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CHAPTER 1 Whole Numbers, Integers, and Introduction to Algebra

1.6 Chapter Review

Review Exercises

Use Place Value with Whole Number

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

1. 26,915

a) 1
b) 2
c) 9
d) 5
e) 6

2. 359,417

a) 9
b) 3
c) 4
d) 7
e) 1

3. 58,129,304

a) 5
b) 0
c) 1
d) 8
e) 2

4. 9,430,286,157

a) 6
b) 4
c) 9
d) 0
e) 5

In the following exercises, name each number.

5. 6,104 6. 493,068
7. 3,975,284 8. 85,620,435

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

9. three hundred fifteen 10. sixty-five thousand, nine hundred twelve
11. ninety million, four hundred twenty-five thousand, sixteen 12. one billion, forty-three million, nine hundred twenty-two thousand, three hundred eleven

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

Round to the nearest ten.

13. a) 407 b) 8,564

Round to the nearest hundred.

14. a) 25,846 b) 25,864

In the following exercises, round each number to the nearest a) hundred b) thousand c) ten thousand.

15. 864,951 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

17. 168 18. 264
19. 375 20. 750
21. 1430 22. 1080

Find Prime Factorizations and Least Common Multiples

In the following exercises, find the prime factorization.

23. 420 24. 115
25. 225 26. 2475
27. 1560 28. 56
29. 72 30. 168
31. 252 32. 391

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

33. 6,15 34. 60, 75

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

35. 24, 30 36. 70, 84

Use Variables and Algebraic Symbols

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

37. 25 – 7 38. 5 · 6
39. 45 ÷ 5 40. x + 8
41. 42 ≥ 27 42. 3n = 24
43. 3 ≤ 20 ÷ 4 44. a ≠ 7 · 4

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

45. 6 · 3 + 5 46. y – 8 = 32

Simplify Expressions Using the Order of Operations

In the following exercises, simplify each expression.

47. 35 48. 108

In the following exercises, simplify

49. 6 + 10/2 + 2 50. 9 + 12/3 + 4
51. 20 ÷ (4 + 6) · 5 52. 33 · (3 + 8) · 2
53. 42 +52 54. (4 + 5)2

Evaluate an Expression

In the following exercises, evaluate the following expressions.

55. 9x + 7 when x = 3 56. 5x – 4 when x = 6
57. x4 when x = 3 58. 3x when x = 3
59. x2 + 5x – 8 when x = 6 60. 2x + 4y – 5 when x = 7, y = 8

Simplify Expressions by Combining Like Terms

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

61. 12n 62. 9x2

In the following exercises, identify the like terms.

63. 3n, n2, 12, 12p2, 3, 3n2 64. 5, 18r2, 9s, 9r, 5r2, 5s

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

65. 11x2 + 3x + 6 66. 22y3 + y + 15

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

67. 17a + 9a 68. 18z + 9z
69. 9x + 3x + 8 70. 8a + 5a + 9
71. 7p + 6 + 5p – 4 72. 8x + 7 + 4x – 5

Translate an English Phrase to an Algebraic Expression

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

73. the sum of 8 and 12 74. the sum of 9 and 1
75. the difference of x and 4 76. the difference of x and 3
77. the product of 6 and y 78. the product of 9 and y
79. Derek bought a skirt and a blouse. The skirt cost $15 more than the blouse. Let b represent the cost of the blouse. Write an expression for the cost of the skirt. 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.

Use Negatives and Opposites of Integers

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

81.
a) 6___2
b) -7___4
c) -9___-1
d) 9___-3		 82.
a) -5___1
b) -4___-9
c) 6___10
d) 3___-8

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

83. a) -8 b) 1 84. a) -2 b) 6

In the following exercises, simplify.

85. (–19) 86. (–53)

In the following exercises, simplify.

87. −m when
a) m = 3
b) m=-3		 88. −p when
a) p = 6
b) p = -6

Simplify Expressions with Absolute Value

In the following exercises,, simplify.

89. a) |7| b) |-25| c) |0| 90. a) |5| b) |0| c) |-19|

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

91.
a) – 8 ___ |–8|
b) – |–2|___ –2		 92.
a) –3|___ – | –3|
b) 4 ___ – | –4|

In the following exercises, simplify.

93. |8 – 4| 94. |9 – 6|
95. 8 (14 – 2 |- 2|) 96. 6(13 – 4 |-2|)

In the following exercises, evaluate.

97. a) |x| when x = -28 b) |-x| when x =-15 98. a) |y| when y = -37 b) |-z| when z=-24

Add Integers

In the following exercises, simplify each expression.

99. -200 + 65 100. -150 + 45
101. 2 + (-8) + 6 102. 4 + (-9) + 7
103. 140 + (-75) + 67 104. -32 + 24 + (-6) + 10

Subtract Integers

In the following exercises, simplify.

105. 9 – 3 106. -5 – (-1)
107. a) 15 – 6 b) 15 + (-6) 108. a) 12 – 9 b) 12 + (-9)
109. a) 8 – (-9) b) 8 + 9 110. a) 4 – (-4) b) 4 + 4

In the following exercises, simplify each expression.

111. 10 – (-19) 112. 11 – ( -18)
113. 31 – 79 114. 39 – 81
115. -31 – 11 116. -32 – 18
117. -15 – (-28) + 5 118. 71 + (-10) – 8
119. -16 – (-4 + 1) – 7 120. -15 – (-6 + 4) – 3

Multiply Integers

In the following exercises, multiply.

121. -5 (7) 122. -8 (6)
123. -18(-2) 124. -10 (-6)

Divide Integers

In the following exercises, divide.

125. -28 ÷ 7 126. 56 ÷ ( -7)
127. -120 ÷ -20) 128. -200 ÷ 25

Simplify Expressions with Integers

In the following exercises, simplify each expression.

129. -8 (-2) -3 (-9) 130. -7 (-4) – 5(-3)
131. (-5)3 132. (-4)3
133. -4 · 2 · 11 134. -5 · 3 · 10
135. -10(-4) ÷ (-8) 136. -8(-6) ÷ (-4)
137. 31 – 4(3-9) 138. 24 – 3(2 – 10)

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

139. x + 8 when
a) x = -26
b) x = -95		 140. y + 9 when
a) y = -29
b) y = -84
141. When b = -11, evaluate:
a) b + 6
b) −b + 6		 142. When c = -9, evaluate:
a) c + (-4)
b) −c + (-4)
143. p2 – 5p + 2 when p = -1 144. q2 – 2q + 9 when q = -2
145. 6x – 5y + 15 when x = 3 and y = -1 146. 3p – 2q + 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.

147. the sum of -4 and -17, increased by 32 148. a) the difference of 15 and -7 b) subtract 15 from -7
149. the quotient of -45 and -9 150. the product of -12 and the difference of c and d.

Use Integers in Applications

In the following exercises, solve.

151. Temperature The high temperature one day in Miami Beach, Florida, was 76° F. That same day, the high temperature in Buffalo, New York was −8° F. What was the difference between the temperature in Miami Beach and the temperature in Buffalo? 152. CheckingAccount Adrianne has a balance of -$22 in her checking account. She deposits $301 to the account. What is the new balance?

Review Exercise Answers

1. a) tens b) ten thousands c) hundreds d) ones e) thousands 3. a) ten millions b) tens c) hundred thousands d) millions e) ten thousands 5. six thousand, one hundred four
7. three million, nine hundred seventy-five thousand, two hundred eighty-four 9. 315 11. 90,425,016
13. a)410b)8,560 15. a)865,000 b)865,000c)860,000 17. by 2,3,6
19. by 3,5 21. by 2,5,10 23. 2 · 2 · 3 · 5 · 7
25. 3 · 3 · 5 · 5 27. 2 · 2 · 2 · 3 · 5 · 13 29. 2 · 2 · 2 · 3 · 3
31. 2 · 2 · 3 · 3 · 7 33. 30 35. 120
37. 25 minus 7, the difference of twenty-five and seven 39. 45 divided by 5, the quotient of forty-five and five 41. forty-two is greater than or equal to twenty-seven
43. 3 is less than or equal to 20 divided by 4, three is less than or equal to the quotient of twenty and four 45. expression 47. 243
49. 13 51. 10 53. 41
55. 34 57. 81 59. 58
61. 12 63. 12 and 3, n2 and 3n2 65. 11×2, 3x, 6
67. 26a 69. 12x + 8 71. 12p + 2
73. 8 + 12 75. x – 4 77. 6y
79. b + 15 81. a) > b) < c) < d) > 83. a) 8 b) -1
85. 19 87. a) -3 b) 3 89. a) 7 b) 25 c) 0
91. a) < b) = 93. 4 95. 80
97. a) 28 b) 15 99. -135 101. 0
103. 132 105. 6 107. a) 9 b) 9
109. a) 17 b) 17 111. 29 113. -48
115. -42 117. 18 119. -20
121. -35 123. 36 125. -4
127. 6 129. 43 131. -125
133. -88 135. -5 137. 55
139. a) -18 b) -87 141. a) -5 b) 17 143. 8
145. 38 147. (-4 + (-17)) + 32; 11 149. \dfrac{-45}{-9} ;5
151. 84 degrees F

Practice Test

1. Write as a whole number using digits: two hundred five thousand, six hundred seventeen. 2. Find the prime factorization of 504.
3. Find the Least Common Multiple of 18 and 24. 4. Combine like terms: 5n + 8 + 2n – 1.

In the following exercises, evaluate.

5. −|x| when x = -2 6. 11 – a when a = -3
7. Translate to an algebraic expression and simplify: twenty less than negative 7. 8. Monique has a balance of  −$18 in her checking account. She deposits $152 to the account. What is the new balance?
9. Round 677.1348 to the nearest hundredth. 10. Simplify  expression  -6 (-2) –  3 · 4 ÷ (-6)
11.  Simplify  expression   4(-2) + 4 ·2 –  {(-3)}^{3} 12. Simplify  expression  -8(-3) ÷ (-6)
13.Simplify  expression  21 – 5(2 – 7) 14. Simplify  expression  2 + 2(3 – 10) – {(2)}^{3}

Practice Test Answers

1. 205,617 2.  2 · 2 · 2 · 3 · 3 · 7 3. 72
4. 7n + 7 5. -2 6. 14
7. -7 – 20; -27 8. $ 134 9. 677.13
10. 10 11. 27 12. -4
13. 46 14. -20

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Introductory Algebra Copyright © 2021 by Izabela Mazur is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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