## Basic Math and Pre-Algebra

**APPENDIX B. Extra Practice Answers**

*Part I: Arithmetic*

You used the number 8,472,019 to answer questions 1-5.

1. 0 is in the hundreds place.

2. 4 is in the hundred-thousands place.

3. 2 is in the thousands place.

4. 1 is in the tens place.

5. 8 is in the millions place.

6. 7,300 = 7.3 x 10^{3}

7. 12,000 = 1.2 x 10^{4}

8. 903 = 9.03 x 10^{2}

9. 2,450,000 = 2.45 x 10^{6}

10. 691,000 = 6.91 x 10^{5}

11. 8 x 3 + 5^{2} = 24 + 25 = 49

12. 27 - 8 ÷ 4 X 10 = 27 - 2 x 10 = 27 - 20 = 7

13. 4(7 -3) - 3(7 - 4) = 4(4) - 3(3) = 16 - 9 = 7

14. (56 - 8) + 4 - 10 = 48 ÷ 4 - 10 = 12 - 10 = 2

15. 8 x (3 + 5)^{2} = 8 x (8)^{2} = 8 x 64 = 512

16. -19 + 39 ÷ -3 = -19 + -13 = -32

17. -5(-4 + -8) + 5(4 + 7) = -5(-12) + 5(11) = 60 + 55 = 115

18. (16 - 37) ÷ -7 = -21 ÷ -7 = 3

19. 20 x -3 + (-7)^{2} = 20 x -3 + 49 = 60 – 49 = 11

20. 17 - 33 - 9(12 - 8) = 17 - 33 - 9(4) = 17 - 33 - 36 = -16 - 36 = -52

21. 28 0 = 2^{3} x 5 x 7

22. 5,005 = 5 x 7 x 11 x 13

23. 510 = 2 x 3 x 5 x 17 and 272 = 2^{4} x 17; GCF = 2 x 17 = 34

24. 91 = 7 x 13 and 119 = 7 x 17; LCM = 7 x 13 x 17 = 1,547

25. 42 = 2 x 3 x 7 and 90= 2 x 3^{2} x 5; GCF = 2 x 3 = 6 and LCM = 2 x 3^{2} x 5 x 7 = 630

31. 3.78 + 9.3 = 13.08

32. 29.3 - 18.53 = 10.77

33. 6.23 x 2.04 = 12.7092

34. 4.374 ÷ 1.2 = 3.645

35. 1.1 ÷ 0.88 = 1.25

36. 20.25 ounces of water

37. 1.5 pounds of dark chocolate candies

38. 30 cups of wheat flour

39. 15 gallons of chili

40. 66 yards of solid fabric

41. 8.1 is 18% of 45.

42. Thirty-three is 30% of 110.

43. 38 is 16% of 237.5.

44. 26% decrease

45. 12.5% increase

57. x + y = 8

58. 3x – y = 7

59. y = 5

60. x = -4

For questions 61 and 62, several answers are possible. Possible answers are given.

61. A ray: and others

62. A line segment: and others

63. An acute angle: ∠PRA

64. An obtuse angle: ∠ART

65. A pair of vertical angles: ∠ITR and ∠CTE or ∠ITE and ∠RTC

66. The angle that corresponds to ∠HDE is ∠JEF.

67. ∠CDH and ∠BEF are a pair of alternate exterior angles.

68. If m∠ADC = 20°, m∠DEJ = 180 - 20 = 160°.

69. The measure of ∠HJK is 90°.

70. If m∠DEJ — 150°, the measure of ∠HDE is 180 - 150 = 30°.

71. If m∠J = 80°, m∠M 80°, then m∠A = 180 - (80° + 80°) = 20°.

72. If AR = 7 cm, RM = 13 cm, and ∆ARM is isosceles, then AM = 7 cm or 13 cm.

73. must be at least 13 cm but not more than 21 cm.

74. ∆MAT cannot be a right triangle because 4^{2} + 4^{2} ≠ 6^{2}.

75. ACOW is a right triangle with right angle AO. If CW = 65 cm and CO = 25 cm, then

76. If ∆PAT ≅ ∆POT and m∠A = 70°, then m∠O = 70!

77. ∆DOG ≅ ∆CAT, and DO = 28 inches, OG = 34 inches, and DG = 45 inches, CT = DG = 45 inches

78. PG = 27 cm

79. RU = 28 cm

80. m∠PAF = m∠L + m∠P, so 115° = 75° + m∠P, and m∠P = 40°

81. ACFH is a quadrilateral with and ACFH is a rectangle.

82. BJ = JK = KD = DB. BDKJ is a rhombus.

83. and JKGI is a parallelogram.

84. In rhombus BDJK, BD = 12 cm. In parallelogram JKGI, GI = 12 cm.

85. A = bh = 12 x 5 = 60 square inches

86. If m∠A = 58°, m∠B = 180 - 58 = 122°.

87. If BC = 29 cm and AD = 41 cm,

88. If the trapezoid is isosceles. If m∠Q = 119°, m∠S = m∠P = 180 – 119 = 61°.

90. The median = so the height is 25 cm.

91. Arc measures 76°, so m∠APB = 1/2(76) = 38°.

94. C = 2 x π x 1 = 14π cm.

95. Diameter is 24 cm, so r = 12 cm. A = π x 12^{2} = 144π cm^{2}

103. A diameter of 20 cm means a radius of 10 cm.

104. cubic inches.

105. A sphere with a diameter of 60 cm has radius of 30 cm.

116. Albuquerque and Fort Worth appear to have had the lowest rate of job growth.

117. Three cities—Boise, Las Vegas, and Austin—appear to have job growth rates above 2.5%.

118. According to the graph, the percent of adults smoking cigarettes showed an increase from about 1990 to 1996 with the sharpest increase from 1995 to 1996.

119. According to the graph, the percent of adults smoking cigarettes remained relatively constant from 1985 to 1990.

120.

Based on the circle graph, 18% + 15% = 33% of people said their favorite food was a fruit or vegetable.

121. Range = 30 - 6 = 24.

122. Median = 18.

123. First quartile = 14. Third quartile = 26.

125. Standard deviation ≈ 7.23.

Data |
Data - Mean |
(Data - Mean) |

6 |
-12.9 |
166.64 |

12 |
-6.9 |
47.74 |

14 |
-4.9 |
24.10 |

16 |
-2.9 |
8.46 |

18 |
-0.9 |
0.83 |

20 |
1.1 |
1.19 |

22 |
3.1 |
9.55 |

26 |
7.1 |
50.28 |

28 |
9.1 |
82.64 |

30 |
11.1 |
123.01 |

Sum of the squared deviations: 522.91

Divided by 10: ÷ 10 = 52.291

Square root: √52.291 ≈ 72.3