108	Chapter 1 Whole Numbers

Using Your CALCULATOR Order of Operations and Parentheses

Calculators have the rules for order of operations built in. A left parenthesis key ( and a right parenthesis key ) should be used when grouping symbols,

including a fraction bar, are needed. For example, to evaluate 20240 5 , the parentheses keys must be used, as shown below.

240 ( 20 5 )

16

On some calculator models, the ENTER key is pressed instead of for the result to be displayed.

If the parentheses are not entered, the calculator will find 240 20 and then subtract 5 from that result, to produce the wrong answer, 7.

THINK IT THROUGH Education Pays

“Education does pay. It has a high rate of return for students from all racial/ethnic groups, for men and for women, and for those from all family backgrounds. It also has a high rate of return for society.”

The College Board, Trends in Higher Education Series

Attending school requires an investment of time, effort, and sacrifice. Is it all worth it? The graph below shows how average weekly earnings in the U.S. increase as the level of education increases. Begin at the bottom of the graph and work upward. Use the given clues to determine each of the missing weekly earnings amounts.

	Average earnings per week in 2007
									?
Doctoral degree		$70 increase
								?
Professional degree		$262 increase
							?
Master’s degree	$178 increase
						?
Bachelor’s degree	$247 increase
					?
Associate degree	$57 increase
				?
Some college, no degree	$79 increase
			?
High-school graduate	$176 increase
Less than a high school diploma		$428 per week

(Source: Bureau of Labor Statistics, Current Population Survey)

ANSWERS TO SELF CHECKS

1. 102 2. 76 3. 40 4. 4,720¢ $47.20 5. a. 19 b. 7 6. 256 7. 42 8. 18

9. 2 10. 290 lb

10. To find the mean (average) of 15, 33, 45, 12, 6, 19, and 3, we add the values and divide by what number?

NOTATION

60 5 2

11. In the expression 5 2 40 , what symbol serves as a grouping symbol? What does it group?

(5 20 82) 28 numerator, what operation should be performed first? In the denominator, what operation should be performed first?

. In the

9. Consider the expression

5 5(7)

S E C T I O N 1.9 STUDY SET

VOCABULARY

Fill in the blanks.

1.Numbers are combined with the operations of addition, subtraction, multiplication, and division to

create .

2.

To evaluate the expression 2 5 4 means to find its

.

3.

The grouping symbols (

) are called

,

and the symbols [

] are called

.

4.

The expression above a fraction bar is called the

. The expression below a fraction bar is

called the

.

5.

In the expression 9 6[8 6(4 1)], the

parentheses are the

most grouping symbols

and the brackets are the

most grouping

symbols.

6.

To find the

of a set of values, we add

the values and divide by the number of values.

CONCEPTS

7.List the operations in the order in which they should be performed to evaluate each expression. You do not have to evaluate the expression.

a.5(2)2 1

b.15 90 (2 2)3

c.7 42

d.(7 4)2

8.List the operations in the order in which they should be performed to evaluate each expression. You do not have to evaluate the expression.

a.50 8 40

b.50 40 8

c.16 2 4

d.16 4 2

1.9 Order of Operations	109

12.Use brackets to write 2(12 (5 4)) in clearer form.

Fill in the blanks.

13. We read the expression 16 (4 9) as “16 minus the of 4 plus 9.”

14. We read the expression (8 3)3 as “The cube of the of 8 minus 3.”

Complete each solution to evaluate the expression.
15.	7 4 5(2)2 7 4 51																	2
			28
16.	2 (5 6 2) 2											15								2
			2
17.	[4(2 7)] 42 C4 1													2D 42
												42
			36
18.	12 5 3		12
	32 2 3						6

	3

GUIDED PRACTICE

Evaluate each expression. See Example 1.

19.	3 52 28			20.	4 22 11
21.	6 32 41			22.	5 42 32
Evaluate each expression. See Example 2.
23.	52 6 3 4			24.	66 8 7 16
25.	32 9 3 31			26.	62 5 8 27
Evaluate each expression. See Example 3.
27.	192 4 4(2)3			28.	455 7 3(4)5
29.	252 3 6(2)6			30.	264 4 7(4)2
Evaluate each expression. See Example 5.
31.	a.	26	2 9	32.	a.	37 4 11
	b.	26	(2 9)		b.	37 (4 11)
33.	a.	51	16 8	34.	a.	73 35 9
	b.	51	(16 8)		b.	73 (35 9)

110	Chapter 1 Whole Numbers
Evaluate each expression. See Example 6.
35.	(4 6)2	36.	(3 4)2
37.	(3 5)3	38.	(5 2)3
Evaluate each expression. See Example 7.
39.	8 4(29 5 3)	40.	33 6(56 9 6)
41.	77 9(38 4 6)	42.	162 7(47 6 7)

Evaluate each expression. See Example 8.

43.46 3[52 4(9 5)]

44.53 5[62 5(8 1)]

45.81 9[72 7(11 4)]

46.81 3[82 7(13 5)]

Evaluate each expression. See Example 9.

2(50) 4		4(34)		1
47.		48.
2(42)		5(32)
25(8) 8		6(31)		26
49.		50.
6(23)		4(23)

Find the mean (average) of each list of numbers. See Example 10.

51.	6, 9, 4, 3, 8	52.	7, 1, 8, 2, 2
53.	3, 5, 9, 1, 7, 5	54.	8, 7, 7, 2, 4, 8
55.	19, 15, 17, 13	56.	11, 14, 12,	11
57.	5, 8, 7, 0, 3, 1	58.	9, 3, 4, 11,	14, 1

TRY IT YOURSELF

Evaluate each expression.
59.	(8 6)2 (4 3)2		60.	(2 1)2 (3 2)2
61.	2 34		62.	33 5
63.	7 4 5		64.	10 2 2
65.	(7 4)2 1		66.	(9 5)3 8
67.	10 5		68.	18 12
	52 47			61 55

69.5 103 2 102 3 101 9

70.8 103 0 102 7 101 4

71.	20	10 5	72.	80 5 4
73.	25	5 5	74.	6 2 3
75.	150 2(2 6 4)2		76.	760 2(2 3 4)2

77.190 2[102 (5 22)] 45

78.161 8[6(6) 62] 22(5)

79.	2 3(0)	80.	5(0) 8
81.	(5 3)2 2	82.	(43 2)	7
	42 (8 2)		5(2 4) 7

83.	42 32				84.	122 52
85.	3 2 34 5				86.	3 23 4 12
	40					200
87.	60 a6			b	88.	7 a53		b
		23					2
89.	(3 5)2 2				90.	25 (2 3 1)
	2(8 5)					2 9 8
91.	(18 12)3 52				92.	(9 2)2 33

93.30(1)2 4(2) 12

94.5(1)3 (1)2 2(1) 6

95.	162			25		6(3)4	96.	152			24		8(2)(3)
	5							6
97.	32 22						98.	52 17
	(3 2)2							6 22
	18							12
99.	3a		b 2(2)				100.	2a		b 3(5)
		3							3
101.	4[50 (33 52)]						102.	6[15 (5 22)]

103.80 2[12 (5 4)]

104.15 5[12 (22 4)]

APPLICATIONS

Write an expression to solve each problem and evaluate it.

105.SHOPPING At the supermarket, Carlos is buying 3 cases of soda, 4 bags of tortilla chips, and 2 bottles of salsa. Each case of soda costs $7, each bag of chips costs $4, and each bottle of salsa costs $3. Find the total cost of the snacks.

106.BANKING When a customer deposits cash, a teller must complete a currency count on the back of the deposit slip. In the illustration, a teller has written the number of each type of bill to be deposited. What is the total amount of cash being deposited?

Currency count, for financial use only

24

x 1's

—x 2's

6	x	5's
10	x	10's
12	x	20's
2	x	50's

1x 100's TOTAL $

107.DIVING The scores awarded to a diver by seven judges as well as the degree of difficulty of his dive are shown on the next page. Use the following two-step process to calculate the diver’s overall score.

Step 1 Throw out the lowest score and the highest score.

Step 2 Add the sum of the remaining scores and multiply by the degree of difficulty.

Judge	1	2	3	4	5	6	7

Score 9 8 7 8 6 8 7

Degree of difficulty: 3

108.WRAPPING GIFTS How much ribbon is needed to wrap the package shown if 15 inches of ribbon are needed to make the bow?

4 in.

in.

9in.

109.SCRABBLE Illustration (a) shows part of the game board before and illustration (b) shows it after the words brick and aphid were played. Determine the scoring for each word. (Hint: The number on each tile gives the point value of the letter.)

Before				After
TRIPLE					B3
LETTER
SCORE
DOUBLE				DOUBLE	R1
LETTER				LETTER
SCORE				SCORE
DOUBLE	TRIPLE			A1 P3 H4	I1 D2
LETTER	WORD
SCORE	SCORE
DOUBLE				DOUBLE	C3
LETTER				LETTER
SCORE				SCORE
TRIPLE					K5
LETTER
SCORE
(a)				(b)

110.THE GETTYSBURG ADDRESS Here is an excerpt from Abraham Lincoln’s Gettysburg Address:

Fourscore and seven years ago, our fathers brought forth on this continent a new nation, conceived in liberty, and dedicated to the proposition that all men are created equal.

Lincoln’s comments refer to the year 1776, when the United States declared its independence. If a score is 20 years, in what year did Lincoln deliver the Gettysburg Address?

111.PRIME NUMBERS Show that 87 is the sum of the squares of the first four prime numbers.

1.9 Order of Operations

111

112.SUM-PRODUCT NUMBERS

a.Evaluate the expression below, which is the sum of the digits of 135 times the product of the digits of 135.

(1 3 5)(1 3 5)

b.Write an expression representing the sum of the digits of 144 times the product of the digits of 144. Then evaluate the expression.

113.CLIMATE One December week, the high temperatures in Honolulu, Hawaii, were

75°, 80°, 83°, 80°, 77°, 72°, and 86°. Find the week’s mean (average) high temperature.

114.GRADES In a science class, a student had test scores of 94, 85, 81, 77, and 89. He also overslept, missed the final exam, and received a 0 on it. What was his test average (mean) in the class?

115.ENERGY USAGE See the graph below. Find the mean (average) number of therms of natural gas used per month for the year 2009.

Acct 45-009	2009 Energy Audit	Tri-City Gas Co.
Janice C. Milton	23 N. State St. Apt. B	Salem, OR

	50							42
		39	40				41
used	40			37				34
						33
				31
Therms	30
				22	23
	20				14	16
	10
		J F M A M J J A S O N D

116.COUNTING NUMBERS What is the average (mean) of the first nine counting numbers:

1, 2, 3, 4, 5, 6, 7, 8, and 9?

117.FAST FOODS The table shows the sandwiches Subway advertises on its 6 grams of fat or less menu. What is the mean (average) number of calories for the group of sandwiches?

6-inch subs	Calories
Veggie Delite	230
Turkey Breast	280
Turkey Breast & Ham	295
Ham	290
Roast Beef	290
Subway Club	330
Roasted Chicken Breast	310
Chicken Teriyaki	375

(Source: Subway.com/NutritionInfo)

112Chapter 1 Whole Numbers

118.TV RATINGS The table below shows the number of viewers* of the 2008 Major League Baseball World Series between the Philadelphia Phillies and the Tampa Bay Rays. How large was the average (mean) audience?

Game 1	Wednesday, Oct. 22	14,600,000
Game 2	Thursday, Oct. 23	12,800,000
Game 3	Saturday, Oct. 25	9,900,000
Game 4	Sunday, Oct. 26	15,500,000
Game 5	Monday, Oct. 27	13,200,000
(suspended in 6th
inning by rain)
Game 5	Wednesday, Oct. 29	19,800,000
(conclusion
of game 5)

* Rounded to the nearest hundred thousand (Source: The Nielsen Company)

AP Images

119.YOUTUBE A YouTube video contest is to be part of a kickoff for a new sports drink. The cash prizes to be awarded are shown below.

a.How many prizes will be awarded?

b.What is the total amount of money that will be awarded?

c.What is the average (mean) cash prize?

YouTube Video Contest

Grand prize: Disney World vacation plus $2,500

Four 1st place prizes of $500

Thirty-five 2nd place prizes of $150

Eighty-five 3rd place prizes of $25

120.SURVEYS Some students were asked to rate their college cafeteria food on a scale from 1 to 5. The responses are shown on the tally sheet.

a.How many students took the survey?

b.Find the mean (average) rating.

WRITING

121.Explain why the order of operations rule is necessary.

122.What does it mean when we say to do all additions and subtractions as they occur from left to right?

Give an example.

123.Explain the error in the following solution:

Evaluate:

8 2[6 3(9 8)] 8 2[6 3(1)]

8 2[6 3]

8 2(3)

10(3)

30

124. Explain the error in the following solution: Evaluate:

24 4 16 24 20

4

REVIEW

Write each number in words.

125.254,309

126.504,052,040

113

C H A P T E R 1 SUMMARY AND REVIEW

S E C T I O N 1.1 An Introduction to the Whole Numbers

DEFINITIONS AND CONCEPTS

The set of whole numbers is {0, 1, 2, 3, 4, 5, p}.

When a whole number is written using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, it is said to be in standard form.

The position of a digit in a whole number determines its place value. A place-value chart shows the place value of each digit in the number.

To make large whole numbers easier to read, we use commas to separate their digits into groups of three, called periods.

To write a whole number in words, start from the left. Write the number in each period followed by the name of the period (except for the ones period, which is not used). Use commas to separate the periods.

To read a whole number out loud, follow the same procedure. The commas are read as slight pauses.

To change from the written-word form of a number to standard form, look for the commas. Commas are used to separate periods.

To write a number in expanded form (expanded notation) means to write it as an addition of the place values of each of its digits.

Whole numbers can be shown by drawing points on a number line.

Inequality symbols are used to compare whole numbers:

means is greater than

means is less than

EXAMPLES

Some examples of whole numbers written in standard form are:

2, 16, 530, 7,894, and 3,201,954

P E R IO D S

trillions

Trillions

Billions

Millions

Thousands

Ones

billions

millions

thousands

s

ns

trillions

billions

millions

thousand

Te

Ones

Hundred

Trillions

Billions

Millions

ThousandsHundreds

Ten

Hundred

Ten

Hundred

Ten

Hundred

Ten

5 , 2 0 6 , 3 7 9 , 8 1 4 , 2 5 6

The place value of the digit 7 is 7 ten millions.

The digit 4 tells the number of thousands.

Millions Thousands								Ones
	2		,	5 6 8			,	0 1 9

Two million, five hundred sixty-eight thousand, nineteen

Six billion , forty-one million , two hundred eight thousand , thirty-six

6,041,208,036

The expanded form of 32,159 is:

30,000 2,000 100 50 9

The graphs of 3 and 7 are shown on the number line below.

0

1

2

3

4

5

6

7

8

9 8	and	2,343	762
1 2	and	9,000	12,453

114		Chapter 1 Whole Numbers
		When we don’t need exact results, we often Round 9,842 to the nearest ten.
		round numbers.		Rounding digit: tens column

Rounding a Whole Number

1.To round a number to a certain place value, locate the rounding digit in that place.

2.Look at the test digit, which is directly to the right of the rounding digit.

9,842

Test digit: Since 2 is less than 5, leave the rounding digit unchanged and replace the test digit with 0.

Thus, 9,842 rounded to the nearest ten is 9,840.

Round 63,179 to the nearest hundred.

	3. If the test digit is 5 or greater, round up by						Rounding digit: hundreds column
	adding 1 to the rounding digit and	63,179
	replacing all of the digits to its right with 0.						Test digit: Since 7 is 5 or greater, add 1 to the rounding digit and
	If the test digit is less than 5, replace it and all						replace all the digits to its right with 0.
		Thus, 63,179 rounded to the nearest hundred is 63,200.
	of the digits to its right with 0.
	Whole numbers are often used in tables, bar	See page 9 for an example of a table, a bar graph, and a line graph.
	graphs, and line graphs.

REVIEW EXERCISES

Consider the number 41,948,365,720.

1.Which digit is in the ten thousands column?

2.Which digit is in the hundreds column?

3.What is the place value of the digit 1?

4.Which digit tells the number of millions?

5.Write each number in words.

a.97,283

b.5,444,060,017

6.Write each number in standard form.

a.Three thousand, two hundred seven

b.Twenty-three million, two hundred fifty-three thousand, four hundred twelve

Write each number in expanded form.

7.570,302

8.37,309,154

13.Round 2,507,348

a.to the nearest hundred

b.to the nearest ten thousand

c.to the nearest ten

d.to the nearest million

14.Round 969,501

a.to the nearest thousand

b.to the nearest hundred thousand

15.CONSTRUCTION The following table lists the number of building permits issued in the city of Springsville for the period 2001–2008.

Year	2001	2002	2003	2004	2005	2006	2007	2008
Building	12	13	10	7	9	14	6	5
permits

a. Construct a bar graph of the data.

Graph the following numbers on a number line.

9. 0, 2, 8, 10

0

1

2

3

4

5

6

7

8

9

10

10. the whole numbers between 3 and 7

0

1

2

3

4

5

6

7

8

9

10

Place an or an symbol in the box to make a true statement.

Permits issued

Bar graph

15

10

5

2001 2002 2003 2004 2005 2006 2007 2008 Year

11.	9		7	12.	301		310

b. Construct a line graph of the data.

Line graph

	issued	15
		10
	Permits
		5

2001 2002 2003 2004 2005 2006 2007 2008 Year

Chapter 1 Summary and Review

115

16.GEOGRAPHY The names and lengths of the five longest rivers in the world are listed below. Write them in order, beginning with the longest.

Amazon (South America)	4,049 mi
Mississippi-Missouri (North America)	3,709 mi
Nile (Africa)	4,160 mi
Ob-Irtysh (Russia)	3,459 mi
Yangtze (China)	3,964 mi

(Source: geography.about.com)

S E C T I O N 1.2

Adding Whole Numbers

DEFINITIONS AND CONCEPTS

EXAMPLES

To add whole numbers, think of combining

Add:

10,892 5,467 499

sets of similar objects.

Carrying

Vertical

form: Stack

the addends. Add the

digits in the ones column, the tens column, the

1

2 1

10,892

Addend

To check,

hundreds column, and so on. Carry when

5,467

Addend

add

necessary.

499

Addend

bottom

to top

Sum

16,858

Commutative property of addition: The order

6 5 5 6

in which whole numbers are added does not

By the commutative property, the sum is the same.

change their sum.

Associative property of addition: The way in

(17 5) 25 17 (5 25)

which whole numbers are grouped does not

By the associative property, the sum is the same.

change their sum.

To estimate a sum, use front-end rounding to

Estimate the sum:

approximate the addends. Then add.

7,219

7,000

Round to the nearest thousand.

592

600

Round to the nearest hundred.

3,425

3,000

Round to the nearest thousand.

10,600

The estimate is 10,600.

To solve the application problems, we must

Translate the words to numbers and symbols:

often translate the key words and phrases of

VACATIONS There

were

4,279,439

visitors to Grand Canyon

the problem to numbers and symbols. Some

National Park in 2006. The following year, attendance increased by

key words and phrases that are often used to

134,229. How many people visited the park in 2007?

indicate addition are:

The phrase increased by indicates addition:

gain

increase

up

forward

rise

more than

total

combined

The number of

in all

in the future

extra

altogether

visitors to the

4,279,439

134,229

park in 2007

116		Chapter 1 Whole Numbers
		The distance around a rectangle or a square is			Find the perimeter of the rectangle shown below.
		called its perimeter.
						15 ft
		Perimeter
		of a	length length width width				10 ft
		rectangle
		Perimeter			Perimeter 15 15 10 10 Add the two lengths and
		of a	side side side side
						the two widths.
		square		50
					The perimeter of the rectangle is 50 feet.

REVIEW EXERCISES

Add.
17.	27 436	18.	(9 3) 6
19.	4 (36 19)	20.	236
			782
21.	5,345	22.	2 1 38 3 6
	655
23.	4,447 7,478 676	24.	32,812
			65,034
			54,323

25.Add from bottom to top to check the sum. Is it correct?

1,291

859

345226 1,821

26.What is the sum of three thousand seven hundred six and ten thousand nine hundred fifty-five?

27.Use front-end rounding to estimate the sum.

615 789 14,802 39,902 8,098

28.a. Use the commutative property of addition to complete the following:

24 61

b.Use the associative property of addition to complete the following:

9 (91 29)

29.AIRPORTS The nation’s three busiest airports in 2007 are listed below. Find the total number of passengers passing through those airports.

Airport	Total passengers
Hartsfield-Jackson Atlanta	89,379,287
Chicago O’Hare	76,177,855
Los Angeles International	61,896,075

Source: Airports Council International–North America

30.What is 451,775 more than 327,891?

31.CAMPAIGN SPENDING In the 2004 U.S. presidential race, candidates spent $717,900,000. In the 2008 presidential race, spending increased by $606,800,000 over 2004. How much was spent by the candidates on the 2008 presidential race? (Source: Center for Responsive Politics)

32.Find the perimeter of the rectangle shown below.

731 ft

642 ft

Chapter 1 Summary and Review

117

S E C T I O N 1.3 Subtracting Whole Numbers

DEFINITIONS AND CONCEPTS

To subtract whole numbers, think of taking away objects from a set.

Vertical form: Stack the numbers. Subtract the digits in the ones column, the tens column, the hundreds column, and so on. Borrow when necessary.

To check: Difference subtrahend minuend

Be careful when translating the instruction to subtract one number from another number. The order of the numbers in the sentence must be reversed when we translate to symbols.

Every subtraction has a related addition statement.

To estimate a difference, use front-end rounding to approximate the minuend and subtrahend. Then subtract.

Some of the key words and phrases that are often used to indicate subtraction are:

loss	decrease	down	backward
fell	less than	fewer	reduce
remove	debit	in the past	remains
declined			take away

To answer questions about how much more or how many more, we use subtraction.

To evaluate (find the value of) expressions that involve addition and subtraction written in horizontal form, we perform the operations as they occur from left to right.

EXAMPLES

Subtract: 4,957 869

	14				Borrowing		Check using addition:
8	4	17			Minuend					1 1
4,9 5 7										4,088
8 6 9					Subtrahend			869
4,0 8 8					Difference					4,957

Translate the words to numbers and symbols:

	Subtract 41 from						97.		Since 41 is the number to be
									subtracted, it is the subtrahend.
				97 41
10 3 7				because				7 3 10
Estimate the difference:
59,033				60,000		Round to the nearest ten thousand.
4,124				4,000		Round to the nearest thousand.
				56,000

The estimate is 56,000.

WEIGHTS OF CARS A Chevy Suburban weighs 5,607 pounds and a Smart Car weighs 1,852 pounds. How much heavier is the Suburban?

The phrase how much heavier indicates subtraction:

5,607 Weight of the Suburban

1,852 Weight of the Smart Car

3,755

The Suburban weighs 3,755 pounds more than the Smart Car.

Evaluate: 75 23 9

75 23 9 52 9 Working left to right, do the subtraction first.

61	Now do the addition.

118	Chapter 1 Whole Numbers

REVIEW EXERCISES

Subtract.
33. 148 87	34. 343
	269

35.Subtract 10,218 from 10,435.

36.5,231 5,177

37. 750 259 14

38. 7,800

42.LAND AREA Use the data in the table to determine how much larger the land area of Russia is compared to that of Canada.

Country	Land area (square miles)
Russia	6,592,115
Canada	3,551,023

	5,725			(Source: The World Almanac, 2009)
				BANKING A savings account contains $12,975.
			43.
39. Check the subtraction using addition.				If the owner makes a withdrawal of $3,800 and
				later deposits $4,270, what is the new account
	8,017
				balance?
	6,949		44.	SUNNY DAYS In the United States, the city of
	1,168
				Yuma, Arizona, typically has the most sunny
40.	Fill in the blank: 20 8 12 because		.	days per year—about 242. The city of Buffalo, New
				York, typically has 188 days less than that.
41.	Estimate the difference: 181,232 44,810
				How many sunny days per year does Buffalo
				have?

S E C T I O N 1.4

Multiplying Whole Numbers

DEFINITIONS AND CONCEPTS

EXAMPLES

Multiplication of whole numbers is repeated

Repeated addition:

addition but with different notation.

The sum of four 6’s

Multiplication

6 6 6 6 4 6

24

To write multiplication, we use a times symbol

, a raised dot , and parentheses ( ).

4 6

4 6

4(6) or (4)(6) or (4)6

Vertical form: Stack the factors. If the bottom

Multiply:

24 163

factor has more

than one digit, multiply in

163

Factor

steps to find the partial products. Then add

24

Factor

them to find the product.

652

Partial product: 4 163

3260

Partial product: 20 163

3,912

Product

To find the product of a whole number and

Multiply:

10, 100, 1,000, and so on, attach the number of

8 1,000 8,000

Since 1,000 has three zeros, attach three

zeros in that number to the right of the whole

0’s after 8.

number.

43(10,000) 430,000

Since 10,000 has four zeros, attach four

This rule can be extended to multiply any two

0’s after 43.

whole numbers that end in zeros.

160 20,000 3,200,000 160 and 20,000 have a total of five trailing

zeros. Attach five 0’s after 32.

Multiply 16 and 2

to get 32.

Chapter 1 Summary and Review

119

Multiplication Properties of 0 and 1

The product of any whole number and 0 is 0.

0 9 0

and

3(0) 0

The product of any whole number and 1 is

15 1 15

and

1(6) 6

that whole number.

Commutative property of multiplication: The

5 9 9 5

order in which whole numbers are multiplied

By the commutative property, the product is the same.

does not change their product.

Associative property of multiplication: The

(3 7) 10 3 (7 10)

way in

which whole numbers are

grouped

By the associative property, the product is the same.

does not change their product.

To estimate a product, use front-end rounding

To estimate the product for 74 873, find 70 900.

to approximate the factors. Then multiply.

Round to the nearest ten

873

70 900

74

Application problems that involve repeated

Round to the nearest hundred

HEALTH CARE A doctor’s office is open 210 days a year. Each day

addition are often more easily solved using

the doctor sees 25 patients. How many patients does the doctor see in

multiplication.

1 year?

This repeated addition can be calculated by multiplication:

The number of

patients seen

25 210

each year

We can use multiplication to count objects

CLASSROOMS A large lecture hall has 16 rows of desks and there

arranged in rectangular patterns of neatly

are 12 desks in each row. How many desks are in the lecture hall?

arranged rows and columns called rectangular

The rectangular array of desks indicates multiplication:

arrays.

Some key words and phrases that are often

The number of

used to indicate multiplication are:

desks in the

16 12

double

triple

twice

of

times

lecture hall

The area of a rectangle is the measure of the

Find the area of the rectangle shown below.

amount of surface it encloses. Area is measured

25 in.

in square units, such as square inches (written

4 in.

in.2) or square centimeters (written cm2).

A lw

Area of a rectangle

length width

or

25 4

Replace l with 25 and w with 4.

A lw

100

Multiply.

Letters (or symbols) that are used to represent

The area of the rectangle is 100 square inches, which can be written in

numbers are called variables.

more compact form as 100 in.2.

120	Chapter 1 Whole Numbers

REVIEW EXERCISES

Multiply.

45.	47 9	46.	5 (7 6)
47.	72 10,000	48.	110(400)
49.	157 59	50.	3,723
			46
51.	5,624	52.	502 459

281

53.Estimate the product: 6,891 438

54.Write the repeated addition 7 7 7 7 7 as a multiplication.

55.Find each product:

a. 8 0

b. 7 1

56.What property of multiplication is shown?

a.2 (5 7) (2 5) 7

b.100(50) 50(100)

Find the area of the rectangle and the square.

57.8 cm

4 cm

58.78 in.

78in.

59.SLEEP The National Sleep Foundation recommends that adults get from 7 to 9 hours of sleep each night.

a.How many hours of sleep is that in one year using the smaller number? (Use a 365-day year.)

b.How many hours of sleep is that in one year using the larger number?

60.GRADUATION For a graduation ceremony, the graduates were assembled in a rectangular 22-row and 15-column formation. How many members are in the graduating class?

61.PAYCHECKS Sarah worked 12 hours at $9 per hour, and Santiago worked 14 hours at $8 per hour. Who earned more money?

62.SHOPPING There are 12 eggs in one dozen, and 12 dozen in one gross. How many eggs are in a shipment of 100 gross?

S E C T I O N 1.5

Dividing Whole Numbers

DEFINITIONS AND CONCEPTS

EXAMPLES

To divide whole numbers, think of separating

Dividend

Divisor

a quantity into equal-sized groups.

4

8

2

To write division,

we can use a

division

8 2 4

8

4

2

symbol , a long division symbol

, or a

Quotient

fraction bar

.

Another way to answer a division problem is

8 2 4 because

4 2 8

to think in terms of multiplication and write a

related multiplication statement.

A process called long division can be used

Divide: 8,317 23

to divide whole numbers. Follow a four-step

Quotient

process:

• Estimate

Divisor

23

361 R 14

8,317

Dividend

• Multiply

6 9

• Subtract

1 41

• Bring down

1 38

37

23

14

Remainder

To check the result of a division, we multiply the divisor by the quotient and add the remainder. The result should be the dividend.

Properties of Division

Any whole number divided by 1 is equal to that number.

Any nonzero whole number divided by itself is equal to 1.

Division with Zero

Zero divided by any nonzero number is equal to 0.

Division by 0 is undefined.

There are divisibility tests to help us decide whether one number is divisible by another. They are listed on page 61.

There is a shortcut for dividing a dividend by a divisor when both end with zeros. We simply remove the ending zeros in the divisor and remove the same number of ending zeros in the dividend.

To estimate quotients, we use a method that approximates both the dividend and the divisor so that they divide easily.

Application problems that involve forming equal-sized groups can be solved by division.

Some key words and phrases that are often used to indicate division:

split equally	distributed equally
shared equally	how many does each
how many left (remainder)		per
how much extra (remainder)		among

Chapter 1 Summary and Review

121

For the division shown on the previous page, the result checks.

Quotient		divisor	remainder
	( 361	23 )		14			8,303 14
							8,317				Dividend
4	4		and		58	58
1					1
9	1		and		103		1
9					103
0	0		and		0	0
7					23
7	is undefined		and		2,190			is undefined
0					0

Is 21,507 divisible by 3?

21,507 is divisible by 3, because the sum of its digits is divisible by 3.

2 1 5 0 7 15 and 15 3 5

Divide:

64,000 1,600 640 16

Remove two zeros from the dividend and the divisor, and divide.

Estimate the quotient for 154,908 46 by finding 150,000 50.

				The dividend is approximately
				46			150,000 50
	154,908
							The divisor is approximately

BRACES An orthodontist offers his patients a plan to pay the $5,400 cost of braces in 36 equal payments. What is the amount of each payment?

The phrase 36 equal payments indicates division:

The amount of

5,400 36

each payment

REVIEW EXERCISES

Divide, if possible.
63.	72				64.	595
	4					35
	1,443 39					68
65.					66.		20,876
	1,269 54					21
67.					68.		405
69.	0				70.	165
	10					0
	127					1,482,000 3,900
71.			5,347		72.

73.Write the related multiplication statement for 160 4 40.

74.Use a check to determine whether the following division is correct.

45 R 6

7 320

75. Is 364,545 divisible by 2, 3, 4, 5, 6, 9, or 10?

122		Chapter 1 Whole Numbers
	76.	Estimate the quotient: 210,999 53	78. PURCHASING A county received an $850,000
77.		TREATS If 745 candies are distributed equally	grant to purchase some new police patrol cars. If a

	among 45 children, how many will each child	fully equipped patrol car costs $25,000, how many can
		the county purchase with the grant money?
	receive? How many candies will be left over?

S E C T I O N 1.6 Problem Solving

DEFINITIONS AND CONCEPTS

To become a good problem solver, you need a plan to follow, such as the following five-step strategy for problem solving:

1.Analyze the problem by reading it carefully. What information is given? What are you asked to find? What vocabulary is given? Often, a diagram or table will help you visualize the facts of the problem.

2.Form a plan by translating the words of the problem into numbers and symbols.

3.Solve the problem by performing the calculations.

4.State the conclusion clearly. Be sure to include the units in your answer.

5.Check the result. An estimate is often helpful to see whether an answer is reasonable.

EXAMPLES

CEO PAY A recent report claimed that in 2007 the top chief executive officers of large U.S. companies averaged 364 times more in pay than the average U.S. worker. If the average U.S. worker was paid $30,000 a year, what was the pay of a top CEO? (Source: moneycentral.msn.com)

Analyze

• Top CEOs were paid 364 times more than the
	average worker	Given
•	An average worker was paid $30,000 a year.	Given
•	What was the pay of a top CEO in 2007?	Find

Form Translate the words of the problem to numbers and symbols.

					the pay of
	The pay of a top
		was equal to	364	times	the average
	CEO in 2007
					U.S. worker.
	The pay of a top
			364		30,000
	CEO in 2007

Solve Use a shortcut to perform this multiplication.

364 30,000 10,920,000

								1 1
		Multiply			Attach			364
	364 and 3				four 0’s			3
	to get 1092.		after 1092.					1092

State In 2007, the annual pay of a top CEO was $10,920,000.

Check Use front-end rounding to estimate the product: 364 is approximately 400.

400 30,000 12,000,000

Since the estimate, $12,000,000, and the result, $10,920,000, are close, the result seems reasonable.

REVIEW EXERCISES

79.SAUSAGE To make smoked sausage, the

sausage is first dried at a temperature of 130°F. Then the temperature is raised 20° to smoke the meat. The temperature is raised another 20° to cook the meat. In the last stage, the temperature is raised another 15°. What is the final temperature in the process?

80.DRIVE-INS The high figure for drive-in theaters in the United States was 4,063 in 1958. Since then, the number of drive-ins has decreased by 3,680. How many drive-in theaters are there today? (Source: United Drive-in Theater Owners Association)

81.WEIGHT TRAINING For part of a woman’s upper body workout, she does 1 set of twelve repetitions of 75 pounds on a bench press machine. How many total pounds does she lift in that set?

82.PARKING Parking lot B4 at an amusement park opens at 8:00 AM and closes at 11:00 PM. It costs $5 to park in the lot. If there are twenty-four rows and each row has fifty parking spaces, how many cars can park in the lot?

83.PRODUCTION A manufacturer produces

15,000 light bulbs a day. The bulbs are packaged 6 to a box. How many boxes of light bulbs are produced each day?

Chapter 1 Summary and Review

123

84.EMBROIDERED CAPS A digital embroidery machine uses 16 yards of thread to stitch a team logo on the front of a baseball cap. How many hats can be embroidered if the thread comes on spools of 1,100 yards? How many yards of thread will be left on the spool?

85.FARMING In a shipment of 350 animals, 124 were hogs, 79 were sheep, and the rest were cattle. Find the number of cattle in the shipment.

86.HALLOWEEN A couple bought 6 bags of mini Snickers bars. Each bag contains 48 pieces of candy. If they plan to give each trick-or-treater 3 candy bars, to how many children will they be able to give treats?

S E C T I O N 1.7

Prime Factors and Exponents

DEFINITIONS AND CONCEPTS

EXAMPLES

Numbers that are multiplied together are

The pairs of whole numbers whose product is 6 are:

called factors.

1 6 6

and

2 3 6

To factor a whole number means to express it

From least to greatest, the factors of 6 are 1, 2, 3, and 6.

as the product of other whole numbers.

If a whole number is a factor of a given

Each of the factors of 6 divides 6 exactly (no remainder):

number, it also

divides the given number

6

6

6

3

6

2

6

1

exactly.

1

2

3

6

If a whole number is divisible by 2, it is called

Even whole numbers:

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, . . .

an even number.

If a whole number is not divisible by 2, it is

Odd whole numbers:

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, . . .

called an odd number.

A prime number is a whole number greater

Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, . . .

than 1 that has only 1 and itself as factors.

There are infinitely many prime numbers.

The composite numbers are whole numbers

Composite numbers:

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, . . .

greater than 1 that are not prime. There are

infinitely many composite numbers.

To find the prime factorization of a whole

Use a factor tree to find the prime factorization of 30.

number means to write it as the product of

30

only prime numbers.

Factor each number that is encountered as a

A factor tree and a division ladder can be used

2

15

product of two whole numbers (other than 1 and

itself) until all the factors involved are prime.

to find prime factorizations.

3

5

The prime factorization of 30 is 2 3 5.

Use a division ladder to find the prime factorization of 70.

2 70

Perform repeated divisions by prime numbers until

5 35

the final quotient is itself a prime number.

7

The prime factorization of 70 is 2 5 7.

124		Chapter 1 Whole Numbers

An exponent is used to indicate repeated multiplication. It tells how many times the base is used as a factor.

Exponent

2 2 2 2 24 24 is called an exponential expression.

Repeated factors Base

We can use the definition of exponent to	Evaluate:	73
evaluate (find the value of) exponential	73	7 7 7		Write the base 7 as a factor 3 times.
expressions.		49 7		Multiply, working left to right.
		343		Multiply.
	Evaluate:	22 33
	22 33		4 27	Evaluate the exponential expressions first.
			108	Multiply.

REVIEW EXERCISES

Find all of the factors of each number. List them from least to greatest.

87.

18

88.

75

89.Factor 20 using two factors. Do not use the factor 1 in your answer.

90.Factor 54 using three factors. Do not use the factor 1 in your answer.

Tell whether each number is a prime number, a composite number, or neither.

91. a.	31	b.	100
c.	1	d.	0
e.	125	f.	47

Tell whether each number is an even or an odd number.

92. a.	171	b.	214
c.	0	d.	1

Find the prime factorization of each number. Use exponents in your answer, when helpful.

93.	42	94.	75
95.	220	96.	140
Write each expression using exponents.
97.	6 6 6 6	98.	5(5)(5)(13)(13)
Evaluate each expression.
99.	53	100.	112
101.	24 72	102.	22 33 52

S E C T I O N 1.8 The Least Common Multiple and the Greatest Common Factor

DEFINITIONS AND CONCEPTS EXAMPLES

The multiples of a number are the products of that number and 1, 2, 3, 4, 5, and so on.

The least common multiple (LCM) of two whole numbers is the smallest common multiple of the numbers.

The LCM of two whole numbers is the smallest whole number that is divisible by both of those numbers.

Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, p

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, p

The common multiples of 2 and 3 are: 6, 12, 18, 24, 30, p

The least common multiple of 2 and 3 is 6, which is written as: LCM (2, 3) 6.

6	3	and	6	2
2			3

			Chapter 1		Summary and Review		125
To find the LCM of two (or more) whole Find the LCM of 3 and 5.
numbers by listing:	Multiples of 5: 5,	10,	15,	20,	25,	. . .

1.Write multiples of the largest number by

multiplying it by 1, 2, 3, 4, 5, and so on.

Not divisible

Not divisible

Divisible by 3.

2. Continue this process until you find the

by 3.

by 3.

first multiple of the larger number that is

Since 15 is the first multiple of 5 that is divisible by 3, the LCM

divisible by each of the smaller numbers.

(3, 5) 15.

That multiple is their LCM.

To find the LCM of two (or more) whole

Find the LCM of 6 and 20.

numbers using prime factorization:

6 2

3

The greatest number of times 3 appears is once.

1.

Prime factor each number.

20 2 2

5

The greatest number of times 2 appears is twice.

2.

The LCM is a product of prime factors,

The greatest number of times 5 appears is once.

where each factor is used the greatest

Use the factor 2 two times.

number of times it appears in any one

factorization.

Use the factor 3 one time.

Use the factor 5 one time.

⎬ ⎭

5 60

LCM (6, 20) 2 2

3

The greatest common factor (GCF) of two (or

The factors of 18:

1 ,

2 ,

3 ,

6,

9 ,

18

more) whole numbers is the largest common

The factors of 30:

1 ,

2 ,

3 ,

5,

6 ,

10, 15, 30

factor of the numbers.

The common factors of 18 and 30 are 1, 2, 3, and 6.

The greatest common factor of 18 and 30 is 6, which is written as:

GCF (18, 30) 6.

The greatest common factor of two (or more)

18

3

and

30

5

numbers is the largest whole number that

6

6

divides them exactly.

To find the GCF of two (or more) whole

Find the GCF of 36 and 60.

numbers using prime factorization:

36 2 2 3 3

36 and 60 have two common factors

1. Prime factor each number.

of 2 and one common factor of 3.

2. Identify the common prime factors.

60 2 2 3 5

3. The GCF is a product of all the common

The GCF is the product of the circled prime factors.

prime factors found in Step 2.

GCF (36, 60) 2 2 3 12

If there are no common prime factors, the

GCF is 1.

REVIEW EXERCISES

	103. Find the first ten multiples of 9.	Find the LCM of the given numbers.
	104. a. Find the common multiples of 6 and 8 in the	105.	4, 6	106.	3, 4
		107.	9, 15	108.	12, 18
	lists below.
		109.	18, 21	110.	24, 45
	Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54 p
		111.	4, 14, 20	112.	21, 28, 42
	Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72 p
	b. Find the common factors of 6 and 8 in the lists	Find the GCF of the given numbers.
		113.	8, 12	114.	9, 12
	below.
		115.	30, 40	116.	30, 45
	Factors of 6: 1, 2, 3, 6
		117.	63, 84	118.	112, 196
	Factors of 8: 1, 2, 4, 8
		119.	48, 72, 120	120.	88, 132, 176

126		Chapter 1 Whole Numbers
	121.	MEETINGS The Rotary Club meets every	a. What is the greatest number of arrangements
		14 days and the Kiwanis Club meets every 21 days.	that he can make if every carnation is used?
		If both clubs have a meeting on the same day, in
		how many more days will they again meet on the	b. How many of each type of carnation will be
		same day?	used in each arrangement?
	122.	FLOWERS A florist is making flower
		arrangements for a 4th of July party. She has 32 red
		carnations, 24 white carnations, and 16 blue
		carnations. He wants each arrangement to be
		identical.

S E C T I O N 1.9

Order of Operations

DEFINITIONS AND CONCEPTS

EXAMPLES

To evaluate (find the value of) expressions

Evaluate: 10 3[24 3(5 2)]

that involve more than one operation, use the

Work within

the

innermost

parentheses first

and then within the

order-of-operations rule.

outermost brackets.

Order of Operations

10 3[24 3(5 2)] 10 3[24 3(3)]

Do the subtraction

1.

Perform all calculations within

within the

parentheses.

parentheses and other grouping symbols

10 3[16 3(3)]

Evaluate the

following the order listed in Steps 2–4

below, working from the innermost pair of

exponential

expression within the

grouping symbols to the outermost pair.

brackets: 24 16.

2.

Evaluate all exponential expressions.

10 3[16 9]

Do the multiplication

3.

Perform all multiplications and divisions

within the brackets.

as they occur from left to right.

10 3[7]

Do the subtraction

4.

Perform all additions and subtractions as

within the brackets.

they occur from left to right.

10 21

Do the multiplication:

When grouping symbols have been removed,

3[7] 21.

repeat Steps 2–4 to complete the calculation.

31

Do the addition.

If

a fraction bar is

present, evaluate the

Evaluate:

33 8

expression above the bar (called the numerator)

7(15 14)

and the expression below the bar (called the

Evaluate the expressions above and below the fraction bar separately.

denominator) separately. Then perform the

division indicated by the fraction bar, if possible.

33 8

27 8

In the numerator, evaluate the exponential

7(15 14)

7(1)

expression. In the denominator, subtract.

35

In the numerator, add. In the denominator,

7

multiply.

5

Divide.

The arithmetic mean, or average, of a set of

Find the mean (average) of the test scores 74, 83, 79, 91, and 73.

numbers is a value around which the values of

the numbers are grouped.

To find the mean (average) of a set of values,

Mean

74 83 79 91 73 Since there are 5

divide the sum of the values by the number of

5

scores, divide by 5.

values.

400

Do the addition in the numerator.

5

80

Divide.

The mean (average) test score is 80.

REVIEW EXERCISES

Evaluate each expression.
123.	32 12 3	124.	35 5 3 3
125.	(6 2 3)2 3	126.	(35 5 3) 5
127.	23 5 4 2 4	128.	8 (5 4 2)2

129.2 3a 10010 22 2b

130.4(42 5 3 2) 4

4(6) 6		6 2 3 7
131.		132.
2(32)		52 2(7)

133.7 3[33 10(4 2)]

134.5 2 c a24 3 82b 2 d

Chapter 1 Summary and Review

127

Find the arithmetic mean (average) of each set of test scores.

	135.	Test	1	2	3	4
		Score	80	74	66	88
	136.
		Test	1	2	3	4	5
		Score	73	77	81	0	69

128

C H A P T E R 1

TEST

1. a.

The set of

numbers is {0, 1, 2, 3, 4, 5, p }.

b.

The symbols and are

symbols.

c.

To evaluate an expression such as 58 33 9

means to find its

.

d. The

of a rectangle is a measure of the amount

of surface it encloses.

e.

One number is

by another number if,

when we divide them, the remainder is 0.

f.

The grouping symbols ( ) are called

,

and the symbols [

] are called

.

g. A

number is a whole number greater than

1 that has only 1 and itself as factors.

2.Graph the whole numbers less than 7 on a number line.

0

1

2

3

4

5

6

7

8

9

3.Consider the whole number 402,198.

a.What is the place value of the digit 1?

b.What digit is in the ten thousands column?

4.a. Write 7,018,641 in words.

b.Write “one million, three hundred eighty-five thousand, two hundred sixty-six” in standard form.

c.Write 92,561 in expanded form.

5.Place an or an symbol in the box to make a true statement.

a. 15

10

b. 1,247

1,427

6.Round 34,759,841 to the p

a.nearest million

b.nearest hundred thousand

c.nearest thousand

7.THE NHL The table below shows the number of teams in the National Hockey League at various times during its history. Use the data to complete the bar graph in the next column.

Year	1960	1970	1980	1990	2000	2008
Number of teams	6	14	21	21	28	30

		35
	teamsof	30
		25
	Number	20
		15
		10
		5

1960 1970 1980 1990 2000 2008 Year

8.Subtract 287 from 535. Show a check of your result.

9.Add: 136,231

82,574

6,359

10.Subtract: 4,521

3,579

11.Multiply: 53

8

12.Multiply: 74 562

13.Divide: 6 432

14.Divide: 8,379 73. Show a check of your result.

15.Find the product of 23,000 and 600.

16.Find the quotient of 125,000 and 500.

17.Use front-end rounding to estimate the difference: 49,213 7,198

18.A rectangle is 327 inches wide and 757 inches long.

Find its perimeter.

Source: www.rauzulusstreet.com

19. Find the area of the square shown.

23 cm

23 cm

20.a. Find the factors of 12.

b.Find the first six multiples of 4.

c.Write 5 5 5 5 5 5 5 5 as a multiplication.

21.Find the prime factorization of 1,260.

22.TEETH Children have one set of primary (baby) teeth used in early development. These 20 teeth are generally replaced by a second set of larger permanent (adult) teeth. Determine the number of adult teeth if there are 12 more of those than baby teeth.

23.TOSSING A COIN During World War II, John Kerrich, a prisoner of war, tossed a coin 10,000 times and wrote down the results. If he recorded

5,067 heads, how many tails occurred? (Source:

Figure This!)

24.P.E. CLASSES In a physical education class, the students stand in a rectangular formation of 8 rows and 12 columns when the instructor takes attendance. How many students are in the class?

25.FLOOR SPACE The men’s, women’s, and children’s departments in a clothing store occupy a total of 12,255 square feet. Find the square footage of each department if they each occupy the same amount of floor space.

26.MILEAGE The fuel tank of a Hummer H3 holds 23 gallons of gasoline. How far can a Hummer travel on one tank of gas if it gets 18 miles per gallon on the highway?

27.INHERITANCE A father willed his estate, valued at $1,350,000, to his four adult children. Upon his death, the children paid legal expenses of $26,000 and then split the remainder of the inheritance equally among themselves. How much did each one receive?

Chapter 1 Test

129

28.What property is illustrated by each statement?

a.18 (9 40) (18 9) 40

b.23,999 1 1 23,999

29.Perform each operation, if possible.

a.	15 0		b.		0
					15
c.	8		d.		8
	8				0

30.Find the LCM of 15 and 18.

31.Find the LCM of 8, 9, and 12.

32.Find the GCF of 30 and 54.

33.Find the GCF of 24, 28, and 36.

34.STOCKING SHELVES Boxes of rice are being stacked next to boxes of instant mashed potatoes on the same bottom shelf in a supermarket display. The boxes of rice are 8 inches tall and the boxes of instant potatoes are 10 inches high.

a.What is the shortest height at which the two stacks will be the same height?

b.How many boxes of rice and how many boxes of potatoes will be used in each stack?

35.Is 521,340 divisible by 2, 3, 4, 5, 6, 9, or 10?

36.GRADES A student scored 73, 52, 95, and 70 on four exams and received 0 on one missed exam. Find his mean (average) exam score.

Evaluate each expression.

37.9 4 5

38.34 10 2(6)(4)

39.20 2[42 2(6 22)]

33 2(15 14)2

40.

33 9 1

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The Integers

from Campus to Careers

Personal Financial Advisor

Personal financial advisors help people manage their money how to make their money grow. They offer advice on how to for monthly expenses, as well as how to save for

retirement. A bachelor’s degree in business, accounting, finance, economics, or statistics provides good preparation for the occupation. Strong communication

and problem-solving skills are equally important to achieve success in this field.

In Problem 90 of Study Set 2.2, you will see how a personal financial planner uses integers to determine whether a duplex rental unit would be a money-making investment for client.

2

2.1An Introduction to the Integers

2.2Adding Integers

2.3Subtracting Integers

2.4Multiplying Integers

2.5Dividing Integers

2.6Order of Operations and Estimation

Chapter Summary and Review

Chapter Test Cumulative Review

© OJO Images Ltd/Alamy

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