,135,712,004.

3. Look at the bar graph at the beginning of the lesson. In which yearswas the population between 5,500,000,000 and 6,500,000,000?

2E X A M P L E

Using Place Value to Compare Whole Numbers

Belgium’s 2005 population was 10,364,388 people. The CzechRepublic’s 2005 population was 10,241,138 people. Which countryhad more people?

Belgium:

Czech Republic:

200 thousand is less than 300 thousand.10,241,138 is less than 10,364,388.So, Belgium had more people.

To order numbers, you can compare them using place value and thenwrite them in order from least to greatest. You can also graph thenumbers on a number line. As you read the numbers from left toright, they will be ordered from least to greatest.

Using a Number Line to Order Whole Numbers

Order the numbers from least to greatest.923; 835; 1,266Graph the following numbers on a number line:

The number 923 is between 900 and 1,000.

The number 835 is between 800 and 900.

The number 1,266 is between 1,200 and 1,300.

The numbers are ordered when you read the number line from left to right.

The numbers in order from least to greatest are 835, 923, and 1,266.

1 0, 2 4 1, 1 3 8

1 0, 3 6 4, 3 8 8

� means “is less than.”

3 � 5 120 � 504

� means “is greater than.”

17 � 9 212 � 831,000 1,3001,2001,100

835 923 1,266

800 900

Start at the left and comparedigits in the same place valueposition. Look for the first placewhere the values are different.

E X A M P L E 1

Belgium

CzechRepublic

1-1 Comparing and Ordering Whole Numbers 7


1-1 ExercisesExercises

1. Geography Mount McKinley, in Alaska, is 20,320 feet tall. Mount Aconcagua,in Argentina, is 22,834 feet tall. Which mountain is taller?

2. The area of the Caribbean Sea is 971,400 square miles. The area of theMediterranean Sea is 969,100 square miles. Which sea is smaller in area?

Order the numbers from least to greatest.

3. 726; 349; 642 4. 513; 915; 103 5. 497; 1,264; 809

6. 672; 1,421; 1,016 7. 982; 5,001; 3,255 8. 4,079; 9,976; 2,951

9. The attendance in 1999 at a theme park was 17,459,000 people. The attendance in 1999 at a water park was 15,200,000 people. Which parkhad the higher attendance?

10. According to the table, which river is longer, the Missouri or the Mississippi?

11. A New York City driving range reported 413,497 golf balls were hit by customers last year. A Philadelphia range reported customers hit 408,959 golf balls. Which range had more golf balls hit?


12. 367; 597; 279 13. 619; 126; 480 14. 946; 705; 810

15. 423; 1,046; 805 16. 1,523; 2,913; 111 17. 1,764; 1,359; 666

18. 742; 777; 711 19. 4,228; 1,502; 978 20. 6,704; 5,902; 2,792

Compare. Write �, �, or �.

21. 46,495 46,594 22. 162,648 126,498 23. 3,654 3,654

24. 512,105 512,099 25. 29,448 29,488 26. 913,203 913,600

27. 23,172,458 231,724 28. 21,782 21,782 29. 1,556,982 1,556,983

Order the numbers from greatest to least.

30. 591; 924; 341 31. 601; 533; 823; 149 32. 291; 911; 439; 747

33. 2,649; 3,461; 1,947 34. 5,349; 5,389; 5,480 35. 7,467; 7,239; 7,498

36. Americans own about 74,000,000 dogs as pets and 90,000,000 cats as pets. Do Americans own more dogs or cats?

KEYWORD: MR7 Parent

KEYWORD: MR7 1-1

GUIDED PRACTICE

PRACTICE AND PROBLEM SOLVING

INDEPENDENT PRACTICE

River Length (mi)

Mississippi 2,340

Missouri 2,315

Ohio 618

Red 1,290

Rio Grande 1,900

See Example 2

See Example 1

See Example 1

See Example 2

Extra PracticeSee page 714.

1-1 Comparing and Ordering Whole Numbers 9

42. Multiple Choice Which list shows the numbers in order from least to greatest?

101; 10,001; 1,001 502; 205; 5,002

9,428; 9,454; 9,478 2,123; 2,078; 2,055

43. Multiple Choice The 2000 populations of four major Texas cities were asfollows: Amarillo, 17,627; Brownsville, 139,722; Laredo, 176,576; and Lubbock,199,564. Which of the cities had the greatest population?

Amarillo Brownsville Laredo Lubbock

Write each number in word form. (Previous course)

44. 1,645 45. 24,498 46. 306,927 47. 4,605,926

Write the value of the red digit in each number. (Previous course)

48. 649,809 49. 349,239 50. 27,463 51. 16,239

JHGF

DB

CA

A B

37. Geography The three biggest states in the continental United States are California, 159,869 square miles; Montana, 147,047 square miles; and Texas, 267,277 square miles. Write the states in order from smallest area to largest area.

38. History The two drawings show another way to represent numbers. The rod on the far left of each drawing represents the hundred thousands place. The number of beads on a rod tells the value for that place. Which drawing represents the greater number?

39. What’s the Error? A student said 19,465,405 is greater than 19,465,425.Explain the error. Write the statement correctly.

40. Write About It Explain how you would compare 19,465,146 and 19,460,146.

41. Challenge In Roman numerals, letters represent numbers. For example, I � 1, V � 5, X � 10, L � 50, and C � 100. Letters in Romannumerals are written next to each other; this is how the value of the number isshown. To read the numbers below, add the values of all of the letters. Whatnumbers do the following represent?

a. CLX b. LVI c. CIII

Long ago, the aba-cus was used tosolve math prob-lems. The rods repre-sent place values,and the beads areused as counters.

KEYWORD: MR7 Abacus

History

Learn to estimate with whole numbers.

Vocabulary

overestimate

underestimate

compatible number

Sometimes in math you do not need an exact answer. Instead, youcan use an estimate. Estimates are close to the exact answer but areusually easier and faster to find.

When estimating, you can round the numbers in the problem tocompatible numbers. are close to the numbersin the problem, and they can help you do math mentally.

Estimating a Sum or Difference by Rounding

Estimate each sum or difference by rounding to the place value indicated.

A 5,439 � 7,516; thousands

The sum is about 13,000.

B 62,167 � 47,511; ten thousands

The difference is about 10,000.

An estimate that is less than the exact answer is an .

An estimate that is greater than the exact answer is an .overestimate

underestimate

60,000� 50,000��

10,000

5,000� 8,000��

13,000

Compatible numbers

When rounding, lookat the digit to theright of the place towhich you arerounding.

• If that digit is 5 orgreater, round up.

• If that digit is lessthan 5, rounddown.

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E X A M P L E 1

Round 5,439 down.Round 7,516 up.

Round 62,167 down.Round 47,511 up.

Estimating withWhole Numbers

1-2


Estimating a Product by Rounding

Ms. Escobar is planning a graduation celebration for the entireeighth grade. There are 9 eighth-grade homeroom classes of 27students. Estimate how many cups Ms. Escobar needs to buy forthe students if they all attend the celebration.

Find the number of students in the eighth grade.

9 � 27 9 � 30 Overestimate the number of students.

9 � 30 � 270 The actual number of students is less than 270.

If Ms. Escobar buys 270 cups, she will have enough for every student.

Estimating a Quotient Using Compatible Numbers

Mrs. Byrd will drive 120 miles to take Becca to the state fair. She can drive65 mi/h. About how long will the trip take?

To find how long the trip will be, divide themiles Mrs. Byrd has to travel by how manymiles per hour she can drive.

miles � miles per hour

120 � 65 120 � 60 120 and 60 arecompatible numbers.

Underestimate thespeed.

120 � 60 � 2 Because sheunderestimated the speed, the actual time will be less than 2 hours.

It will take Mrs. Byrd about two hours to reach the state fair.

Think and Discuss

1. Suppose you are buying items for a party and you have $50.Would it be better to overestimate or underestimate the cost of the items?

2. Suppose your car can travel between 20 and 25 miles on a gallonof gas. You want to go on a 100-mile trip. Would it be better tooverestimate or underestimate the number of miles per gallonyour car can travel?

3. Describe situations in which you might want to estimate.

2E X A M P L E

3E X A M P L E

1-2 Estimating with Whole Numbers 11


1-2 ExercisesExercisesKEYWORD: MR7 Parent

KEYWORD: MR7 1-2


1. 4,689 � 2,469; thousands 2. 50,498 � 35,798; ten thousands

3. The graph shows the numberof bottles of water used inthree bicycle races last year. Ifthe same number of ridersenter the races each year,estimate the number of bottles that will be needed forraces held in May over thenext five years.

4. If a local business provided half the bottled water needed for the August bicyclerace, about how many bottles did the company provide?

5. Carla drives 80 miles on her scooter. If the scooter gets about 42 miles per gallonof gas, about how much gas did she use?




10. The recreation center has provided softballs every year to the city league. Use the table to estimate the number ofsoftballs the league will use in 5 years.

11. The recreation center has a girls’ golf teamwith 8 members. About how many golfballs will each girl on the team get?

12. If the recreation center loses about 4 tabletennis balls per year, and they are not replaced, about how many years will ittake until the center has none left?

Estimate each sum or difference by rounding to the greatest place value.

13. 152 � 269 14. 797 � 234 15. 242 � 179

16. 6,152 � 3,195 17. 9,179 � 2,206 18. 10,982 � 4,821

19. 82,465 � 38,421 20. 38,347 � 17,039 21. 51,201 � 16,492

22. 639,069 � 283,136 23. 777,060 � 410,364 24. 998,927 � 100,724

Bicycle-Race Bottled-Water Use

May

Aug

Nov

0 600150 300 450

Mon

th

Bottles

Recreation Center Balls Supplied

Sport Number of Balls

Basketball 21

Golf 324

Softball 28

Table tennis 95

See Example 2

See Example 3

See Example 1

See Example 2

See Example 3

See Example 1


GUIDED PRACTICE

PRACTICE AND PROBLEM SOLVINGExtra Practice

See page 714.

32. Multiple Choice Which number is the best estimate for 817 � 259?

10,000 2,000 1,100 800

33. Short Response The National Football League requires home teams to have36 new footballs for outdoor games and 24 new footballs for indoor games.Estimate how many new footballs the Washington Redskins must buy for 8 outdoor games. Explain how you determined your estimate.

Find each product or quotient. (Previous course)

34. 148 � 4 35. 523 � 5 36. 1,054 � 31 37. 312 � 8

Write each number in expanded form. (Lesson 1-1)

38. 269 39. 1,354 40. 32,498 41. 416,703

DCBA

Use the bar graph for Exercises 25–31.

25. On one summer day there were 2,824 sailboats on LakeErie. Estimate the number ofsquare miles available to eachboat.

26. If the areas of all the Great Lakesare rounded to the nearest thousand, which two of the lakes would be the closest in area?

27. About how much larger is Lake Huron than Lake Ontario?

28. The Great Lakes are called “great” because of the huge amount of fresh water they contain. Estimate the total area of all the Great Lakes combined.

29. What’s the Question? Lake Erie is about 50,000square miles smaller. What is the question?

30. Write About It Explain how you would estimatethe areas of Lake Huron and Lake Michigan to compare their sizes.

31. Challenge Estimate the average area of the Great Lakes.

Areas of the Great Lakes

Are

a (m

i2)

Great Lakes

100,000

80,000

60,000

40,000

20,000

0Erie

Superior

Huron

Michigan

Ontario

Area includes the water surface anddrainage basin within the United Statesand Canada.

Social Studies

1-2 Estimating with Whole Numbers 13

Learn to representnumbers by usingexponents.

Vocabulary

exponential form

base

exponent

Since 1906, the height of MountVesuvius in Italy has increased by 73 feet. How many feet is this?

The number 73 is written with anexponent. An tells howmany times a number called the

is used as a factor.

So the height of Mount Vesuvius has increased by 343 ft.

A number is in when it is written with a base and an exponent.

Writing Numbers in Exponential Form

Write each expression in exponential form.

4 � 4 � 4 9 � 9 � 9 � 9 � 9

43 4 is a factor 3 times. 95 9 is a factor 5 times.

Finding the Value of Numbers in Exponential Form

Find each value.

27 64

27 � 2 � 2 � 2 � 2 � 2 � 2 � 2 64 � 6 � 6 � 6 � 6

� 128 � 1,296

exponential form

base

exponent

Base

Exponent

7 � 7 � 7 � 343

E X A M P L E 1

2E X A M P L E

Exponents1-3

The most recent eruption of Mount Vesuvius took place in 1944.


Exponential Read Multiply ValueForm

101 “10 to the 1st power” 10 10

102 “10 squared,” or “10 to the 2nd power” 10 � 10 100

103 “10 cubed,” or “10 to the 3rd power” 10 � 10 � 10 1,000

104 “10 to the 4th power” 10 � 10 � 10 � 10 10,000

PROBLEM SOLVING APPLICATION

If Dana’s school closes, a phone tree is used to contact eachstudent’s family. The secretary calls 3 families. Then each familycalls 3 other families, and so on. How many families will benotified during the 6th round of calls?

1. Understand the Problem

The answer will be the number of families called in the 6th round.

List the important information:

• The secretary calls 3 families.

• Each family calls 3 families.

2. Make a Plan

You can draw a diagram to see how many calls are in each round.

3. Solve

Notice that in each round, the number of calls is a power of 3.1st round: 3 calls � 3 � 31

2nd round: 9 calls � 3 � 3 � 32

So during the 6th round there will be 36 calls.

36 � 3 � 3 � 3 � 3 � 3 � 3 � 729

During the 6th round of calls, 729 families will be notified.

4. Look Back

Drawing a diagram helps you visualize the pattern, but the numbersbecome too large for a diagram after the third round of calls. Solvingthis problem by using exponents can be easier and faster.

Secretary

1st round—3 calls

2nd round—9 calls

Think and Discuss

1. Read each number: 48, 123, 32.

2. Give the value of each number: 71, 132, 33.

1

2

3

4

E X A M P L E 3

1-3 Exponents 15



KEYWORD: MR7 1-3


1. 8 � 8 � 8 2. 7 � 7 3. 6 � 6 � 6 � 6 � 6

4. 4 � 4 � 4 � 4 5. 5 � 5 � 5 � 5 � 5 6. 1 � 1

Find each value.

7. 42 8. 33 9. 54 10. 82 11. 73

12. At Russell’s school, one person will contact 4 people and each of thosepeople will contact 4 other people, and so on. How many people will becontacted in the fifth round?


13. 2 � 2 � 2 � 2 � 2 � 2 14. 9 � 9 � 9 � 9 15. 8 � 8

16. 1 � 1 � 1 17. 6 � 6 � 6 � 6 � 6 18. 5 � 5 � 5

19. 7 � 7 � 7 � 7 � 7 � 7 � 7 20. 3 � 3 � 3 � 3 21. 4 � 4

Find each value.

22. 24 23. 35 24. 62 25. 92 26. 74

27. 83 28. 14 29. 162 30. 108 31. 122

32. To save money for a video game, you put one dollar in an envelope. Each dayfor 5 days you double the number of dollars in the envelope from the daybefore. How much will be saved on the fifth day?

Write each expression as repeated multiplication.

33. 163 34. 222 35. 316 36. 465 37. 503

38. 41 39. 19 40. 176 41. 85 42. 124

Find each value.

43. 106 44. 731 45. 94 46. 802 47. 105

48. 192 49. 29 50. 571 51. 53 52. 113


53. 61 51 54. 92 201 55. 101 1,000,0001

56. 73 37 57. 55 251 58. 1002 104

See Example 2

See Example 3

See Example 3

See Example 1

GUIDED PRACTICE



See Example 2

See Example 1


1-3 Exponents 17

Life Science

KEYWORD: MR7 Cell

You are able to grow because your body produces new cells. New cellsare made when old cells divide. Single-celled bodies, like bacteria, divide by binary fission, which means “splitting into two parts.”A cycle is the length of time a cell type needs to divide.

59. In science lab, Carol has a dish containing 45 cells. How many cells are represented by this number?

60. A certain colony of bacteria triples in length every 15 minutes. Its length is now 1 mm. How long will it be in 1 hour? (Hint: There are four cycles of 15 minutes in 1 hour.)

Use the bar graph for Exercises 61–64.

61. Determine how many times cell type A will divide in a 24-hour period. If you begin with one type A cell, how many cells will be produced in 24 hours?

62. Multi-Step If you begin with one typeB cell and one type C cell, what is thedifference between the number of typeB cells and the number of type C cellsproduced in 24 hours?

63. Write About It Explain how tofind the number of type A cells produced in 48 hours.

64. Challenge How many hours will it take one C cell to divide into at least 100 C cells?

Cell Division Cycles

9

6

3

0CA B

Cycl

e le

ngth

(hr

)

Cell type

This plant cell shows theanaphase stage of mitosis.Mitosis is the process ofnuclear division in complexcells called eukaryotes.

65. Multiple Choice Which of the following shows the expression 4 � 4 � 4 in exponential form?

64 444 34 43

66. Multiple Choice Which expression has the greatest value?

25 34 43 52

Order the numbers from least to greatest. (Lesson 1-1)

67. 8,452; 8,732; 8,245 68. 991; 1,010; 984 69. 12,681; 11,901; 12,751

Estimate each sum or difference by rounding to the place value indicated. (Lesson 1-2)


JHGF

DCBA

Rea

dy

to G

o O

n?

Quiz for Lessons 1-1 Through 1-3

1-1 Comparing and Ordering Whole Numbers

Compare. Write <, >, or =.

1. 12,563,284 12,587,802 2. 783,100,570 780,223,104

3. In 2006, a university sold 1,981,299 tickets to its football games. In 2005, the same university sold 1,881,702 tickets. During which year were more tickets sold?


4. 1,052; 1,803; 1,231 5. 4,344; 3,344; 3,444 6. 10,463; 14,063; 10,643

1-2 Estimating with Whole Numbers


7. 61,582 � 13,281; ten thousands 8. 86,125 � 55,713; ten thousands

9. 7,903 � 2,654; thousands 10. 34,633 � 32,087; thousands

11. 1,896,345 � 3,567,194; hundred thousands

12. 56,129,482 � 37,103,758; ten millions

13. Marcus wants to make a stone walkway in his garden. The rectangular walkway will be 3 feet wide and 18 feet long. Each 2-foot by 3-foot stone covers an area of 6 square feet. How many stones will Marcus need?

14. Jenna’s sixth-grade class is taking a bus to the zoo. The zoo is 156 miles from the school. If the bus travels an average of 55 mi/h, about how long will it take the class to get to the zoo?

1-3 Exponents


15. 7 � 7 � 7 16. 5 � 5 � 5 � 5

17. 3 � 3 � 3 � 3 � 3 � 3 18. 10 � 10 � 10 � 10

19. 1 � 1 � 1 � 1 � 1 20. 4 � 4 � 4 � 4

Find each value.

21. 33 22. 24 23. 62 24. 83

25. To start reading a novel for English class, Sara read 1 page. Each day for 4 days shereads double the number of pages she read the day before. How many pages will she read on the fourth day?


Solve • Choose the operation: addition or subtraction

Read the whole problem before you try to solve it. Determine whataction is taking place in the problem. Then decide whether youneed to add or subtract in order to solve the problem.

If you need to combine or put numbers together, you need to add. If you need to take away or compare numbers, you need to subtract.

Read each problem. Determine the action in each problem.Choose an operation in order to solve the problem. Then solve.

Action Operation Picture

Combining AddPutting together

Removing SubtractTaking away

Comparing SubtractFinding the difference

Most hurricanes that occur over the Atlantic Ocean, the Caribbean Sea,or the Gulf of Mexico occur between June and November. Since 1886, ahurricane has occurred in every month except April.

Use the table for problems 1 and 2.

How many out-of-season hurricanes haveoccurred in all?

How many more hurricanes have occurredin May than in December?

There were 14 named storms during the2000 hurricane season. Eight of thesebecame hurricanes, and three othersbecame major hurricanes. How many of thenamed storms were not hurricanes ormajor hurricanes?

3

2

1

Number of Out-of-SeasonHurricanes Since 1886

Month Number

Jan 1

Feb 1

Mar 1

May 14

Dec 10

Focus on Problem Solving 19

Explore the Order ofOperations

Use with Lesson 1-4

1-4

KEYWORD: MR7 Lab1

Use pencil and paper to evaluate 3 � 2 � 8 two different ways.

Add first, and 3 � 2 � 5then multiply by 8. 5 � 8 � 40

Multiply first, and 2 � 8 � 16then add 3. 16 � 3 � 19

Now evaluate 3 � 2 � 8 using a graphing or scientific calculator.

The result, 19, shows that this calculator multiplied first, eventhough addition came first in the expression.

If there are no parentheses, then multiplication and division aredone before addition or subtraction. If the addition is to be donefirst, parentheses must be used.

When you evaluate (3 � 2) � 8 on a calculator, the result is 40.Because of the parentheses, the calculator adds before multiplying.

Graphing and scientific calculators follow a logical system called the algebraic order of operations. The order of operations tells you to multiply and divide before you add or subtract.

Think and Discuss

Evaluate each expression with pencil and paper. Check your answer with a calculator.

1. 4 � 12 � 7 2. 15 � 3 � 10 3. 4 � 2 � 6 4. 10 � 4 � 2

1. In 4 � 15 � 5, which operation do you perform first? How do you know?

2. Tell the order in which you would perform the operations in the expression 8 � 2 � 6 � 3 � 4.

Try This

Look at the expression 3 � 2 � 8. To evaluate this expression, decide whether to add first or multiply first. Knowing the correct order of operations is important. Without this knowledge, you could get an incorrect result.

Activity 1


Try This

What should you do if the same operation appears twice in an expression? Use a calculator to decide which subtraction is done first in the expression 7 � 3 � 2.

If 7 � 3 is done first, the value of the expression is 4 � 2 � 2.

If 3 � 2 is done first, the value of the expression is 7 � 1 � 6.

On the calculator, the value of 7 � 3 � 2 is 2. The subtraction onthe left, 7 � 3, is done first.

Addition and subtraction (or multiplication and division) aredone from left to right.

Without parentheses, the expression 8 � 2 � 10 � 3 equals 25. Insert parentheses to make the value of the expression 22.

What happens What happens if you add first? if you subtract first?(8 � 2) � 10 � 3 8 � 2 � (10 � 3)

10 � 10 � 3 8 � 2 � 7100 � 3 8 � 14

97 22

For the expression to equal 22, the subtraction must be done first.

Try This

Evaluate each expression. Check your answer with a calculator.

1. 8 � 6 � 1 2. 20 � 5 � 2 3. 3 � 6 � 2 4. 19 � 6 � 5

Think and Discuss

Think and Discuss

1. In 15 � 5 � 4, does it matter which operation you perform first? Explain.

2. Does it matter which operation you perform first in 15 � 5 � 4? Explain.

1. To evaluate 13 � 5 � 255 on a calculator, you type 13 � 5 and then press the key. But before you can type in the 255, the display changes to 18!

a. Does this calculator follow the correct order of operations? Why?

b. How could you use this calculator to evaluate 13 � 5 � 255?

Insert parentheses to make the value of each expression 12.

1. 56 � 40 � 4 2. 3 � 1 � 10 � 4 3. 18 � 2 � 1 � 6 4. 100 � 8 � 2 � 2 � 5

Activity 2

Activity 3

1-4 Technology Lab 21

A is a mathematical phrase that includes onlynumbers and operation symbols.

When you a numerical expression, you find its value.

Erika and Jamie each evaluated 3 � 4 � 6. Their work is shown below. Whose answer is correct?

When an expressionhas more than oneoperation, you mustknow which operationto do first. To makesure that everyonegets the same answer,we use the

.

3 � 4 � 6 There are no parentheses or exponents. Multiply first.

3 � 24 Add.

27 Erika has the correct answer.

Using the Order of Operations

Evaluate each expression.

9 � 12 � 29 � 12 � 2 There are no parentheses or exponents.

9 � Multiply.

Add.33

24

operationsorder of

evaluate


Numerical4 � 8 � 2 � 6 371 � 203 � 2 5,006 � 19Expressions

Learn to use the orderof operations.

Vocabulary

order of operations

evaluate


ErikaErika3 +3 + 4 x 64 x 6

3 + 4 x 6 = 273 + 4 x 6 = 273 + 243 + 24

2727

Jamie3 + 4 x 6

3 + 4 x 6 = 42

42 7 x 6

The first letters ofthese words can helpyou remember theorder of operations.

Please ParenthesesExcuse ExponentsMy Multiply/Dear DivideAunt Add/Sally Subtract

ORDER OF OPERATIONS

1. Perform operations in parentheses.

2. Find the values of numbers with exponents.

3. Multiply or divide from left to right as ordered in the problem.

4. Add or subtract from left to right as ordered in the problem.

E X A M P L E 1

Order of Operations1-4


Think and Discuss

1. Explain why 6 � 7 � 10 � 76 but (6 � 7) � 10 � 130.

2. Tell how you can add parentheses to the numerical expression 22 � 5 � 3 so that 27 is the correct answer.


7 � (12 � 3) � 67 � (12 � 3) � 6

7 � 36 � 6 Perform operations within parentheses.

7 � 6 Divide.

Add.

Using the Order of Operations with Exponents


33 � 8 � 1633 � 8 � 16 There are no parentheses.

27 � 8 � 16 Find the values of numbers with exponents.

� 16 Add

Subtract.

8 � (1 � 3) � 52 � 28 � (1 � 3) � 52 � 2

8 � � 52 � 2 Perform operations within parentheses.

8 � � 25 � 2 Find the values of numbers with exponents.

� 25 � 2 Divide.

� 2 Multiply.

Subtract.

Consumer Application

Regina bought 5 carved wooden beads for $3 each and 8 glassbeads for $2 each. Evaluate 5 � 3 � 8 � 2 to find the amountRegina spent for beads.

5 � 3 � 8 � 2

�

Regina spent $31 for beads.

31

1615

48

50

2

4

4

19

35

13

E X A M P L E 3

E X A M P L E 2

1-4 Order of Operations 23



KEYWORD: MR7 1-4


1. 36 � 18 � 6 2. 7 � 24 � 6 � 2 3. 62 � 4 � (15 � 5)

4. 11 � 23 � 5 5. 5 � (28 � 7) � 42 6. 5 � 32 � 6 � (10 � 9)

7. Coach Milner fed the team after the game by buying 24 Chicken Deals for $4 each and 7 Burger Deals for $6 each. Evaluate 24 � 4 � 7 � 6 to find thecost of the food.


8. 9 � 27 � 3 9. 2 � 7 � 32 � 8 10. 45 � (3 � 6) � 3

11. (6 � 2) � 4 12. 9 � 3 � 6 � 2 13. 5 � 3 � 2 � 12 � 4

14. 42 � 48 � (10 � 4) 15. 100 � 52 � 7 � 3 16. 6 � 22 � 28 � 5

17. 62 � 12 � 3 � (15 � 7) 18. 21 � (3 � 4) � 9 � 23 19. (32 � 6 � 2) � (36 � 6 � 4)

20. The nature park has a pride of 5 adult lions and 3 cubs. The adults eat 8 lb ofmeat each day and the cubs eat 4 lb. Evaluate 5 � 8 � 3 � 4 to find the amountof meat consumed each day by the lions.

21. Angie read 4 books that were each 150 pages long and 2 books that were each325 pages long. Evaluate 4 � 150 � 2 � 325 to find the total number of pagesAngie read.


22. 12 � 3 � 4 23. 25 � 21 � 3 24. 1 � 7 � 2

25. 60 � (10 � 2) � 42 � 23 26. 10 � (28 � 23) � 72 � 37 27. (5 � 3) � 2

28. 72 � 9 � 2 � 4 29. 12 � (1 � 72) � 5 30. 25 � 52

31. (15 � 6)2 � 34 � 2 32. (2 � 4)2 � 3 � (5 � 3) 33. 16 � 2 � 3

Add parentheses so that each equation is correct.

34. 23 � 6 � 5 � 4 � 12 35. 7 � 2 � 6 � 4 � 3 � 53

36. 32 � 6 � 3 � 3 � 36 37. 52 � 10 � 5 � 42 � 36

38. 2 � 8 � 5 � 3 � 23 39. 92 � 2 � 15 � 16 � 8 � 11

40. 5 � 7 � 2 � 3 � 21 41. 42 � 3 � 2 � 4 � 4

42. Critical Thinking Jon says the answer to 1 � 3 � (6 � 2) � 7 is 25. Juliesays the answer is 18. Who is correct? Explain.

See Example 3

See Example 1

See Example 2

See Example 3

See Example 1

GUIDED PRACTICE



See Example 2


1-4 Order of Operations 25

Archaeologists study cultures of the past by uncovering items from ancient cities. An archaeologist has chosen a site in Mexico for her team’s next dig. She divides the location into rectangular plots and labels each plot so that uncovered items can be identified by the plot in which they were found.

43. The archaeologist must order a cover for the plot where the team is digging.Evaluate the expression 3 � (22 � 6) tofind the area of the plot in square meters.

44. In the first week, the archaeology team digs down 2 meters and removes a certain amount of dirt. Evaluate the expression 3 � (22 � 6) � 2 to find the volume of the dirt removed from the plot in the first week.

45. Over the next two weeks, the archaeology team digs down an additional 23 meters. Evaluate the expression 3 � (22 � 6) � (2 � 23)to find the total volume of dirt removed from the plot after 3 weeks.

46. Write About It Explain why the archaeologist must follow theorder of operations to determine the area of each plot.

47. Challenge Write an expression for the volume of dirt thatwould be removed if the archaeologist’s team were to dig down an additional 32 meters after the first three weeks.

22 m

23 m

3 m6 m

2 m

Archaeologists uncovered pieces of pottery at the La Ventilla site in Mexico.

48. Multiple Choice Which operation should you perform first when you evaluate81 � (6 � 30 � 2) � 5?

Addition Division Multiplication Subtraction

49. Multiple Choice Which expression does NOT have a value of 5?

22 � (3 � 2) (22 � 3) � 2 22 � 3 � 2 22 � (3 � 2)

50. Gridded Response What is the value of the expression 32 � (9 � 3 � 2)?

Write each number in standard form. (Lesson 1-1)

51. 3,000 � 200 � 70 � 3 52. 10,000 � 500 � 20 � 1 53. 70,000 � 7

Find each value. (Lesson 1-3)

54. 85 55. 53 56. 38 57. 44 58. 72

JHGF

DCBA

Social Studies

Learn to use numberproperties to computementally.

Vocabulary

DistributiveProperty

AssociativeProperty

CommutativeProperty

ASSOCIATIVE PROPERTY (Grouping)

Words

When you are only adding oronly multiplying, you can groupany of the numbers together.

Numbers

(17 � 2) � 9 � 17 � (2 � 9)

(12 � 2) � 4 � 12 � (2 � 4)

E X A M P L E 1

COMMUTATIVE PROPERTY (Ordering)

Words

You can add or multiplynumbers in any order.

Numbers

18 � 9 � 9 � 18

15 � 2 � 2 � 15


1-5

Mental math means “doing math in your head.” Shakuntala Devi is extremely good at mental math. When she was asked to multiply 7,686,369,774,870 by 2,465,099,745,779,she took only 28 seconds to multiply the numbers mentally and gave the correct answer of 18,947,668,177,995,426,462,773,730!

Most people cannot do calculations like that mentally. But you can learn to solve some problems very quickly in your head.

Many mental math strategies use number properties that you already know.

Using Properties to Add and Multiply Whole Numbers

Evaluate 12 � 4 � 18 � 46.

Look for sums that are multiples of 10.

Use the Commutative Property.

(12 � 18) � (4 � 46) Use the Associative Property to make

� groups of compatible numbers.

Use mental math to add.80

5030

12 � 18 � 4 � 46

12 � 4 � 18 � 46

Mental Math

Evaluate 5 � 12 � 2.

5 � 12 � 2 Look for products that are multiples of 10.

12 � 5 � 2 Use the Commutative Property.

12 � (5 � 2) Use the Associative Property to group

12 � compatible numbers.

Use mental math to multiply.

When you multiply two numbers, you can “break apart” one of thenumbers into a sum and then use the Distributive Property.

Using the Distributive Property to Multiply

Use the Distributive Property to find each product.

4 � 23

4 � 23 � 4 � (20 � 3) “Break apart” 23 into 20 � 3.

� (4 � 20) � (4 � 3) Use the Distributive Property.

� � Use mental math to multiply.

� Use mental math to add.

8 � 74

8 � 74 � 8 � (70 � 4) “Break apart” 74 into 70 � 4.

� (8 � 70) � (8 � 4) Use the Distributive Property.

� � Use mental math to multiply.

� Use mental math to add.592

32560

92

1280

120

10

E X A M P L E 2

DISTRIBUTIVE PROPERTY

Words

When you multiply a numbertimes a sum, you can

• find the sum first and thenmultiply, or

• multiply by each number inthe sum and then add.

Numbers

6 � (10 � 4) � 6 � 14�

6 � (10 � 4) � (6 � 10) � (6 � 4)� �

� 842460

84

Break the greaterfactor into a sumthat contains amultiple of 10 and aone-digit number.You can add andmultiply thesenumbers mentally.

Think and Discuss

1. Give examples of the Commutative Property and the AssociativeProperty.

2. Name some situations in which you might use mental math.

1-5 Mental Math 27


KEYWORD: MR7 1-5

Evaluate.

1. 13 � 9 � 7 � 11 2. 19 � 18 � 11 � 32 3. 25 � 7 � 13 � 5

4. 5 � 14 � 4 5. 4 � 16 � 5 6. 5 � 17 � 2


7. 5 � 24 8. 8 � 52 9. 4 � 39 10. 6 � 14

11. 3 � 33 12. 2 � 78 13. 9 � 12 14. 2 � 87

Evaluate.

15. 15 � 17 � 3 � 5 16. 14 � 7 � 16 � 13 17. 6 � 21 � 14 � 9

18. 5 � 25 � 2 19. 2 � 32 � 10 20. 6 � 12 � 5


21. 3 � 36 22. 4 � 42 23. 6 � 71 24. 2 � 94 25. 6 � 23

26. 5 � 25 27. 6 � 62 28. 7 � 21 29. 8 � 41 30. 2 � 94

Use mental math to find each sum or product.

31. 8 � 13 � 7 � 12 32. 2 � 25 � 4 33. 4 � 22 � 16 � 18

34. 5 � 8 � 12 35. 5 � 98 � 95 36. 6 � 5 � 14

37. 11 � 75 � 25 38. 8 � 11 � 5 39. 19 � 1 � 11 � 39

40. Paul is writing a story for the school newspaper about the landscaping done by his class. The students planted 15 vines, 12 hedges, 8 trees, and 35 flowering plants. How many plants were used in the project?

41. Earth Science The temperature on Sunday was 58°F. The temperature ispredicted to rise 4°F on Monday, then rise 2°F more on Tuesday, and then riseanother 6°F by Saturday. What is the predicted temperature on Saturday?

42. Multi-Step Janice wants toorder disks for her computer. Sheneeds to find the total cost,including shipping and handling.If Janice orders 7 disks, what willher total cost be?

Description Number

Shipping & Handling

Total

Unit Costwith Tax

Price

ComputerDisk

7 $24.00

$7.00

See Example 2

See Example 1

See Example 2

See Example 1

GUIDED PRACTICE





1-5 Mental Math 29

Multiply using the Distributive Property.

43. 9 � 17 44. 4 � 27 45. 11 � 18 46. 7 � 51

47. 2 � 28 48. 9 � 42 49. 5 � 55 50. 3 � 78

51. 4 � 85 52. 6 � 36 53. 8 � 24 54. 11 � 51

55. Life Science Poison-dart frogs can breed underwater, and the females layfrom 4 to 30 eggs. What would be the total number of eggs if four female poison-dart frogs each laid 27 eggs?

Use the table for Exercises 56 and 57.

56. Rickie wants to buy 3 garden hosesat the home center clearance sale.How much will they cost?

57. The boys in Josh’s family are saving money to buy 4 ceilingfans at the home center sale. Howmuch will they need to save?

58. Critical Thinking Give a problem that you could simplify using theCommutative and Associative Properties. Then, show the steps to solve theproblem and label the Commutative and Associative Properties.

59. What’s The Error? A student wrote 5 � 24 � 25 � 6 � 5 � 25 � 24 � 6 bythe Associative Property. What error did the student make?

60. Write About It Why can you simplify 5(50 � 3) using the DistributiveProperty? Why can’t you simplify 5(50) � 3 using the Distributive Property?

61. Challenge Explain how you could find the product of 52 � 112 using theDistributive Property. Evaluate the expression.

62. Multiple Choice Which expression does NOT have the same value as 7 � (4 � 23)?

7 � 27 (7 � 4) � (7 � 23) 7 � 4 � 23 28 � (7 � 23)

63. Gridded Response Michelle flew 1,240 miles from Los Angeles to Dallas, andanother 718 miles from Dallas to Atlanta. From Atlanta, she flew 760 miles toNew York City. How many miles did Michelle fly in all?

Estimate each sum or difference by rounding to the nearest thousands place. (Lesson 1-2)

64. 5,237 � 1,586 65. 915,178 � 451,836 66. 39,187 � 24,999

Evaluate each expression. (Lesson 1-4)

67. 4 � 14 � 12 � 2 68. 16 � 42 � 15 � 2 69. 62 � 14 � (5 � 4)

DCBA

Home Center Clearance Sale

Table lamp $15

Garden hose $16

Ceiling fan $52

Life Science

Poison-dart frogs aremembers of thefamily Dendrobati-dae, which includesabout 170 species.Many are brightlycolored.

Learn to choose anappropriate method ofcomputation and justifyyour choice.

Earth has one moon. Scientists have determined that other planets in our solar system have as many as 63 moons. Mercury and Venus have no moons at all.

Astronomy Application

Choose a solution method and solve. Explain your choice.

How many known moons are in our solar system?

It might be hard to keep track of all ofthese numbers if you tried to addmentally. But the numbers themselvesare small. You can use paper and pencil.

There are 156 known moons in our solar system.

The average temperature on Earth is 59°F. The averagetemperature on Venus is 867°F. How much hotter is Venus’s average temperature?

Venus temperature � Earth temperature

867 � 59

These numbers are small, and 59 is close to a multiple of 10. Youcan use mental math.

(867 � 1) � (59 � 1) Think: Add 1 to 59 to make 60. Add 1 to 867 to compensate.

The average temperature on Venus is 808°F hotter than theaverage temperature on Earth.

808

868 � 60

1

2

63

50

27

�13�156

Planet Moons

Mercury 0

Venus 0

Earth 1

Mars 2

Jupiter 63

Saturn 50

Uranus 27

Neptune 13

Source: The Planetary Society, 2006

E X A M P L E 1


Choose the Method of Computation

Problem Solving Skill

1-6

Think and Discuss

1. Give an example of a situation in which you would use mentalmath to solve a problem. When would you use paper and pencil?

2. Tell how you could use mental math in Example 1B if the problemwere 867 � 59.


Every day, about 120 tons of cosmic dust—debris from outerspace—enter Earth’s atmosphere. How many tons of cosmic dustenter Earth’s atmosphere each year?

tons per day � days per year Think: There are 365 days in a year.

120 � 365

These numbers are not compatible, so mental math is not a good choice.

You could use paper and pencil. But finding a product of 3-digitnumbers requires several steps. Using a calculator will probably be faster.

Carefully enter the numbers on a calculator. Record the product.

120 � 365 � 43,800

Each year, about 43,800 tons of cosmic dust enter Earth’s atmosphere.

244 9 8 7 5 3 88

U.S. Germany France Canada Japan Italy Russia


1. Astronomy What is the total number of astronauts who have space flightexperience?

2. Sports In the 2004 Summer Olympic Games, 929 medals were given. TheU.S. team brought home the most medals, 103. How many medals were notwon by the U.S. team?

3. A factory produces 126 golf balls per minute. How many golf balls can be produced in 515 minutes?

KEYWORD: MR7 Parent

KEYWORD: MR7 1-6

See Example 1

GUIDED PRACTICE

1-6 ExercisesExercises

1-6 Choose the Method of Computation 31

18. Multiple Choice It takes Mars 687 days to revolve around the Sun. It takesVenus only 225 days to revolve around the Sun. How many more days does ittake Mars to revolve around the Sun than it takes Venus?

462 days 500 days 900 days 912 days

19. Short Response Hector biked 13 miles on Monday, Wednesday, and Friday ofevery week for 24 weeks. Find the total number of miles he biked during the 24weeks. Explain your answer.

Evaluate each expression. (Lesson 1-4)

20. (2 � 7 � 5) � 2 21. 10(6 � 3) 22. 5 � 8 � 7 � 1 23. 5 � (8 � 2) � 3

Identify the property illustrated by each equation. (Lesson 1-5)

24. 3 � (4 � 5) � (3 � 4) � 5 25. 19(24) � 19(20) � 19(4) 26. 2(13) � 13(2)

DCBA

Choose a solution method and solve. Explain your choice.For 4 and 5, use the diagram at right.

4. The highest score is a total of all the squares on theboard. What is that score?

5. What score is higher, the total of the squares in themiddle row or middle column?

6. If each store in a chain of 108 furniture stores sells 135 sofas a year, what is the total number of sofas sold?

Evaluate the expression, and state the method of computation you used.

7. 5 � 24 � 7 � 1 � 64 � 2 � 8 8. 16 � 2 � 4 � 13 � 5 � 1 � 14

9. 828 � 623 10. 742 � 167 11. 41 � 169 12. 499 � 201 13. 338 � 12

14. A satellite travels 985,200 miles per year. How many miles will it travel if it stays in space for 12 years?

15. What’s the Question? An astronaut has spent the following minutes training in a tank that simulates weightlessness: 2, 15, 5, 40, 10, and 55. The answer is 127. What is the question?

16. Write About It Explain how you can decide whether to use pencil and paper, mental math, or a calculator to solve a subtraction problem.

17. Challenge A list of possible astronauts was narrowed down by twocommittees. The first committee selected 93 people to complete a written form. The second selected 31 of those people to come to an interview. If 837were not asked to complete a form, how many were on the original list?

6 9 5

10 20 8

3 7 4

See Example 1





Each month, Eva chooses 3 new DVDsfrom her DVD club.

The number of DVDs Eva has after each month shows a pattern: Add 3. This pattern can be written as a sequence. 3, 6, 9, 12, 15, . . .

A is an ordered set of numbers. Each number in thesequence is called a . In this sequence, the first term is 3, thesecond term is 6, and the third term is 9.

When the terms of a sequence change by the same amount eachtime, the sequence is an .

Extending Arithmetic Sequences

Identify a pattern in each arithmetic sequence and then find themissing terms.

3, 15, 27, 39, , , . . .

Look for a pattern.A pattern is to add 12 to each term to get the next term.

39 � 12 � 51 51 � 12 � 63So 51 and 63 are the missing terms.

12, 21, 30, 39, , , . . .

Use a table to find a pattern.

� 9 � 9 � 9 � 9 � 9A pattern is to add 9 to each term to get the next term.39 � 9 � 48 48 � 9 � 57So 48 and 57 are the missing terms.

arithmetic sequence

termsequence

Learn to find patternsand to recognize, describe,and extend patterns insequences.

Vocabulary

arithmetic sequence

term

sequence

Look for a relation-ship between the 1st term and the 2nd term. Check ifthis relationshipworks between the2nd term and the3rd term, and so on.

Eva’s DVDs

Month DVDs

1 3

2 6

3 9

4 12

E X A M P L E 1

�3

�3

�3

Position

Position 1 2 3 4 5 6

Value of Term 12 21 30 39

Value ofTerm

3, 15, 27, 39, , , . . .�12 �12 �12 �12 �12

1-7 Patterns and Sequences 33


Not all sequences are arithmetic sequences.

In nonarithmetic sequences, look for patterns that involve multiplication ordivision. Some sequences may even be combinations of different operations.

Completing Other Sequences

Identify a pattern in each sequence. Name the missing terms.

4, 15, 8, 19, 12, 23, 16, , , , . . .

4 15 8 19 12 23 16

�11 �7 �11 �7 �11 �7 �11 �7 �11

A pattern is to add 11 to one term and subtract 7 from the next.

16 � 11 � 27 27 � 7 � 20 20 � 11 � 31

So 27, 20, and 31 are the missing terms.

�6 �3 �6 �3 �6 �3 �6 �3

A pattern is to multiply one term by 6 and divide the next by 3.

12 � 3 � 4 8 � 6 � 48

So 4 and 48 are the missing terms.

E X A M P L E 2

Arithmetic Sequences Not Arithmetic Sequences

2, 4, 6, 8,... 20, 35, 50, 65,... 1, 3, 6, 10,... 2, 6, 18, 54,...

�2 �2 �2 �15 �15 �15 �2 �3 �4 �3 �3 �3

Position 1 2 3 4 5 6 7 8 9

Value of Term 1 6 2 12 24 8 16

Position 1 2 3 4 5 6 7 8 9

Value of Term 1 6 2 12 24 8 16

Think and Discuss

1. Tell how you could check whether the next two terms in the arithmetic sequence 5, 7, 9, 11, . . . are 13 and 15.

2. Explain how to find the next term in the sequence 16, 8, 4, 2, , ….

3. Explain how to determine whether 256, 128, 64, 32, . . . is an arithmetic or nonarithmetic sequence.


Identify a pattern in each arithmetic sequence and then find the missing terms.

8. 9, 19, 29, 39, 49, , , , . . . 9. 98, 84, 70, 56, 42, , , , . . .

10.

11.


12. 50, 40, 43, 33, , 26, , . . . 13. 7, 28, 24, 45, , , , . . .

14.

15.

Identify a pattern in each arithmetic sequence and then find the missing terms.

1. 12, 24, 36, 48, , , , . . . 2. 105, 90, 75, 60, 45, , , , . . .

3.

4.


5. 2, 9, 7, 14, , , . . . 6. 80, 8, 40, 4, , 2, 10, , . . .

7.


KEYWORD: MR7 1-7

GUIDED PRACTICE





Position 1 2 3 4 5 6 7 8

Value of Term 1 6 3 18 54 27





Position 1 2 3 4 5 6 7

Value of Term 120 60 180 90 405

See Example 2

See Example 1

See Example 2

See Example 1


Position 1 2 3 4 5 6 7

Value of Term 400 100 200 50 50

1-7 Patterns and Sequences 35

PRACTICE AND PROBLEM SOLVINGExtra Practice

See page 715.Use the pattern to write the first five terms of the sequence.

16. Start with 1; multiply by 3. 17. Start with 5; add 9. 18. Start with 100; subtract 7.

19. Social Studies The Chinese lunar calendar is based on a 12-year cycle, with each of the 12 years named after a different animal. The year 2006 is the year of the dog.a. When will the next year of the dog occur?b. When was the last year of the dog?c. Will the year 2030 be a year of the dog? Explain.

Identify whether each given sequences could be arithmetic. If not, identify thepattern of the sequence.

20. 10, 16, 22, 28, 34, . . . 21. 60, 56, 61, 57, 62, . . . 22. 111, 121, 131, 141, 151, . . .

23. Choose a Strategy The * shows where a piece is missingfrom the pattern. What piece is missing?

24. Whole numbers raised to the second power are called perfect squares. This is because they can be represented by objects arranged in the shape of a square. Perfectsquares can be written as the sequence 1, 4, 9, 16, . . .a. Find the next two perfect squares in the sequence.b. Explain how can you know whether a number is a perfect square?

25. Write About It Explain how to determine if a sequence is arithmetic.

26. Challenge Find the missing terms in the following sequence: , 23, 27, 43, 125, , 343, . . .

YDyCBByA

27. Multiple Choice Identify the pattern in the sequence 6, 11, 16, 21, 26, . . .

Add 5. Add 6. Multiply by 5. Multiply by 6.

28. Extended Response Identify the first term and a pattern for the sequence 5, 8, 11, 14, 17, . . . Is the sequence arithmetic? Explain why or why not. Find thenext three terms in the sequence.

Use mental math to find each sum or product. (Lesson 1-5)

29. 13 � 6 � 17 � 24 30. 4 � 11 � 5 31. 45 � 11 � 35 � 29

Choose a solution method and solve. Explain your choice. (Lesson 1-6)

32. As of 2005, Hank Aaron was Major League Baseball’s career home run leader with755 home runs. Sadaharu Oh was the career home run leader of Japanese baseballwith 868 home runs. How many more home runs did Oh hit than Aaron?

DCBA

BYybB

yb

BY

*bB

BYybB

BYy

ybBYy


Find a Pattern in Sequences

Activity

Think and Discuss

Try This

1. How do you use a sequence’s pattern when you use your spreadsheet togenerate the terms?

Identify a pattern in each sequence. Then use a spreadsheet to generatethe first 12 terms.

1. 9, 14, 19, 24, 29, 34, … 2. 7, 13, 19, 25, 31, 37, … 3. 105, 98, 91, 84, 77, 70, …

4. 21, 29, 37, 45, 53, 61, … 5. 150, 174, 198, 222, 246, 270, … 6. 600, 550, 500, 450, 400, 350, …

1-7

KEYWORD: MR7 Lab1

The numbers 4, 7, 10, 13, 16, 19, … form an arithmetic sequence. To continue the sequence, identify a pattern. Here is a possible pattern:

4, 4 � 3 � 7, 7 � 3 � 10, 10 � 3 � 13,…

Use a spreadsheet to generate the first seven terms of the sequence above.

To start with 4, type 4 in cell A1.

To add 3 to the value in cell A1,type �A1 � 3 in cell B1.

Press ENTER.

To continue the sequence, click the square in the lower right corner of cell B1,hold down the mouse button, and drag the cursor across through cell G1.

When you release the mouse button, A1 through G1 will list the first seventerms of the sequence.

Use with Lesson 1-7

1-7 Technology Lab 37

Quiz for Lessons 1-4 Through 1-7

1-4 Order of Operations


1. 3 � 4 � (10 � 4) 2. 52 � 10 � 2 � 1 3. 4 � (12 � 8) � 6 4. (23 � 2) � 10

5. Mrs. Webb buys 7 cards for $2 each, 3 metallic pens for $1 each, and 1 pad ofwriting paper for $4. Evaluate 7 � 2 � 3 � 1 � 1 � 4 to find the total amount Mrs. Webb spends.

1-5 Mental Math

Evaluate.

6. 4 � 21 � 9 � 6 7. 5 � 17 � 2 8. 45 � 19 � 1 � 55 9. 2 � 17 � 10


10. 5 � 62 11. 9 � 41 12. 4 � 23 13. 7 � 14 14. 5 � 34

1-6 Choose the Method of Computation

Choose a solution method and solve.Explain your choice.

15. How many Texas state parks are shown in thetable?

16. How many more parks are there in the Prairies and Lakes region than in the Big Bend region?


Identify a pattern in the arithmetic sequence and then find the missing terms.

17.


18. 4, 20, 15, 31, , , 37, … 19. 16, 32, 8, 16, , 8, 2, , 1, …

20. A concert hall has 5 seats in the front row, 9 seats in the second row, 13 seats in the third row, and 17 seats in the fourth row. If this pattern continues, how many seats are in the sixth row?

Region of Parks

Big Bend 7

Gulf Coast 11

Hill Country 11

Panhandle Plains 12

Pineywoods 13

Prairies and Lakes 22

South Texas Plains 5

Rea

dy

to G

o O

n?


Texas State Parks

Number

Position 1 2 3 4 5 6 7


Multi-Step Test Prep 39

Mu

lti-Step Test Prep

Year Site Gold Silver Bronze

1992 Barcelona 37 34 37

1996 Atlanta 44 32 25

2000 Sydney 40 24 33

2004 Athens 35 39 29

Olympic Medals Won by U.S. Athletes

Go for the Gold The table shows the number ofmedals won by the United States at four SummerOlympic Games.

1. Find the total number of medals won by the United States at each Olympics. Then order the Olympic sites from the greatest number of medals won to the least.

2. Estimate the total number of gold medals won by the United States at these four Olympics. Explain how you found your estimate.

3. To compare the performances of U.S. athletes at differentOlympics, Jocelyn assigns 3 points to each gold medal, 2 points to each silver medal, and 1 point to each bronzemedal. To find the total number of U.S. points for theBarcelona Olympics, she writes the expression 3 � 37 � 2 � 34 � 1 � 37. Explain how to evaluate this expression, and then find the point total.

4. In 1996, Romania won 22 gold medals, 71 silver medals, and 32 bronze medals. How many of each medal did Romania win? Find the difference in the number of medals won by the United States and the number of medals won by Romania in 1996.

5. The total number of medals won by the United States at each Summer Olympics since 1896 is 37 � 2. About how many more medals do U.S. athletes need to win in order to have a total of 2,200?

PalindromesA palindrome is a word, phrase, or numberthat reads the same forward and backward.

Examples:race car Madam, I’m Adam. 3710173

You can turn almost any number into apalindrome with this trick.

Think of any number. 283Now add that number in reverse. + 382

665

Use the sum to repeat the previous 665step and keep repeating until the + 566final sum is a palindrome. 1,231

1,231+ 1,321

2,552

It took only three steps to create a palindrome by starting with thenumber 283. What happens if you start with the number 196? Doyou think you will ever create a palindrome if you start with 196?One man who started with 196 did these steps until he had anumber with 70,928 digits and he still had not created a palindrome!

Spin-a-MillionSpin-a-Million

The object of this game is to create the number closest to 1,000,000.

Taking turns, spin the pointer and write the number on your place-value chart. The number cannot be moved once it has been placed.

After six turns, the player whose number is closest to one million wins the round and scores a point. The first player to get five points wins the game.

A complete copy of the rules and game pieces are available online.

KEYWORD: MR7 Games


Materials • plastic DVD case• card stock • markers• scissors• glue stick• library pocket• index cards• brass fastener• large paper clip

Make a game in an empty DVD case to review con-cepts from this chapter.

DirectionsCut a piece of card stock that can be folded inhalf to fit inside the DVD case. Lay the cardstock flat and draw a path for a board game. Besure to have a start and a finish. Figure A

Close the game board and decorate the front.Glue a library pocket onto the front to hold theindex cards. Figure B

On the index cards, write problems that can besolved using math from the chapter. Place thecards in the pocket.

Cut a piece of card stock to fit the other side ofthe DVD box. Glue directions for your game atthe top. At the bottom, make a spinner the sizeof a DVD. Attach a brass fastener to the middle of the spinner, and then attach a paper clip tothe fastener. Figure C

Putting the Math into ActionPlay your game with a partner. Use buttons or coins as playing pieces. Players should take turns spinning the spinner and then be required to solve a problem correctly in order to move their piece.

4

3

2

1

A

C

B

Picture ThisPROJECT

It’s in the Bag! 41

Complete the sentences below with vocabulary words from thelist above.

1. An ordered set of numbers is called a(n) . Each numberin a sequence is called a(n) .

2. In the expression 85, 8 is the , and 5 is the .

3. The is a set of rules used to evaluate an expression thatcontains more than one operation.

4. When you a numerical expression, you find its value.?

?

??

??

Vocabulary

Comparing and Ordering Whole Numbers (pp. 6–9)1-1

E X A M P L E EXERCISES

■ Order the numbers from least to greatest.

4,913; 4,931; 4,391

4,9134,913 � 4,931

4,9314,391 � 4,931

4,931 4,391

4,9134,391 � 4,913

4,391

4,391 � 4,913 � 4,931


5. 8,731; 8,737; 8,735; 8,740

6. 53,341; 53,337; 53,456; 53,452

7. 87,091; 8,791; 87,901; 81,790

8. 26,551; 25,615; 2,651; 22,561

9. 96,361; 96,631; 93,613; 91,363

10. 10,101; 11,010; 10,110; 11,110

Stu

dy

Gu

ide:

Rev

iew

4,700 4,900 5,1004,5004,300

4,9314,9134,391

. . . . . . . . . . . . . . . . . . . 33

. . . . . . . . . . . . . . . . . . 26

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

. . . . . . . . . . . . . . . . . 26

. . . . . . . . . . . . . . . . . . . 10

. . . . . . . . . . . . . . . . . . 27

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

. . . . . . . . . . . . . . . . . . . . . 14

. . . . . . . . . . . . . . . . . . 22

. . . . . . . . . . . . . . . . . . . . 22

. . . . . . . . . . . . . . . . . . . . . . . . . . 10

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

. . . . . . . . . . . . . . . . . . . . . . . . 10underestimate

term

sequence

overestimate

order of operations


exponential form

exponent

evaluate

Distributive Property

compatible number

Commutative Property

base

Associative Property

arithmetic sequence


Stud

y Gu

ide: R

eview

■ Estimate the sum 837 � 710 byrounding to the hundreds place.800 � 700 � 1,500 The sum is about 1,500.

■ Estimate the quotient of 148 and 31.150 � 30 � 5The quotient is about 5.

Estimate each sum or difference byrounding to the place value indicated.

11. 4,671 � 3,954; thousands

12. 3,123 � 2,987; thousands

13. 53,465 � 27,465; ten thousands

14. Ralph has 38 photo album sheets with22 baseball cards in each sheet. Abouthow many baseball cards does he have?


Estimating with Whole Numbers (pp. 10–13)1-2


Exponents (pp. 14–17)1-3

■ Write 6 � 6 in exponential form.

62 6 is a factor 2 times.

Find each value.

■ 52■ 63

52 � 5 � 5 63 � 6 � 6 � 6� 25 � 216


15. 5 � 5 � 5 16. 3 � 3 � 3 � 3

17. 7 � 7 � 7 � 7 � 7 18. 8 � 8

19. 4 � 4 � 4 � 4 20. 1 � 1 � 1

Find each value.

21. 44 22. 24 23. 63

24. 33 25. 15 26. 74

27. 53 28. 102 29. 92


Order of Operations (pp. 22–25)1-4

■ Evaluate 8 � (7 � 5) � 22 � 2 � 9.

8 � (7 � 5) � 22 � 2 � 9

8 � 2 � 22 � 2 � 9 Subtract inparentheses.

8 � 2 � 4 � 2 � 9 Simplify theexponent.

4 � 4 � 2 � 9 Divide.

16 � 2 � 9 Multiply.

14 � 9 Subtract.

23 Add.

Evaluate each expression.3

30. 9 � 8 � 13

31. 21 � 3 � 4

32. 6 � 4 � 5

33. 19 � 12 � 6

34. 30 � 2 � 5 � 2

35. (7 � 3) � 2 � 32

36. 8 � (7 � 5) � 42 � 9 � 3

37. 32 � 5 � (10 � 3 � 2)

Study Guide: Review 43

Stu

dy

Gu

ide:

Rev

iew

Evaluate.

■ 4 � 13 � 6 � 7 ■ 5 � 9 � 64 � 6 � 13 � 7 5 � 6 � 9(4 � 6) � (13 � 7) (5 � 6) � 9

10 � 20 30 � 930 270

■ Use the Distributive Property to find 3 � 16.

3 � 16 � 3 � (10 � 6)

� (3 � 10) � (3 � 6)� 30 � 18� 48

Evaluate.

38. 9 � 5 � 1 � 15 39. 8 � 13 � 5

40. 31 � 16 � 19 � 14 41. 6 � 12 � 15

42. 17 � 12 � 8 � 3 43. 16 � 5 � 4

44. 11 � 23 � 27 � 39 45. 13 � 5 � 2

Use the Distributive Property to find eachproduct.

46. 7 � 24 47. 9 � 15

48. 6 � 34 49. 8 � 19

50. 8 � 27 51. 5 � 33


Mental Math (pp. 26–29)1-5

Choose the Method of Computation (pp. 30–32)1-6


■ Choose a solution method and solve.Explain your choice.

The average annual rainfall in Washington,D.C., is 39 inches. How much rain doesWashington, D.C., average in 8 years?

These numbers are not so big that youmust use a calculator. Use pencil and paperto find the answer. 39 � 8 � 312 inches

Choose a solution method and solve.Explain your choice.

52. The average high temperature forWashington, D.C., in January is 42�F. The record high temperature forWashington, D.C., is 104�F. How muchhigher is the record temperature thanthe average high temperature inJanuary?

Patterns and Sequences (pp. 33–36)1-7


Identify a pattern in the sequence. Namethe missing terms.

■ 1, 3, 5, 7, , , . . .

�2 �2 �2 �2 �2

The pattern is to add 2 to each term. Themissing terms are 9 and 11.■ 6, 12, 11, 22, , 42, , . . .

�2 �1 �2 �1 �2 �1

The pattern is to multiply one term by 2 andsubtract the next by 1. The missing termsare 21 and 41.

Identify the pattern in each arithmeticsequence and then find the missing terms.

53. 4, 9, 14, 19, , , . . .

54. 21, 19, 17, 15, , , . . .

Identify a pattern in each sequence. Namethe missing terms.

55. 16, 20, 18, 22, , 24, , . . .

56. 1, 3, 9, 27, , , . . .

57. 65, 70, 68, 73, , 76, , . . .


Chapter 1 Test 45


1. 3,241 324 2. 16,880,953 16,221,773 3. 22,481,093 23,662,840


4. 801; 798; 921 5. 4,835; 7,505; 4,310 6. 10,101; 101; 1,001



Estimate.

9. Kaitlin’s family is planning a trip from Washington, D.C., to New York City.New York City is 227 miles from Washington, D.C., and the family can drive anaverage of 55 mi/h. About how long will the trip take?


10. 4 � 4 � 4 � 4 � 4 11. 10 � 10 � 10 12. 6 � 6 � 6 � 6

Find each value.

13. 23 14. 52 15. 44 16. 112 17. 93


18. 12 � 8 � 2 19. 32 � 5 � 10 � 7 20. 12 � (28 � 15) � 4 � 2

Evaluate.

21. 15 � 23 � 47 � 5 22. 5 � 48 � 2 23. 2 � 5 � 11 24. 44 � 18 � 12 � 6


25. 3 � 32 26. 52 � 6 27. 24 � 5 28. 81 � 6 29. 6 � 21


30. At 5:00 A.M., the temperature was 41°F. By noon, the temperature was 69°F. By how many degrees did the temperature increase?


31. 8, 22, 36, 50, , , , . . . 32. 2, 10, 7, 15, , 20, , . . .

33. A tile pattern has 1 tile in the first row, 3 tiles in the second row, and 5 tiles inthe third row. If this pattern continues, how many tiles are in the fifth row?

Ch

apter Test

Test

Tac

kler


Which number is the closest estimate for 678 � 189?

700 1,000

900 5,000

You can use logical reasoning to eliminate choice A because it is too small. The estimated sum has to be greater than 700 because 678 � 189 is greater than 700.

Choice D may also be eliminated because the value is too large. Theestimated sum will be less than 5,000.

Round 678 up to 700 and 189 up to 200. Then find the sum of 700 and200: 700 � 200 � 900. You can eliminate choice C because it is greaterthan 900.

Choice B is the closest estimate.

DB

CA

Multiple Choice: Eliminate Answer ChoicesYou can solve some math problems without doing detailed calculations.You can use mental math, estimation, or logical reasoning to help youeliminate answer choices and save time.

Which of the following numbers is the standard form of fourmillion, six hundred eight thousand, fifteen?

468,015 4,068,150

4,608,015 4,600,815,000

Logical reasoning can be used to eliminate choices. Numbers thathave a place value in the millions must have at least seven but nomore than nine digits. Choices F and J can be eliminated becausethey do not have the correct number of digits.

Both choices G and H have the correct range of digits, so narrow itdown further. The number must end in 15. Choice H ends in 50, so itcannot be correct. Eliminate it.

The correct answer choice is G.

JG

HF

Read each item and answer the questionsthat follow.

Test Tackler 47

Test TacklerSome answer choices, called distracters,may seem correct because they are basedon common errors made in calculations.

1. Are there any answer choices you caneliminate immediately? If so, whichones and why?

2. Describe how you can find the correctanswer.

3. Can F be eliminated? Why or why not?

4. Can H be eliminated? Why or why not?

5. Explain how to use mental math tosolve this problem.

6. Which answer choice can be eliminated immediately? Explain.

7. Explain how you can use the Distributive Property to solve thisproblem.

City Middle School Populations

Central Middle School 652

Eastside Middle School 718

Northside Middle School 663

Southside Middle School 731

Westside Middle School 842

Item AWhich number is the greatest?

599,485 5,569,003

5,571,987 5,399,879DB

CA

Item CWhich expression does NOT have thesame value as 8 � (52 � 12)?

8 � 64

(8 � 52) � (8 � 12)

8(60) � 8(4)

8 � 52 � 12D

C

B

A

Item BThe school district receives $30 a dayin state funding for every studentenrolled in a public school. Find theapproximate number of students thatattend all of the city middle schools.

2,000 3,600

3,300 4,000JG

HF

Item DStacey is beginning a new exerciseprogram. She plans to cycle 2 kilometerson her first day. Each day after that, shewill double the number of kilometersshe cycled from the day before. Whichexpression shows how many kilometersshe will cycle on the sixth day?

2 � 6 26

2 � 2� 2� 2� 2� 2 62JG

HF

10. Which answer choice(s) can beimmediately eliminated and why?

11. Explain how to solve this problem.

8. Are there any answer choices you caneliminate immediately? If so, whichchoices and why?

9. Explain how you can use a table tohelp you solve this problem.

Item EJames is driving to his aunt’s house.If he drives about 55 miles per hour for5 hours, about how many miles will hehave driven?

12 miles 60 miles

300 miles 600 milesDB

CA

Stan

dar

diz

ed T

est

Prep

KEYWORD: MR7 TestPrep

1. Jonah has 31 boxes of baseball cards. Ifeach box contains 183 cards, abouthow many baseball cards does Jonahhave in his collection?

3,000 cards 9,000 cards

6,000 cards 12,000 cards

2. Which of the following does NOT havea value of 27?

33 3 � 3 � 18

32 � 3 � 7 92 � 3

3. What are the next two terms in thefollowing sequence?

6, 3, 12, 6, 24, …

3, 12 12, 48

6, 36 18, 72

4. Which of the following correctly showsthe use of the Distributive Property tofind the product of 64 and 8?

64 � 8 � (8 � 60) � (8 � 4)

64 � 8 � 8 � 64

64 � 8 � 8 � (60 � 4)

64 � 8 � (8 � 4) � 60

5. What is five billion, two hundred fifty-two million, six hundred thousand,three hundred eleven in standardform?

5,252,603,011 5,252,600,311

52,526,311 5,252,060,311

6. The attendance at a local library isshown in the table below. How manypeople visited the library last week?

450 650

550 750

7. Which number is the greatest?

5,432,873 5,221,754

5,201,032 5,332,621

8. What is 6 � 6 � 6 � 6 written inexponential form?

244

1,296

64

1000 � 200 � 90 � 6

9. The expression 6 � 3 � 4 � 3 � 6 � 4is an example of which property?

Associative Distributive

Commutative ExponentialDB

CA

J

H

G

F

DB

CA

JG

HF

DB

CA

J

H

G

F

DB

CA

JG

HF

DB

CA

CUMULATIVE ASSESSMENT, CHAPTER 1Multiple Choice


Last Week’s Attendance

Sunday Closed

Monday 78

Tuesday 125

Wednesday 122

Thursday 96

Friday 104

Saturday 225

Cumulative Assessment, Chapter 1 49

10. Which list of numbers is in order fromleast to greatest?

1,231; 1,543; 1,267; 1,321

3,210; 3,357; 3,366; 3,401

4,321; 4,312; 4,211; 4,081

5,019; 5,187; 5,143; 5,314

11. There are 2,347 seats in the towntheater. A ticket to the Friday nightconcert costs $32. Which method ofcomputation should be used to find howmuch money the theater will make ifthe Friday night concert sells out?

Paper and pencil

Calculator

Mental Math

Estimation

Gridded Response12. What is the value of

3 � 8 � 6 �(12 � 4)?

13. What is the value of 24?

14. Martha walked 4 minutes on Monday,7 minutes on Tuesday, and 10 minuteson Wednesday. If the patterncontinues, how many minutes will shewalk on Saturday?

15. At 2:00 P.M., the water temperature inthe pool was 88°F. By 10:00 P.M. thewater temperature in the pool was75°F. By how many degrees did thewater temperature drop?

16. Estimate the sum of 3,820 and 4,373 byrounding to the nearest thousand.

17. What is the base of 63?

Short Response18. Megan deposited $2 into her savings

account on the first Friday of themonth. Each week she doubles herdeposit from the week before.

a. If this pattern continues, how muchmoney will she deposit in week 4?

b. What is the total amount inMegan’s account after her fourthdeposit? Explain how you foundyour answer.

19. Create a numerical expression that canbe simplified in four steps. Include oneset of parentheses and an exponent.The same mathematical operation maybe used no more than two times. Showhow to evaluate your expression.

Extended Response20. The student population at Southside

Middle School is listed in the tablebelow.

a. Use the information in the table tofind the total number of studentswho attend Southside MiddleSchool. Show your work.

b. About how many more girls areenrolled in the school than boys?Show your work. Explain how youfound your answer.

c. The school board wants the school to have one teacher for every 20students. If there are 8 sixth-gradeteachers, does the school need to hiremore sixth-grade teachers? If so, howmany more? Explain your answer.

D

C

B

A

J

H

G

F

Stand

ardized

Test Prep

When you read a word problem,underline the information you need tohelp you answer the question.

Student Population atSouthside Middle School

Boys Girls

6th Grade 98 102

7th Grade 89 105

8th Grade 123 117

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