36. {ME, MA, MD, MI, MN, MO, MS, MT, TX, LA, AL,

(1)

 2012 BJU Press. Unauthorized reproduction prohibited.

1.1 Sets of Numbers

1 – 10.

3 1

31.313131… 0.5 Q Z

W N

0 ]6

Q₉

4.868668666… –7.21721172111… 4

11 ]

5 4

11. true

12. true

13. false

14. true

15. false

16. true

17. true

18. false

19. false

20. true

21. false

22. true

23. false

24. false

(2)

Section 1.1

 2012 BJU Press. Unauthorized reproduction prohibited. 26. false

27. false

28. true

29. {1, 3}

30. {–1, 1, 2, 3, 4, …}

31. {–1}

32. ∅

33. {–1, 5}

34. {1, 3, 5}

35. {MN, WI, IA, IL, MO, KY, TN, AR, MS, LA, ME, MA, MD, MI, MT}

36. {ME, MA, MD, MI, MN, MO, MS, MT, TX, LA, AL, FL}

37. {TX, LA, MS, AL, FL, NM, ND, SD, WV, NC, SC, NJ, NY, RI, NH}

38. {MS}

39. ∅

40. {MT, MN, ME}

41. {ND, NY, NH}

42. {MN, MO, MS, TX, LA, AL, FL}

(3)

Section 1.1

44. {… , –2, –1, 0, 1, 2, …}

45.

46. 9 ∉_R∪_S

47. {5, 7} ⊆_{{1, 3, 5, …}}

48. A ∩_{B = B}∩_A

49. finite: {5, 7};

infinite: {1, 3, 5, …}

50. ∅

51. 4

3 units

52a_{. 16}

52b_.1

9 unit

52c_.16

9 units

J K

6

10 8

0 1

2

3 4

–1 –3

(4)

Section 1.1

 2012 BJU Press. Unauthorized reproduction prohibited. 53.

53a_{. 64}

53b_. 1

27 unit

53c_.64

27 units

54. GCF = 5, LCM = 180

55. GCF = 8, LCM = 720

56. 51

5 or 26

5

57. 37

24 or 1

13 24

58. 13

5 or 8 5

59. 5

24

60. 153

25 or 6

3 25

61. 7

12

62. 17

9 or 1

8 9

63. 21

16 or 1

(5)

 2012 BJU Press. Unauthorized reproduction prohibited. L K ]2 0 2 4 ]4 N M 0 1 2 ]1 ]2 P Q 0 1 1.5 0.5 –0.5 –1 –1.5 H G

–2 –1 0 1 2

1.2 Number Lines, Opposites, and Absolute Values

1.

2.

3.

4.

5. 6. 7. 8.

A B

]6 ]5 ]4 ]3 ]2 ]1 0 1 2 3 4 5 6

D C

]30 ]20 ]10 0 10 20 30 40

F E

–1.5 –1 –0.5 0 0.5 1

(6)

Section 1.2

 2012 BJU Press. Unauthorized reproduction prohibited. 9. –1

10. 1.5

11. 3

12. 20

13. –15

14. –5

15. 1

2

16. –3

4

17. 11

4 = 5 4

18. –17

19. 9

20. 1.3

21. –1

2

22. 2

23. 17

24. 1

2

25. 2.8

26. 45

27. 315

(7)

Section 1.2

29. 1

8

30. 13

31. 12

32. 76

33. 1.6

34. 0

35. 10; 17

36. 122; 198

37. 13; 18.5

38. 87; 58.5

39. They are equal.

40. 0

41. 133 mi

42. 10

43. 0

44. 31

(8)

Section 1.2

Iteration Number of

Segments

Length of Each Segment

Total Length of the Curve

Decimal Equivalent

0 1 1 1 1

1 4 1

3

4 3

1.33

2 16 1

9

16 9

1.78

3 64 1

27

64 27

(9)

Section 1.2

47a_{. There are four times as}

many segments.

47b_{. It is}1

3 the length.

47c_{. It is}4

3 the length.

48.

Iteration Number of

Segments

Decimal Equivalent

4 256 1

81

256 81

3.16

5 1024 1

243

1024 243

(10)

Section 1.2

Integers Whole Natural

Real numbers

Rational Irrational

49. {h_,m_}

50. {a_,e_,h_,i_,j_,k_,l_,m_,n_,o_,u_}

51. true

52. false

(11)

1.3 Adding Rational Numbers

1. –3 2. 6 3. –4 4. 3 5. 24 6. 19 7. –2 8. –15 9. –91 10. 4 11. –21

12. 360 13. 0 14. 4

15. –617.1 16. –624.17

17. 103

35

18. –1

19. 7

15

20. –82

(12)

Section 1.3

88

22. 44

189

23. 0 24. 0 25. –2 26. –17 27. 10 28. 9 29. 28 30. 1

31. –12 32. –6 33. –4 34. 0

35. 5 + 2; 7 36. 4 + 9; 13 37. 2 + 7; 9 38. –8 + 3; –5 39. –6 + 5; –1

40. –6°F

(13)

Section 1.3

42. Commutative Property 43. Associative Property

44. Additive Inverse Property

45a. 1

3 n ⎛ ⎞ ⎜ ⎟

⎝ ⎠ or

1 3n

45b. 4

(14)

Section 1.3

Iteration Number of Segments

Decimal Equivalent

nth 4n 1

3

n

⎛ ⎞ ⎜ ⎟

⎝ ⎠ or 1 3n

4 3

n

⎛ ⎞ ⎜ ⎟

⎝ ⎠ NA

10 1,048,576 1

59, 049

1, 048,576

59, 049 17.76

100 1.61 × 1060 1.94 × 10–48

60 47

1.61 10 5.15 10

×

(15)

Section 1.3

48. true 49. false 50. true 51. false

(16)

1.4 Subtracting Rational Numbers

1. 5

2. –1

3. –17

4. –6

5. –24

6. 10

7. –2

8. 15

9. –130

10. 13

11. 14

12. –9

13. 621.17

14. 15.316

15. 7

9

16. 22

9

17. –29

10

18. – 5

(17)

Section 1.4

19. 5

36

20. –327

35

21. 2

22. 6

23. 0

24. –2

25. –9

26. 25

27. 6 – 2; 4

28. 7 – 4; 3

29. 8 – 3; 5

30. 5 – 16; –11

31. 16 – 5; 11

32. 17°_F

33. $15.92

34. 5

8 in.

35. 4

36. –14

37. 28

(18)

Section 1.4

39. 65

84

40. 1024

81 ≈ 12.64 units

41a_{. would continue to increase}

forever

41b_{. would get closer and closer}

to zero

41c_{. would continue to increase}

forever

42. rational

43. 19

44. 5

45. no

46. 11.583

47. Associative Property of Addition

48. No; 5 – 3 = 2, but 3 – 5 = –2

49. 8

50. 18

(19)

1.5 Multiplying Rational Numbers

1. –6

2. 56

3. 24

4. –48

5. 3

6. –21

7. 36

8. –96

9. 287

10. –632

11. –546

12. –8928

13. –78.96

14. 32.838

15. –126

16. 640

17. 0

18. 5

21

19. – 7

33

20. 3

(20)

Section 1.5

21. 3

8

22. – 9

40

23. –2

3

24. –12

5

25. 49

5

26. 46

5

27. 5(4); 20

28. 7(3); 21

29. –2(9); –18

30. 2(–11); –22

31. 6(8); 48

32. 12

3 gal

33. 11

5 gal

34. 11

2 in.

35. 29.4 yd

36. 4.7 mi

37. 33.02 cm

(21)

Section 1.5

39. –a_{= –1}_× a

40. –(–a_{) =}a

41. –3 + (–3) + (–3) + (–3) +

(–3) + (–3) + (–3) + (–3)

42.

43. Answers will vary.

44. 39

45. 44

46. 6.5

47. –64

48. –1

3

49. –11

12

50. –15.03

51. 7

6

52. 7

12

(22)

1.6 Dividing Rational Numbers

1. 9

2. –7

3. undefined

4. 5

5. –9

6. –8

7. –7

8. 42

9. –9

10. 0

11. undefined

12. –6

13. 8

14. –282

15. 5

16. 0.87

17. –11

18

18. 4

9

19. –10

(23)

Section 1.6

20. 1

68

21. 21

19

22. –2

3

23. – 9

40

24. 5

6

25. 8

15

26. –21

11

27. –42

5

28. – 6

35

29. 81

3

− ; –27

30. 12

4 ; 3

31. 9

2; 4.5

32. 50

6

−

; – 25

3

33. 11

(24)

Section 1.6

34. 3

4 gal

35. 4

5 ft

36.

0

a

= b_{would mean 0}_× b₌

a,_{but 0}_× b_{= 0}

37. 0

a = 0

38. –35

39. 0.073

40. ±₃₂

41. No; 6 ÷_{3 = 2, but 3}÷_{6 =}1

(25)

Section 1.6

 2012 BJU Press. Unauthorized reproduction prohibited. 42 – 43.

Iteration 0 1 2 3 4

Number of upward-pointing triangles

1 3 9 27 81

Area of each upward-pointing triangles

1 1

4

1 16

1 64

1 256

Total area of upward-pointing triangles

1 3

4

9 16

27 64

(26)

Section 1.6

5

7

9

0

2

4 1

3

A B

5

7

9

0

2

4 1

3

A B

45. Additive Identity Property

46. Commutative Property of Addition

47. Associative Property of Addition

48. 22

49. 5.7

50. – 9

16

51. 3

4

52. 157.56468

53. – 3

(27)

1.7 Exponents

1. 4 × 4 × 4 = 64

2. –2(–2)(–2)(–2) = 16

3. –3(–3)(–3)(–3)(–3) = –243 4. 1 × 1 × 1 × 1 = 1

5. 1

6. 3 3

4 4 ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ = 9 16

7. 1

4 4× = 1 16

8. 1

–3(–3)(–3) = – 1 27

9. – 1

2× × ×2 2 2 = – 1 16

10. 8 × 8 = 64

11. –3(–3)(–3)(–3) = 81

12. 3 3 3

2 2 2

⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ =

27 8

(28)

Section 1.7

19. 1015 20. 47 21. 3–5 22. 7–12 23. 92

24. 25 × 34 × 53

25. 1₁₁

7

26. 84 27. 1754

28. 1₆

7

29. 288 30. 511 31. 22 32. 1

33. 1₇

4

34. 1₈

8

35. 1

36.

6

3

(29)

Section 1.7

38. negative 39. positive 40. 27; 128 41. 94; 6561

42. 106; 1,000,000 43. 82; 64

44. 53; 125

45.

6

2 5

46.

8

11

2 7 3

×

47. 1₁₂

81x

48.

6

8

4 x

(30)

Section 1.7

Iteration n 10 100

Number of upward-pointing

triangles

3n 59,049 _5.15×₁₀47

Area of each upward-pointing

triangle

1 4

n ⎛ ⎞ ⎜ ⎟

⎝ ⎠ or

1 4n

1 1, 048,579

6.22 × 10–61

Total area of upward-pointing

triangles

3 4

n ⎛ ⎞ ⎜ ⎟ ⎝ ⎠

59,049

1, 048,579 ≈ 0.056

(31)

Section 1.7

52. 521 53. –2214 54. –27 55. –416

(32)

1.8 Order of Operations

1. 17

2. 11

3. 10

4. –11

5. –11

6. 49

7. 14

8. –144

9. –13

10. 29

11. 21

12. –3

13. –1

14. –119

15. –6

16. 65

17. 41

18. 20

19. 3

2

20. 2

(33)

Section 1.8

23. 2

24. 25

4

25. 2 4 + 5; 9

26. 5(6 + 7); 65

27. (20 – 13)2; 49

28. 202 – 132; 231

29. (2 + 5)6; 42

30. 5(6) + 2; 32

31. 5 ×_{6 + 20}÷_{5; 34}

32. 11 × 1

9 – 7; –

52

9 = –5

7 9

33. 9 – u2 + (–15)u; –4

34. 91

120

35. –19

24

36. –4.9

(34)

Section 1.8

S T

]7]6]5]4]3]2]1 0 1 2 3 4 5 6 7 R

38. Possible answer: In each iteration, the midpoints of the segments or the centers of the quadrilaterals are moved a randomly

generated amount,

producing new segments or diamonds. Repeating the process provides greater levels of detail.

39. –2.5

40. –0.5

41. 4

42.

43. 21

44. 6.5

45. N

46. Q

47. Q₉

(35)

R Z

W N

]4

Q₉ Q

7

0.3 A

]5 ]4 ]3 ]2 ]1 0 1 2 3 4 5

B C

Chapter 1 Review

1 – 3.

4. true

5. true

6. false

7. {2}

8. {–5, –3, –2, –1, 0, 1, 2}

9. {–1, 2}

10.

11. –3.5

12. –2

13. 1.5

14. 1.3

15. 7

16. 34; 5

17. 9; 12.5

(36)

Chapter 1 Review

20. –28

21. –20

22. –8

23. 4

24. –2

25. 1

26. –5.2

27. 4.44

28. 1

2

29. 32

21

30. 1

15

31. –11

72

32. –2

33. 815

34. 43

35. 324

36. 14

37. –3

(37)

Chapter 1 Review

 2012 BJU Press. Unauthorized reproduction prohibited. 39. 15

40. –40

41. 93

42. 9

43. –29

44. –(–6); 6

45. 5 – 8; –3

46. 15(–3) – 12; –57

47. 33 + 4; 31

48. j

49. f

50. a

51. h

52. d

53. g

54. e

55. c

(38)

Sequences—Evens, Odds, and Multiples

1. 4, 8, 12, 16, 20

2. –6, –12, –18, –24, –30

3. 11, 22, 33, 44, 55

4. 12, 24, 36, 48, 60

5. 20

6. –100

7. 39

8. recognizing patterns;