5.2 The Integers 233 In Exercises 9 and 10, insert either > or < in the shaded area between the paired numbers to make the statement correct. 9. a) −3 2 . < b) .3 2 − − < c) −3 0 . < d) .3 4 − − > In Exercises 51– 60, evaluate the expression using the order of operations. 51. − ⋅ 15 8 2 −1 52. − + ÷ 15 25 5 −10 53. ÷ ⋅ − − + (32 4 2) (3 4 5) 12 54. ÷ ⋅ − ÷ ⋅ − ⋅ (20 52) (6 23 13) 2 55. − + ⋅ ÷ − ÷ ( 15 19) 3 (13 18 2) 2 12 56. − ⋅ ÷ − ÷ ⋅ (9 11) 3 (32 16 2) 2 −3 57. − − + ÷ − + 3[(5 5) (2 2)] 2 3 2 3 −75 58. − − − ⋅ ÷ 5[( 2 2 ) 2 4 ] 3 2 4 2 60 59. − − − ÷ + − [4 (6 12) ] [9 3 4] 34/2 2 2 1 60. 2[2 (10 4/2) ] 24 3 5 [3 (10 1)] 3 2 2 3 + − + ⋅ − ÷ − + 2 Problem Solving 61. Submarine Depth The USS Virginia submarine is at an underwater depth of 600 feet. It then rises 200 feet, dives 400 feet, and finally dives another 300 feet. What is the USS Virginia’s final depth? 1100 feet under water 62. Dow Jones Industrial Average On June 12, 2023, the Dow Jones Industrial Average (DJIA) opened at 33,907 points. During the day, it gained 204 points. On June 13, it lost 67 points. On June 14, it lost 99 points. Determine the DJIA at the opening on June 15, 2023. 33,945 10. a) .5 8 − − > b) −5 8 . < c) .5 1 − − < d) −5 0 . < In Exercises 11–18, evaluate the expression. 11. 4 9 − + 5 12. 12 ( 4) + − 8 13. − + 7 4 −3 14. − + − 5 ( 5) −10 15. + − + 6 ( 11) 0 −5 16. 2 5 ( 4) + + − 3 17. ( 3) ( 4) 9 − + − + 2 18. + − + − 8 ( 3) ( 2) 3 In Exercises 19–26, evaluate the expression. 19. − 6 8 −2 20. − − 7 4 −11 21. − − 2 5 −7 22. − − 9 ( 5) 14 23. − − − 5 ( 3) −2 24. 4 4 − − −8 25. − 14 20 6− 26. − − 8 ( 3) 11 In Exercises 27–34, evaluate the expression. 27. 4 7 − ⋅ −28 28. ⋅ − 4 ( 3) −12 29. ( 6)( 6) − − 36 30. −15(3) −45 31. − − ⋅ ( 8)( 2) 6 96 32. 4( 5)( 6) − − 120 33. ⋅ − (5 6)( 2) 60 − 34. − − − ( 9)( 1)( 2) −18 In Exercises 35– 42, evaluate the expression. 35. 16 ( 4) − ÷ − 4 36. 63 7 − ÷ −9 37. − 12 12 −1 38. −90 9 −10 39. 56/ 8− −7 40. −75/15 −5 41. −210/14 −15 42. 186/ 6− −31 In Exercises 43–50, evaluate the expression. 43. a) 32 9 b) 23 8 44. a) 25 32 b) 52 25 45. a) −( 5)2 25 b) −52 −25 46. a) −32 −9 b) −( 3)2 9 47. a) −24 −16 b) −( 2)4 16 48. a) −( 3)4 81 b) −34 −81 49. a) 43 − 64 − b) ( 4)3 − 64 − 50. a) 20241 2024 b) 12024 1 63. Elevation Difference Mount Everest in the Himalayas is the highest point on Earth. It is 29,035 ft above sea level. The Mariana Trench in the Pacific Ocean is the lowest point on Earth. It is 36,198 ft below sea level. Determine the vertical height difference between Mount Everest and the Mariana Trench. 65,233 ft 64. Extreme Temperatures The hottest temperature ever recorded in the United States was ° 134 F, which occurred at Greenland Ranch, California, in Death Valley on July 10, 1913. The coldest temperature ever recorded in the United States was −80°F, which occurred at Prospect Creek Camp, Alaska, in the Endicott Mountains on January 23, 1971. Determine the difference between these two temperatures. ° 214 F m The New York Stock Exchange Ted Pink/Alamy Stock Photo
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