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(2) 37 19. − 10. 20.. 79 7. 21. − 22. 8. 2 25. 7 5. 26. −3. 109 5. 27. 3. 2 3. 28. 2. 5 23. 2 8. 24. −1. 2 31. − 5 1 4. 1 18 5 16. 3 29. −12 4 2 9. 30. 12. 5 6. 32. 1 33. −. 10 21. 34. 98 35. 2. 1 2. 7 36. −1 8. 37. 11 38. 12 Section 5.1. BJU Press. Unauthorized reproduction prohibited..
(3) 1 39. −13 3. 40. Answers will vary; possible answer: when the numerator and denominator have no common factors.. BJU Press. Unauthorized reproduction prohibited.. c c Ad c 41. A = A + = + d d d d Ad + c = ; d 8 8 6 (9) 8 + 6 =6+ = 9 9 9 9 6(9) + 8 54 + 8 62 = = = 9 9 9.
(4) 42.. 39. 12. 13. 14. 15. 17. 19. 21. 23. 3.25. 3. 2.79. 2.6. 2.29. 2.05. 1.86. 1.70. 12. 13. 14. 15. 17. 19. 21. 23. 4.42. 4.08. 3.79. 3.53. 3.12. 2.79. 2.52. 2.30. 43.. 53. Section 5.1 BJU Press. Unauthorized reproduction prohibited..
(5) 44. Slowest: 39 : 23 = 1.70 : 1. Fastest: 53 : 12 = 4.42 : 1. The gear ratio represents the number of times the rear wheel will turn for each rotation of the pedals. Thus the more times the rear wheel turns, the faster the bicycle goes.. 45. Easiest: 1.70 : 1; Hardest: 4.42 : 1; It takes less effort to move the bicycle and rider a short distance than to move them a long distance.. Section 5.1 BJU Press. Unauthorized reproduction prohibited..
(6) n 46. – 18 = –17; n = –9 −9. 47. 3n + 8 = –19; n = –9 48. 10(n + 12) = 84; n = –3.6 49.. n−7 = –56; n = 455 −8. 50. 19 =. 51. 2 · 31 52. 5 · 17 53. 3 · 7 · 11 54 22 · 29 55. 23 · 32. n + 9; n = 60 6. Section 5.1 BJU Press. Unauthorized reproduction prohibited..
(7) 5.2 Comparing Rational Numbers. 1–6.. 1 2 7 <2 8. 7. –3 < –3 <. 8.. 1 3 3 < <2 3 4 8. 4 17 ≠ 7 28. 2 84 ≠ 9. 3 124. BJU Press. Unauthorized reproduction prohibited.. 10.. 6 78 = 7 91. 11.. 4 52 = 5 65. 8 5 12. ≠ 17 11. 13.. 8 31 ≠ 31 120. 14. 27 < 35; so. 3 7 < 5 9. 15. 42 > 40; so. 7 5 > 8 6.
(8) 4 24 16. 168 = 168; so = 7 42. 8 4 22. 72 > 68; so > 17 9. 17. 126 < 140; so. 6 20 < 7 21. 23. 147 < 155; so. 18. 128 < 135; so. 8 9 < 15 16. 24.. 5 6 5 3 < ; so < 8 8 8 4. 19. 136 > 125; so. 17 25 > 5 8. 25.. 14 15 2 5 < ; so < 21 21 3 7. 3 7 20. –30 < –28; so − < − 4 10. 21. –95 > –102; so −. 5 6 >− 17 19. 3 31 < 5 49. 13 12 1 2 26. > ; so > 78 78 6 13. 27.. 16 15 8 5 > ; so > 6 6 3 2. Section 5.2 BJU Press. Unauthorized reproduction prohibited..
(9) 68 69 17 23 28. − > − ; so − > − 12 12 3 4. 32.. 2 5 1 1 − <− <− <− 3 8 2 4. 68 69 17 23 29. < ; so < 12 12 3 4. 30. 1 2 5 7 2 <2 <2 <2 2 3 6 8. 33.. 3 1 9 4 17 < < < < 8 2 17 3 9. 34.. 5 2 4 10 6 < < < < 9 3 5 9 5. 35. The inequality sign reverses; the inequality sign remains as it is.. 31. 1 1 7 4 < < < 6 2 10 5. Section 5.2 BJU Press. Unauthorized reproduction prohibited..
(10) 36. Ratios. 16th. 15th. 14th. 13th. 12th. 11th. 10th. 9th. chain-ring to 53:12 53:13 53:14 53:15 39:12 53:17 39:13 53:19 rear sprocket gear. 4.42. 4.08. 3.79. 3.53. 3.25. 3.12. 3.0. 2.79. 8th. 7th. 6th. 5th. 4th. 3rd. 2nd. 1st. 39:14 39:15 53:21 53:23 39:17 39:19 39:21 39:23 2.79. BJU Press. Unauthorized reproduction prohibited.. 2.6. 2.52. 2.3. 2.29. 2.05. 1.86. 1.696.
(11) 37. The four highest gears occur using the larger front chain-ring and smaller rear sprockets, and the four lowest gears occur using the smaller front chain-ring and larger rear sprockets. Gears 5–12 are a mixture of front and rear combinations and could all be considered medium gears.. 40. z ≤ 3 41. z ≥ –11 42. x ≥ 26 43. 3 44. 1 45. 6. 38. y < –2. 46. Yes; the GCF of 48 and 49 is 1.. 39. y ≠ 3. 47. No; 2 is a common factor.. Section 5.2 BJU Press. Unauthorized reproduction prohibited..
(12) Problem Solving 5—Drawing a Picture. 1. 207 mi. 2. 5 times 3. seventh floor; 14 min., 40 sec. 4. 3 or 4 5. sums of 2 through 8; the sum 5 occurs most often. 6. twice–at 12 min. and at 24 min. 7. 270 in.2. BJU Press. Unauthorized reproduction prohibited.. 8. The order from north to south is Philo, Bixler, Grantville, and Palaski. From Palaski to Grantville is 22 mi. From Bixler to Grantville is 7 mi. From Bixler to Philo is 11.5 mi. The total distance from Philo to Palaski is 40.5 mi..
(13) 5.3 Decimal Equivalents. 1. 0.6. 10.. 5 8. 11.. 13 25. 2. 0.05 3. –0.28 4. 0.375. 12. −. 5. 3.4 6. –0.875 7. 3.4375 8. 0.15625 9. 0.225 BJU Press. Unauthorized reproduction prohibited.. 13.. 4 5. 3 8. 14. 2. 11 20. 15. –4. 7 10.
(14) 16. 17.. 9 16 29 32. 18. 5. 17 25. 19. 0.83 20. 1.2 21. −0.4 22. 0.63. 24. 0.53 25. 0.15 26. 6.7 27. −6.2916 28. 0.428571 29. 5.34 30. 0.83 31. 0.3, 0.318 , 0.318 , 0.318 , 0.32, 0.3208 , 0.32. 23. 0.583 Section 5.3 BJU Press. Unauthorized reproduction prohibited..
(15) 61 495. 32. 0.405, 0.45, 0.45, 0.456, 0.47, 0.54, 0.54. 39.. 43 33. 99. 40. 374 in. or 31.2 ft.; 144 in. or 12.0 ft.. 41 34. 333. 41. 8.85 mi./hr. in high gear; 4.77 mi./hr. in low gear. 35. 1. 42. x = 4.5. 3 36. 7. 43. y = –15. 83 37. 660 37 38. 300. 44. z = 23 45. x = 8 46. y = –5 Section 5.3. BJU Press. Unauthorized reproduction prohibited..
(16) 47. –9, –5, –1, 3, 7 48.. 1 3 5 , 1, , 2, 2 2 2. 49. 8, 5, 2, –1, –4 50. 0.7, 1.1, 1.5, 1.9, 2.3. Section 5.3 BJU Press. Unauthorized reproduction prohibited..
(17) 5.4 Ratio and Rate. 1. 2 : 1. 10. 1 to 3. 2. 3 : 2. 11. 5 to 1. 3. 2 : 3. 12. 9 to 5. 4. 6 : 5. 13.. 2 1. 6. 8 : 3. 14.. 5 3. 7. 25 to 1. 10 15. 3. 5. 3 : 1. 8. 24 to 5 9. 4 to 3; 2 to 1; 4 to 1 BJU Press. Unauthorized reproduction prohibited.. 16.. 1 2.
(18) 17.. 6 13. 26. 5.2 yd./carry 27. $0.59/can. 10 9. 28. $2.50/lb.. 19. 4 to 3. 29. $18/lawn. 20. 5 to 8. 30. $8.50/hr.. 21. 3 to 4. 31. 46 bars. 22. 8 to 5. 32. 235 mi.. 23. 35 words/min.. 33. 21 mi./gal.. 24. 90 acres/day. 34. 5 yd./carry. 25. 20 mi./gal.. 35. 1.6 yd./dress. 18.. Section 5.4 BJU Press. Unauthorized reproduction prohibited..
(19) 36. 212 bu./load. 45. 1, 2, 3, 6, 7, 14, 21, 42. 37. $77,400; $129,000; $180,600. 46. yes; –14. 38. firstborn: $350,000; other sons: $175,000. 47. yes; 3. 39. ≈ 21,200 pedal revolutions 40. ≈ 353 min. ≈ 5 hr. 53 min.. 48. no 49. yes; –40 50. no. 41. 1, 2, 19, 38 42. 1, 2, 3, 6, 9, 14, 21, 42, 63, 126 43. 1, 2, 3, 4, 6, 12 44. 1, 2, 7, 14, 28 Section 5.4 BJU Press. Unauthorized reproduction prohibited..
(20) 5.5 Proportions. 1. ratios; proportion. 8.. 2 x = 300 7,000. 9.. 7 340 = x 1,000. 2. a is to b as c is to d. 3. b 4. a and d; the means 5. 6.. 2 x = 5 7 3 x = 5 8. 3 x 7. = 5 60. BJU Press. Unauthorized reproduction prohibited.. 10.. 40 5,000 = 225 x. 11.. 1.5 x = 24 72. 12.. 5 x = 3 8. 13. x = 20.
(21) 14. y = 35. 24. y = 3.6. 15. z = 8. 25. 30 cars. 16. c = 4.8. 26. 7 spruce seedlings. 17. x = 510. 27. 10.5 in.. 18. a = 5. b 28. 5. 19. b = 4 20. n = 3.5 21. d = 16 22. a = 4.5 23. b = 2.5. 29.. 5 3. 30.. 3 a. 31. 2 to 1 Section 5.5. BJU Press. Unauthorized reproduction prohibited..
(22) 32. 22,400 bushels 33. 34.. 2 x = ; 60 ft. 3 90 a 14 21 28 = = = b 6 9 12. 35. No; proportions are true by alternation, which includes units. 36.. a c a c = ⇒ +1= +1 b d b d a b c d ⇒ + = + b b d d a+b c+d ⇒ = b d. 37. π; 2π 38. No; for example, rectangles 4 × 8 and 5 × 10 have areas 32 16 in the ratio = 50 25. ≠. 4 . 5. 39. Yes; for example, rectangles 4×8 and 5×10 have perimeters in the ratio 24 4 = . 30 5. 40. They would be of lengths 2b and 2c. 41. ≈ 84.5 rpm, which is reasonable for a human Section 5.5. BJU Press. Unauthorized reproduction prohibited..
(23) 42. ≈ 26 teeth 43. 1,800 44. 120,000 45. 20 46. 600 47. 80 48. 0.5, 1.5, 4.5, 13.5, 40.5; geometric. 49. –4, –24, –144, –864, –5,184; geometric 50. 7, –1.4, 0.28, –0.056, 0.0112; geometric 51. 12, 17, 22, 27, 32; arithmetic 52. –2, –10, –18, –26, –34; arithmetic 53. –2, –2, –2, –2, –2; both geometric and arithmetic. Section 5.5 BJU Press. Unauthorized reproduction prohibited..
(24) 5.6 Real Numbers. 1. true. 10. true. 2. true. 11. rational. 3. true. 12. integer. 4. false. 13. whole. 5. false. 14. irrational. 6. true. 15. integer. 7. false. 16. irrational. 8. false. 17. rational. 9. true. 18. rational. BJU Press. Unauthorized reproduction prohibited..
(25) 19. rational 20. irrational. 25. Commutative Property of Addition. 21. natural. 26. Associative Property of Multiplication. 22. rational. 27. Distributive Property. 23. irrational. 28. Identity Property of Multiplication. 24.. 29. Identity Property of Addition 30. Inverse Property of Multiplication. Section 5.6 BJU Press. Unauthorized reproduction prohibited..
(26) 31. Inverse Property of Addition. 37. Inverse Property of Addition. 32. Associative Property of Addition. 38. Answers will vary; possible answers include 3x = 2 or x + 6 = 4.. 33. Commutative Property of Multiplication 34. Commutative Property of Addition 35. Inverse Property of Multiplication 36. Commutative Property of Multiplication. 39. Yes, the average of two rational numbers is always rational and is between the two numbers (e.g., the average of 1.2 and 1.3 is 1.25). Thus, there are an infinite number of rational numbers.. Section 5.6 BJU Press. Unauthorized reproduction prohibited..
(27) 40. y > 4. 45. 2, 3, 6, 9. 41. x > –2. 46. 2, 3, 4, 5, 6, 8, 10. 42. x ≤ 1.75. 47. 2, 4, 8. 43. x < 18. 48. none. 44. x ≥ 7. 49. 2, 3, 5, 6, 10. Section 5.6 BJU Press. Unauthorized reproduction prohibited..
(28) Math and Scripture 5. 1. amount of manna for one person per day 2. 10 omers 3. 1 bath = 1 ephah =. 1 homer 10. 4. 1 ephah = 1 bath ≈ 20 qt. ≈ 2.2 L; 1 homer ≈ 50 gal. ≈ 200 dry qt. ≈ 220 L. BJU Press. Unauthorized reproduction prohibited.. 5. A tenth of an ephah of fine floor, which would also be 1 omer. 6. one-fifth of the value of the offering 7. one-fifth more 8. half of a tenth part of an ephah, which would be half an omer each morning and night.
(29) 9. one-fifth 10. one-fifth 11. one-tenth of the flock. Math and Scripture 5 BJU Press. Unauthorized reproduction prohibited..
(30) Chapter 5 Review. 1.. 2 3. 7.. −12 7. 2.. 7 18. 8.. 21 21 =− −20 20. 3. − 4.. 28 5. 28 11. 10. > 11. < 12. <. 3 5. 2 8. 6. –6. 9. <. 1 4. BJU Press. Unauthorized reproduction prohibited..
(31) 13.. 19. 2.3 2 5 7 4 < < < 3 7 9 5. 20. 0.916 21. 0.5625. 14. Answers may vary; Possible −10 −15 −20 answers: , , 14 21 28. 15. Answers may vary; Possible answers:. 18 27 36 , , 4 6 8. 22.. 13 25. 4 23. –4 25. 24. –6. 16. 0.4 17. 0.625. 25.. 2 3. 13 24. 18. 1.875 Chapter 5 Review BJU Press. Unauthorized reproduction prohibited..
(32) 26.. 16 13. 27. 1 28.. 29 21. 29. 25 to 1 30.. 4 1 ; 1 4. 31. 30 mi./gal. 32. $11.50/hr. 33. 48 calories/oz.. 34. $0.15/roll 35. extremes: m and y; means: n and x 36. x =. 12 5. 37. a = 22 38. y =. 22 3. 126 39. z = 5. 40. x = –15. Chapter 5 Review BJU Press. Unauthorized reproduction prohibited..
(33) 41. x =. 28 15. 42. 39 free throws 1 43. 1 cups of flour 3. 44. irrational. 45. integer 46. rational 47. natural 48. Inverse Property of Multiplication 49. Distributive Property. Chapter 5 Review BJU Press. Unauthorized reproduction prohibited..
(34) 50. An understanding of rational numbers is necessary to follow God's commands of giving. The Lord expects recognition of His generous provision for His children by their giving back to Him a small portion.. Chapter 5 Review BJU Press. Unauthorized reproduction prohibited..
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