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 |
2. 359,417 a) 9 |
|
3. 58,129,304 a) 5 |
4. 9,430,286,157 a) 6 |
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. ;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 – | 12. Simplify expression -8(-3) ÷ (-6) |
| 13.Simplify expression 21 – 5(2 – 7) | 14. Simplify expression 2 + 2(3 – 10) – |
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 |