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13.5.12: Chapter 1 Review Exercises

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Chapter Review Exercises

Introduction to Whole Numbers

Use Place Value with Whole Number

In the following exercises find the place value of each digit.

Exercise 13.5.12.1

26,915

  1. 1
  2. 2
  3. 9
  4. 5
  5. 6
Answer
  1. tens
  2. ten thousands
  3. hundreds
  4. ones
  5. thousands
Exercise 13.5.12.2

359,417

  1. 9
  2. 3
  3. 4
  4. 7
  5. 1
Exercise 13.5.12.3

58,129,304

  1. 5
  2. 0
  3. 1
  4. 8
  5. 2
Answer
  1. ten millions
  2. tens
  3. hundred thousands
  4. millions
  5. ten thousands
Exercise 13.5.12.4

9,430,286,157

  1. 6
  2. 4
  3. 9
  4. 0
  5. 5

In the following exercises, name each number.

Exercise 13.5.12.5

6,104

Answer

six thousand, one hundred four

Exercise 13.5.12.6

493,068

Exercise 13.5.12.7

3,975,284

Answer

three million, nine hundred seventy-five thousand, two hundred eighty-four

Exercise 13.5.12.8

85,620,435

In the following exercises, write each number as a whole number using digits.

Exercise 13.5.12.9

three hundred fifteen

Answer

315

Exercise 13.5.12.10

sixty-five thousand, nine hundred twelve

Exercise 13.5.12.11

ninety million, four hundred twenty-five thousand, sixteen

Answer

90,425,016

Exercise 13.5.12.12

one billion, forty-three million, nine hundred twenty-two thousand, three hundred eleven

In the following exercises, round to the indicated place value.

Exercise 13.5.12.13

Round to the nearest ten.

  1. 407
  2. 8,564
Answer
  1. 410
  2. 8,560
Exercise 13.5.12.14

Round to the nearest hundred.

  1. 25,846
  2. 25,864

In the following exercises, round each number to the nearest 1. hundred 2. thousand 3. ten thousand.

Exercise 13.5.12.15

864,951

Answer
  1. 865,000865,000
  2. 865,000865,000
  3. 860,000
Exercise 13.5.12.16

3,972,849

Identify Multiples and Factors

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10.

Exercise 13.5.12.17

168

Answer

by 2,3,6

Exercise 13.5.12.18

264

Exercise 13.5.12.19

375

Answer

by 3,5

Exercise 13.5.12.20

750

Exercise 13.5.12.21

1430

Answer

by 2,5,10

Exercise 13.5.12.22

1080

Find Prime Factorizations and Least Common Multiples

In the following exercises, find the prime factorization.

Exercise 13.5.12.23

420

Answer

22357

Exercise 13.5.12.24

115

Exercise 13.5.12.25

225

Answer

3355

Exercise 13.5.12.26

2475

Exercise 13.5.12.27

1560

Answer

2223513

Exercise 13.5.12.28

56

Exercise 13.5.12.29

72

Answer

22233

Exercise 13.5.12.30

168

Exercise 13.5.12.31

252

Answer

22337

Exercise 13.5.12.32

391

In the following exercises, find the least common multiple of the following numbers using the multiples method.

Exercise 13.5.12.33

6,15

Answer

30

Exercise 13.5.12.34

60, 75

In the following exercises, find the least common multiple of the following numbers using the prime factors method.

Exercise 13.5.12.35

24, 30

Answer

120

Exercise 13.5.12.36

70, 84

Use the Language of Algebra

Use Variables and Algebraic Symbols

In the following exercises, translate the following from algebra to English.

Exercise 13.5.12.37

25−7

Answer

25 minus 7, the difference of twenty-five and seven

Exercise 13.5.12.38

56

Exercise 13.5.12.39

45÷5

Answer

45 divided by 5, the quotient of forty-five and five

Exercise 13.5.12.40

x+8

Exercise 13.5.12.41

4227

Answer

forty-two is greater than or equal to twenty-seven

Exercise 13.5.12.42

3n=24

Exercise 13.5.12.43

320÷4

Answer

3 is less than or equal to 20 divided by 4, three is less than or equal to the quotient of twenty and four

Exercise 13.5.12.44

a74

In the following exercises, determine if each is an expression or an equation.

Exercise 13.5.12.45

63+5

Answer

expression

Exercise 13.5.12.46

y−8=32

Simplify Expressions Using the Order of Operations

In the following exercises, simplify each expression.

Exercise 13.5.12.47

35

Answer

243

Exercise 13.5.12.48

108

In the following exercises, simplify

Exercise 13.5.12.49

6+10/2+2

Answer

13

Exercise 13.5.12.50

9+12/3+4

Exercise 13.5.12.51

20÷(4+6)5

Answer

10

Exercise 13.5.12.52

33÷(3+8)2

Exercise 13.5.12.53

42+52

Answer

41

Exercise 13.5.12.54

(4+5)2

Evaluate an Expression

In the following exercises, evaluate the following expressions.

Exercise 13.5.12.55

9x+7 when x=3

Answer

34

Exercise 13.5.12.56

5x−4 when x=6

Exercise 13.5.12.57

x4 when x=3

Answer

81

Exercise 13.5.12.58

3x when x=3

Exercise 13.5.12.59

x2+5x8 when x=6

Answer

58

Exercise 13.5.12.60

2x+4y5 when
x=7,y=8

Simplify Expressions by Combining Like Terms

In the following exercises, identify the coefficient of each term.

Exercise 13.5.12.61

12n

Answer

12

Exercise 13.5.12.62

9x2

In the following exercises, identify the like terms.

Exercise 13.5.12.63

3n,n2,12,12p2,3,3n2

Answer

12 and 3,n2 and 3n2

Exercise 13.5.12.64

5,18r2,9s,9r,5r2,5s

In the following exercises, identify the terms in each expression.

Exercise 13.5.12.65

11x2+3x+6

Answer

11x2,3x,6

Exercise 13.5.12.66

22y3+y+15

In the following exercises, simplify the following expressions by combining like terms.

Exercise 13.5.12.67

17a+9a

Answer

26a

Exercise 13.5.12.68

18z+9z

Exercise 13.5.12.69

9x+3x+8

Answer

12x+8

Exercise 13.5.12.70

8a+5a+9

Exercise 13.5.12.71

7p+6+5p−4

Answer

12p+2

Exercise 13.5.12.72

8x+7+4x−5

Translate an English Phrase to an Algebraic Expression

In the following exercises, translate the following phrases into algebraic expressions.

Exercise 13.5.12.73

the sum of 8 and 12

Answer

8+12

Exercise 13.5.12.74

the sum of 9 and 1

Exercise 13.5.12.75

the difference of x and 4

Answer

x−4

Exercise 13.5.12.76

the difference of x and 3

Exercise 13.5.12.77

the product of 6 and y

Answer

6y

Exercise 13.5.12.78

the product of 9 and y

Exercise 13.5.12.79

Adele bought a skirt and a blouse. The skirt cost $15 more than the blouse. Let bb represent the cost of the blouse. Write an expression for the cost of the skirt.

Answer

b+15

Exercise 13.5.12.80

Marcella has 6 fewer boy cousins than girl cousins. Let g represent the number of girl cousins. Write an expression for the number of boy cousins.

Add and Subtract Integers

Use Negatives and Opposites of Integers

In the following exercises, order each of the following pairs of numbers, using < or >.

Exercise 13.5.12.81
  1. 6___2
  2. −7___4
  3. −9___−1
  4. 9___−3

Answer
  1. >
  2. <
  3. <
  4. >
Exercise 13.5.12.82
  1. −5___1
  2. −4___−9
  3. 6___10
  4. 3___−8

In the following exercises,, find the opposite of each number.

Exercise 13.5.12.83
  1. −8
  2. 1
Answer
  1. 8
  2. −1
Exercise 13.5.12.84
  1. −2
  2. 6

In the following exercises, simplify.

Exercise 13.5.12.85

−(−19)

Answer

19

Exercise 13.5.12.86

−(−53)

In the following exercises, simplify.

Exercise 13.5.12.87

−m when

  1. m=3
  2. m=−3
Answer
  1. −3
  2. 3
Exercise 13.5.12.88

−p when

  1. p=6
  2. p=−6

Simplify Expressions with Absolute Value

In the following exercises,, simplify.

Exercise 13.5.12.89
  1. |7|
  2. |−25|
  3. |0|
Answer
  1. 7
  2. 25
  3. 0
Exercise 13.5.12.90
  1. |5|
  2. |0|
  3. |−19|

In the following exercises, fill in <, >, or = for each of the following pairs of numbers.

Exercise 13.5.12.91
  1. −8___|−8|
  2. −|−2|___−2
Answer
  1. <
  2. =
Exercise 13.5.12.92
  1. |−3|___−|−3|
  2. 4___−|−4|

In the following exercises, simplify.

Exercise 13.5.12.93

|8−4|

Answer

4

Exercise 13.5.12.94

|9−6|

Exercise 13.5.12.95

8(14−2|−2|)

Answer

80

Exercise 13.5.12.96

6(13−4|−2|)

In the following exercises, evaluate.

Exercise 13.5.12.97

1. |x| when x=−28

Answer
  1. 28
  2. 15
Exercise 13.5.12.98
  1. ∣y∣ when y=−37
  2. |−z| when z=−24

Add Integers

In the following exercises, simplify each expression.

Exercise 13.5.12.99

−200+65

Answer

−135

Exercise 13.5.12.100

−150+45

Exercise 13.5.12.101

2+(−8)+6

Answer

0

Exercise 13.5.12.102

4+(−9)+7

Exercise 13.5.12.103

140+(−75)+67

Answer

132

Exercise 13.5.12.104

−32+24+(−6)+10

Subtract Integers

In the following exercises, simplify.

Exercise 13.5.12.105

9−3

Answer

6

Exercise 13.5.12.106

−5−(−1)

Exercise 13.5.12.107
  1. 15−6
  2. 15+(−6)
Answer
  1. 9
  2. 9
Exercise 13.5.12.108
  1. 12−9
  2. 12+(−9)
Exercise 13.5.12.109
  1. 8−(−9)
  2. 8+9
Answer
  1. 17
  2. 17
Exercise 13.5.12.110
  1. 4−(−4)
  2. 4+4

In the following exercises, simplify each expression.

Exercise 13.5.12.111

10−(−19)

Answer

29

Exercise 13.5.12.112

11−(−18)

Exercise 13.5.12.113

31−79

Answer

−48

Exercise 13.5.12.114

39−81

Exercise 13.5.12.115

−31−11

Answer

−42

Exercise 13.5.12.116

−32−18

Exercise 13.5.12.117

−15−(−28)+5

Answer

18

Exercise 13.5.12.118

71+(−10)−8

Exercise 13.5.12.119

−16−(−4+1)−7

Answer

-20

Exercise 13.5.12.120

−15−(−6+4)−3

Multiply Integers

In the following exercises, multiply.

Exercise 13.5.12.121

−5(7)

Answer

−35

Exercise 13.5.12.122

−8(6)

Exercise 13.5.12.123

−18(−2)

Answer

36

Exercise 13.5.12.124

−10(−6)

Divide Integers

In the following exercises, divide.

Exercise 13.5.12.125

28÷7

Answer

-4

Exercise 13.5.12.126

56÷(7)

Exercise 13.5.12.127

120÷(20)

Answer

6

Exercise 13.5.12.128

200÷25

Simplify Expressions with Integers

In the following exercises, simplify each expression.

Exercise 13.5.12.129

−8(−2)−3(−9)

Answer

43

Exercise 13.5.12.130

−7(−4)−5(−3)

Exercise 13.5.12.131

(5)3

Answer

−125

Exercise 13.5.12.132

(4)3

Exercise 13.5.12.133

4211

Answer

−88

Exercise 13.5.12.134

5310

Exercise 13.5.12.135

10(4)÷(8)

Answer

-5

Exercise 13.5.12.136

8(6)÷(4)

Exercise 13.5.12.137

31−4(3−9)

Answer

55

Exercise 13.5.12.138

24−3(2−10)

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

Exercise 13.5.12.139

x+8 when

  1. x=−26
  2. x=−95
Answer
  1. −18
  2. −87
Exercise 13.5.12.140

y+9 when

  1. y=−29
  2. y=−84
Exercise 13.5.12.141

When b=−11, evaluate:

  1. b+6
  2. −b+6
Answer
  1. −5
  2. 17
Exercise 13.5.12.142

When c=−9, evaluate:

  1. c+(−4)c+(−4)
  2. −c+(−4)
Exercise 13.5.12.143

p25p+2 when
p=1

Answer

8

Exercise 13.5.12.144

q22q+9 when q=2

Exercise 13.5.12.145

6x5y+15 when x=3 and y=1

Answer

38

Exercise 13.5.12.146

3p2q+9 when p=8 and q=2

Translate English Phrases to Algebraic Expressions

In the following exercises, translate to an algebraic expression and simplify if possible.

Exercise 13.5.12.147

the sum of −4 and −17, increased by 32

Answer

(−4+(−17))+32;11

Exercise 13.5.12.148
  1. the difference of 15 and −7
  2. subtract 15 from −7
Exercise 13.5.12.149

the quotient of −45 and −9

Answer

459;5

Exercise 13.5.12.150

the product of −12 and the difference of c and d

Use Integers in Applications

In the following exercises, solve.

Exercise 13.5.12.151

Temperature The high temperature one day in Miami Beach, Florida, was 76°. That same day, the high temperature in Buffalo, New York was −8°. What was the difference between the temperature in Miami Beach and the temperature in Buffalo?

Answer

84 degrees

Exercise 13.5.12.152

Checking Account Adrianne has a balance of −$22 in her checking account. She deposits $301 to the account. What is the new balance?

Visualize Fractions

Find Equivalent Fractions

In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.

Exercise 13.5.12.153

14

Answer

28,312,416 answers may vary

Exercise 13.5.12.154

13

Exercise 13.5.12.155

56

Answer

1012,1518,2024 answers may vary

Exercise 13.5.12.156

27

Simplify Fractions

In the following exercises, simplify.

Exercise 13.5.12.157

721

Answer

13

Exercise 13.5.12.158

824

Exercise 13.5.12.159

1520

Answer

34

Exercise 13.5.12.160

1218

Exercise 13.5.12.161

168192

Answer

78

Exercise 13.5.12.162

140224

Exercise 13.5.12.163

11x11y

Answer

xy

Exercise 13.5.12.164

15a15b

Multiply Fractions

In the following exercises, multiply.

Exercise 13.5.12.165

2513

Answer

215

Exercise 13.5.12.166

1238

Exercise 13.5.12.167

712(821)

Answer

29

Exercise 13.5.12.168

512(815)

Exercise 13.5.12.169

28p(14)

Answer

7p

Exercise 13.5.12.170

51q(13)

Exercise 13.5.12.172

145(15)

Answer

−42

Exercise 13.5.12.173

1(38)

Divide Fractions

In the following exercises, divide

Exercise 13.5.12.174

12÷14

Answer

2

Exercise 13.5.12.175

12÷18

Exercise 13.5.12.176

45÷47

Answer

75

Exercise 13.5.12.177

34÷35

Exercise 13.5.12.178

58÷a10

Answer

254a

Exercise 13.5.12.179

56÷c15

Exercise 13.5.12.180

7p12÷21p8

Answer

29

Exercise 13.5.12.181

5q12÷15q8

Exercise 13.5.12.182

25÷(10)

Answer

125

Exercise 13.5.12.183

18÷(92)

In the following exercises, simplify.

Exercise 13.5.12.184

2389

Answer

34

Exercise 13.5.12.185

45815

Exercise 13.5.12.186

9103

Answer

310

Exercise 13.5.12.187

258

Exercise 13.5.12.188

r5s3

Answer

3r5s

Exercise 13.5.12.189

x689

Simplify Expressions Written with a Fraction Bar

In the following exercises, simplify.

Exercise 13.5.12.190

4+118

Answer

158

Exercise 13.5.12.191

9+37

Exercise 13.5.12.192

30712

Answer

-6

Exercise 13.5.12.193

1549

Exercise 13.5.12.194

22141913

Answer

43

Exercise 13.5.12.195

15+918+12

Exercise 13.5.12.196

5810

Answer

-4

Exercise 13.5.12.197

3424

Exercise 13.5.12.198

15552210

Answer

52

Exercise 13.5.12.199

12932318

Exercise 13.5.12.200

2+4(3)322

Answer

-2

Exercise 13.5.12.201

7+3(5)232

Translate Phrases to Expressions with Fractions

In the following exercises, translate each English phrase into an algebraic expression.

Exercise 13.5.12.202

the quotient of c and the sum of d and 9.

Answer

cd+9

Exercise 13.5.12.203

the quotient of the difference of h and k, and −5.

Add and Subtract Fractions

Add and Subtract Fractions with a Common Denominator

In the following exercises, add.

Exercise 13.5.12.204

49+19

Answer

59

Exercise 13.5.12.205

29+59

Exercise 13.5.12.206

y3+23

Answer

y+23

Exercise 13.5.12.207

7p+9p

Exercise 13.5.12.208

18+(38)

Answer

12

Exercise 13.5.12.209

18+(58)

In the following exercises, subtract.

Exercise 13.5.12.210

4515

Answer

35

Exercise 13.5.12.211

4535

Exercise 13.5.12.212

y17917

Answer

y917

Exercise 13.5.12.213

x19819

Exercise 13.5.12.214

8d3d

Answer

11d

Exercise 13.5.12.215

7c7c

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

Exercise 13.5.12.216

13+15

Answer

815

Exercise 13.5.12.217

14+15

Exercise 13.5.12.218

15(110)

Answer

310

Exercise 13.5.12.219

12(16)

Exercise 13.5.12.220

23+34

Answer

1712

Exercise 13.5.12.221

34+25

Exercise 13.5.12.222

111238

Answer

1324

Exercise 13.5.12.223

58712

Exercise 13.5.12.224

916(45)

Answer

1980

Exercise 13.5.12.225

720(58)

Exercise 13.5.12.226

1+56

Answer

116

Exercise 13.5.12.227

159

Use the Order of Operations to Simplify Complex Fractions

In the following exercises, simplify.

Exercise 13.5.12.228

(15)22+32

Answer

1275

Exercise 13.5.12.229

(13)25+22

Exercise 13.5.12.230

23+123423

Answer

14

Exercise 13.5.12.231

34+125623

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

Exercise 13.5.12.232

x+12 when

  1. x=18
  2. x=12
Answer
  1. 38
  2. 0
Exercise 13.5.12.233

x+23 when

  1. x=16
  2. x=53
Exercise 13.5.12.234

4p2q when p=12 and q=59

Answer

59

Exercise 13.5.12.235

5m2n when m=25 and n=13

Exercise 13.5.12.236

u+vw when
u=4,v=8,w=2

Answer

-6

Exercise 13.5.12.237

m+np when
m=6,n=2,p=4

Decimals

Name and Write Decimals

In the following exercises, write as a decimal.

Exercise 13.5.12.238

Eight and three hundredths

Answer

8.03

Exercise 13.5.12.239

Nine and seven hundredths

Exercise 13.5.12.240

One thousandth

Answer

0.001

Exercise 13.5.12.241

Nine thousandths

In the following exercises, name each decimal.

Exercise 13.5.12.242

7.8

Answer

seven and eight tenths

Exercise 13.5.12.243

5.01

Exercise 13.5.12.244

0.005

Answer

five thousandths

Exercise 13.5.12.245

0.381

Round Decimals

In the following exercises, round each number to the nearest

  1. hundredth
  2. tenth
  3. whole number.
Exercise 13.5.12.246

5.7932

Answer
  1. 5.79
  2. 5.8
  3. 6
Exercise 13.5.12.247

3.6284

Exercise 13.5.12.248

12.4768

Answer
  1. 12.48
  2. 12.5
  3. 12
Exercise 13.5.12.249

25.8449

Add and Subtract Decimals

In the following exercises, add or subtract.

Exercise 13.5.12.250

18.37+9.36

Answer

27.73

Exercise 13.5.12.251

256.37−85.49

Exercise 13.5.12.252

15.35−20.88

Answer

−5.53

Exercise 13.5.12.253

37.5+12.23

Exercise 13.5.12.254

−4.2+(−9.3)

Answer

−13.5

Exercise 13.5.12.255

−8.6+(−8.6)

Exercise 13.5.12.256

100−64.2

Answer

35.8

Exercise 13.5.12.257

100−65.83

Exercise 13.5.12.258

2.51+40

Answer

42.51

Exercise 13.5.12.259

9.38+60

Multiply and Divide Decimals

In the following exercises, multiply.

Exercise 13.5.12.260

(0.3)(0.4)

Answer

0.12

Exercise 13.5.12.261

(0.6)(0.7)

Exercise 13.5.12.262

(8.52)(3.14)

Answer

26.7528

Exercise 13.5.12.263

(5.32)(4.86)

Exercise 13.5.12.264

(0.09)(24.78)

Answer

2.2302

Exercise 13.5.12.265

(0.04)(36.89)

In the following exercises, divide.

Exercise 13.5.12.266

0.15÷5

Answer

0.03

Exercise 13.5.12.267

0.27÷3

Exercise 13.5.12.268

$8.49÷12

Answer

$0.71

Exercise 13.5.12.269

$16.99÷9

Exercise 13.5.12.270

12÷0.08

Answer

150

Exercise 13.5.12.271

5÷0.04

Convert Decimals, Fractions, and Percents

In the following exercises, write each decimal as a fraction.

Exercise 13.5.12.272

0.08

Answer

225

Exercise 13.5.12.273

0.17

Exercise 13.5.12.274

0.425

Answer

1740

Exercise 13.5.12.275

0.184

Exercise 13.5.12.276

1.75

Answer

74

Exercise 13.5.12.277

0.035

In the following exercises, convert each fraction to a decimal.

Exercise 13.5.12.278

25

Answer

0.4

Exercise 13.5.12.279

45

Exercise 13.5.12.280

38

Answer

−0.375

Exercise 13.5.12.281

58

Exercise 13.5.12.282

59

Answer

0.¯5

Exercise 13.5.12.283

29

Exercise 13.5.12.284

12+6.5

Answer

7

Exercise 13.5.12.285

14+10.75

In the following exercises, convert each percent to a decimal.

Exercise 13.5.12.286

5%

Answer

0.05

Exercise 13.5.12.287

9%

Exercise 13.5.12.288

40%

Answer

0.4

Exercise 13.5.12.289

50%

Exercise 13.5.12.290

115%

Answer

1.15

Exercise 13.5.12.291

125%

In the following exercises, convert each decimal to a percent.

Exercise 13.5.12.292

0.18

Answer

18%

Exercise 13.5.12.293

0.15

Exercise 13.5.12.294

0.009

Answer

0.9%

Exercise 13.5.12.295

0.008

Exercise 13.5.12.296

1.5

Answer

150%

Exercise 13.5.12.297

2.2

The Real Numbers

Simplify Expressions with Square Roots

In the following exercises, simplify.

Exercise 13.5.12.298

64

Answer

8

Exercise 13.5.12.299

144

Exercise 13.5.12.300

25

Answer

-5

Exercise 13.5.12.301

81

Identify Integers, Rational Numbers, Irrational Numbers, and Real Numbers

In the following exercises, write as the ratio of two integers.

Exercise 13.5.12.302
  1. 9
  2. 8.47
Answer
  1. 91
  2. 847100
Exercise 13.5.12.303
  1. −15
  2. 3.591

In the following exercises, list the

  1. rational numbers,
  2. irrational numbers.
Exercise 13.5.12.304

0.84,0.79132,1.¯3

Answer
  1. 0.84,1.3
  2. 0.79132
Exercise 13.5.12.305

2.3¯8,0.572,4.93814

In the following exercises, identify whether each number is rational or irrational.

Exercise 13.5.12.306
  1. 121
  2. 48
Answer
  1. rational
  2. irrational
Exercise 13.5.12.307
  1. 56
  2. 16

In the following exercises, identify whether each number is a real number or not a real number.

Exercise 13.5.12.308
  1. 9
  2. 169
Answer
  1. not a real number
  2. real number
Exercise 13.5.12.309
  1. 64
  2. 81

In the following exercises, list the

  1. whole numbers,
  2. integers,
  3. rational numbers,
  4. irrational numbers,
  5. real numbers for each set of numbers.
Exercise 13.5.12.310

4,0,56,16,18,5.2537

Answer
  1. 0,16
  2. 4,0,16
  3. 4,0,56,16
  4. 18,5.2537
  5. 4,0,56,16,18,5.2537
Exercise 13.5.12.311

4,0.¯36,133,6.9152,48,1012

Locate Fractions on the Number Line

In the following exercises, locate the numbers on a number line.

Exercise 13.5.12.312

23,54,125

Answer

This figure is a number line ranging from 0 to 6 with tick marks for each integer. 2 thirds, 5 fourths, and 12 fifths are plotted.

Exercise 13.5.12.313

13,74,135

Exercise 13.5.12.314

213,213

Answer

This figure is a number line ranging from negative 4 to 4 with tick marks for each integer. Negative 2 and 1 third, and 2 and 1 third are plotted.

Exercise 13.5.12.315

135,135

In the following exercises, order each of the following pairs of numbers, using < or >.

Exercise 13.5.12.316

−1___18

Answer

<

Exercise 13.5.12.317

314___−4

Exercise 13.5.12.318

79 ___ 49

Answer

>

Exercise 13.5.12.319

2 ___ 198

Locate Decimals on the Number Line

In the following exercises, locate on the number line.

Exercise 13.5.12.320

0.3

Answer

This figure is a number line ranging from 0 to 1 with tick marks for each tenth of an integer. 0.3 is plotted.

Exercise 13.5.12.321

−0.2

Exercise 13.5.12.322

−2.5

Answer

This figure is a number line ranging from negative 5 to 5 with tick marks for each integer. Negative 2.5 is plotted.

Exercise 13.5.12.323

2.7

In the following exercises, order each of the following pairs of numbers, using < or >.

Exercise 13.5.12.324

0.9___0.6

Answer

>

Exercise 13.5.12.325

0.7___0.8

Exercise 13.5.12.326

−0.6___−0.59

Answer

>

Exercise 13.5.12.327

−0.27___−0.3

Properties of Real Numbers

Use the Commutative and Associative Properties

In the following exercises, use the Associative Property to simplify.

Exercise 13.5.12.328

−12(4m)

Answer

−48m

Exercise 13.5.12.329

30(56q)

Exercise 13.5.12.330

(a+16)+31

Answer

a+47

Exercise 13.5.12.331

(c+0.2)+0.7

In the following exercises, simplify.

Exercise 13.5.12.332

6y+37+(−6y)

Answer

37

Exercise 13.5.12.333

14+1115+(14)

Exercise 13.5.12.334

14113591411

Answer

359

Exercise 13.5.12.335

181529

Exercise 13.5.12.336

(712+45)+15

Answer

1712

Exercise 13.5.12.337

(3.98d+0.75d)+1.25d

Exercise 13.5.12.338

11x+8y+16x+15y

Answer

27x+23y

Exercise 13.5.12.339

52m+(−20n)+(−18m)+(−5n)

Use the Identity and Inverse Properties of Addition and Multiplication

In the following exercises, find the additive inverse of each number.

Exercise 13.5.12.340
  1. 13
  2. 5.1
  3. 14
  4. 85
Answer
  1. 13
  2. 5.1
  3. -14
  4. 85
Exercise 13.5.12.341
  1. 78
  2. 0.03
  3. 17
  4. 125

In the following exercises, find the multiplicative inverse of each number.

Exercise 13.5.12.342
  1. 10
  2. 49
  3. 0.6
Answer
  1. 110
  2. 94
  3. 53
Exercise 13.5.12.343
  1. 92
  2. -7
  3. 2.1

Use the Properties of Zero

In the following exercises, simplify.

Exercise 13.5.12.344

830

Answer

0

Exercise 13.5.12.345

09

Exercise 13.5.12.346

50

Answer

undefined

Exercise 13.5.12.347

0÷23

In the following exercises, simplify.

Exercise 13.5.12.348

43+39+(−43)

Answer

39

Exercise 13.5.12.349

(n+6.75)+0.25

Exercise 13.5.12.350

51357135

Answer

57

Exercise 13.5.12.351

161712

Exercise 13.5.12.352

232837

Answer

8

Exercise 13.5.12.353

9(6x11)+15

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the Distributive Property.

Exercise 13.5.12.354

7(x+9)

Answer

7x+63

Exercise 13.5.12.355

9(u−4)

Exercise 13.5.12.356

−3(6m−1)

Answer

−18m+3

Exercise 13.5.12.357

−8(−7a−12)

Exercise 13.5.12.358

13(15n6)

Answer

5n−2

Exercise 13.5.12.359

(y+10)p

Exercise 13.5.12.360

(a−4)−(6a+9)

Answer

−5a−13

Exercise 13.5.12.361

4(x+3)−8(x−7)

Systems of Measurement

1.1 Define U.S. Units of Measurement and Convert from One Unit to Another

In the following exercises, convert the units. Round to the nearest tenth.

Exercise 13.5.12.362

A floral arbor is 7 feet tall. Convert the height to inches.

Answer

84 inches

Exercise 13.5.12.363

A picture frame is 42 inches wide. Convert the width to feet.

Exercise 13.5.12.364

Kelly is 5 feet 4 inches tall. Convert her height to inches.

Answer

64 inches

Exercise 13.5.12.365

A playground is 45 feet wide. Convert the width to yards.

Exercise 13.5.12.366

The height of Mount Shasta is 14,179 feet. Convert the height to miles.

Answer

2.7 miles

Exercise 13.5.12.367

Shamu weights 4.5 tons. Convert the weight to pounds.

Exercise 13.5.12.368

The play lasted 134 hours. Convert the time to minutes.

Answer

105 minutes

Exercise 13.5.12.369

How many tablespoons are in a quart?

Exercise 13.5.12.370

Naomi’s baby weighed 5 pounds 14 ounces at birth. Convert the weight to ounces.

Answer

94 ounces

Exercise 13.5.12.371

Trinh needs 30 cups of paint for her class art project. Convert the volume to gallons.

Use Mixed Units of Measurement in the U.S. System.

In the following exercises, solve.

Exercise 13.5.12.372

John caught 4 lobsters. The weights of the lobsters were 1 pound 9 ounces, 1 pound 12 ounces, 4 pounds 2 ounces, and 2 pounds 15 ounces. What was the total weight of the lobsters?

Answer

10 lbs. 6 oz.

Exercise 13.5.12.373

Every day last week Pedro recorded the number of minutes he spent reading. The number of minutes were 50, 25, 83, 45, 32, 60, 135. How many hours did Pedro spend reading?

Exercise 13.5.12.374

Fouad is 6 feet 2 inches tall. If he stands on a rung of a ladder 8 feet 10 inches high, how high off the ground is the top of Fouad’s head?

Answer

15 feet

Exercise 13.5.12.375

Dalila wants to make throw pillow covers. Each cover takes 30 inches of fabric. How many yards of fabric does she need for 4 covers?

Make Unit Conversions in the Metric System

In the following exercises, convert the units.

Exercise 13.5.12.376

Donna is 1.7 meters tall. Convert her height to centimeters.

Answer

170 centimeters

Exercise 13.5.12.377

Mount Everest is 8,850 meters tall. Convert the height to kilometers.

Exercise 13.5.12.378

One cup of yogurt contains 488 milligrams of calcium. Convert this to grams.

Answer

0.488 grams

Exercise 13.5.12.379

One cup of yogurt contains 13 grams of protein. Convert this to milligrams.

Exercise 13.5.12.380

Sergio weighed 2.9 kilograms at birth. Convert this to grams.

Answer

2,900 grams

Exercise 13.5.12.381

A bottle of water contained 650 milliliters. Convert this to liters.

Use Mixed Units of Measurement in the Metric System

In the following exerices, solve.

Exercise 13.5.12.382

Minh is 2 meters tall. His daughter is 88 centimeters tall. How much taller is Minh than his daughter?

Answer

1.12 meter

Exercise 13.5.12.383

Selma had a 1 liter bottle of water. If she drank 145 milliliters, how much water was left in the bottle?

Exercise 13.5.12.384

One serving of cranberry juice contains 30 grams of sugar. How many kilograms of sugar are in 30 servings of cranberry juice?

Answer

0.9 kilograms

Exercise 13.5.12.385

One ounce of tofu provided 2 grams of protein. How many milligrams of protein are provided by 5 ounces of tofu?

Convert between the U.S. and the Metric Systems of Measurement

In the following exercises, make the unit conversions. Round to the nearest tenth.

Exercise 13.5.12.386

Majid is 69 inches tall. Convert his height to centimeters.

Answer

175.3 centimeters

Exercise 13.5.12.387

A college basketball court is 84 feet long. Convert this length to meters.

Exercise 13.5.12.388

Caroline walked 2.5 kilometers. Convert this length to miles.

Answer

1.6 miles

Exercise 13.5.12.389

Lucas weighs 78 kilograms. Convert his weight to pounds.

Exercise 13.5.12.390

Steve’s car holds 55 liters of gas. Convert this to gallons.

Answer

14.6 gallons

Exercise 13.5.12.391

A box of books weighs 25 pounds. Convert the weight to kilograms.

Convert between Fahrenheit and Celsius Temperatures

In the following exercises, convert the Fahrenheit temperatures to degrees Celsius. Round to the nearest tenth.

Exercise 13.5.12.392

95° Fahrenheit

Answer

35° C

Exercise 13.5.12.393

23° Fahrenheit

Exercise 13.5.12.394

20° Fahrenheit

Answer

–6.7° C

Exercise 13.5.12.395

64° Fahrenheit

In the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.

Exercise 13.5.12.396

30° Celsius

Answer

86° F

Exercise 13.5.12.397

–5° Celsius

Exercise 13.5.12.398

–12° Celsius

Answer

10.4° F

Exercise 13.5.12.399

24° Celsius

Chapter Practice Test

Exercise 13.5.12.1

Write as a whole number using digits: two hundred five thousand, six hundred seventeen.

Answer

205,617

Exercise 13.5.12.2

Find the prime factorization of 504.

Exercise 13.5.12.3

Find the Least Common Multiple of 18 and 24.

Answer

72

Exercise 13.5.12.4

Combine like terms: 5n+8+2n−1.

In the following exercises, evaluate.

Exercise 13.5.12.5

|x| when x=2

Answer

−2

Exercise 13.5.12.6

11−a when a=−3

Exercise 13.5.12.7

Translate to an algebraic expression and simplify: twenty less than negative 7.

Answer

−7−20;−27

Exercise 13.5.12.8

Monique has a balance of −$18 in her checking account. She deposits $152 to the account. What is the new balance?

Exercise 13.5.12.9

Round 677.1348 to the nearest hundredth.

Answer

677.13

Exercise 13.5.12.10

Convert 45 to a decimal.

Exercise 13.5.12.11

Convert 1.85 to a percent.

Answer

185%

Exercise 13.5.12.12

Locate 23,1.5, and 94 on a number line.

In the following exercises, simplify each expression.

Exercise 13.5.12.13

4+10(3+9)52

Answer

99

Exercise 13.5.12.14

−85+42

Exercise 13.5.12.15

−19−25

Answer

−44

Exercise 13.5.12.16

(2)4

Exercise 13.5.12.17

5(9)÷15

Answer

3

Exercise 13.5.12.18

381112

Exercise 13.5.12.19

45÷920

Answer

169

Exercise 13.5.12.20

12+35156

Exercise 13.5.12.21

m7+107

Answer

m+107

Exercise 13.5.12.22

71238

Exercise 13.5.12.23

5.8+(4.7)

Answer

−10.5

Exercise 13.5.12.24

100−64.25

Exercise 13.5.12.25

(0.07)(31.95)

Answer

2.2365

Exercise 13.5.12.26

9÷0.05

Exercise 13.5.12.27

14(57p)

Answer

−10p

Exercise 13.5.12.28

(u+8)−9

Exercise 13.5.12.29

6x+(−4y)+9x+8y

Answer

15x+4y

Exercise 13.5.12.30

023

Exercise 13.5.12.31

750

Answer

undefined

Exercise 13.5.12.32

−2(13q−5)

Exercise 13.5.12.33

A movie lasted 1\frac{2}{3} hours. How many minutes did it last? ( 1 hour =60 minutes)

Answer

100 minutes

Exercise \PageIndex{34}

Mike’s SUV is 5 feet 11 inches tall. He wants to put a rooftop cargo bag on the the SUV. The cargo bag is 1 foot 6 inches tall. What will the total height be of the SUV with the cargo bag on the roof? (1 foot = 12 inches)

Exercise \PageIndex{35}

Jennifer ran 2.8 miles. Convert this length to kilometers. (1 mile = 1.61 kilometers)

Answer

4.508 km


This page titled 13.5.12: Chapter 1 Review Exercises is shared under a CC BY license and was authored, remixed, and/or curated by OpenStax.

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