chpater 10 by Greg Hancin

Name: ________________________ Class: ___________________ Date: __________

sample test questions on integers Multiple Choice Identify the choice that best completes the statement or answers the question. ____

1. Write an addition statement represented by this number line. Find the sum.

a. ____

(+2) + (−3); –1

(−3) + (+2); +5

2. Use a number line to add. (+2) + (–1) a.

____

(+2) + (+3); +5

+1 d.

–2

____

+3 b.

____

(+2) + (−3); +1

–1

3. Add. (+18) + (+19) a. +1

–37

–1

+37

4. Add. (–28) + (–14) a. –14

+42

–42

+14

5. Add. (–41) + (+11) a. +52

–52

+30

–30

____

6. Gail owns a small business. There was a profit of $17 on Saturday and a loss of $11 on Sunday. Find the total profit or loss for the weekend. a. $6 loss b. $28 profit c. $6 profit d. $28 loss

____

7. During the day the temperature was 16°C. At night, the temperature dropped 19°C. What was the temperature at night? a. 35°C b. 3°C c. –35°C d. –3°C

____

8. Add. (–10) + (–5) + (–6) a. –9 b.

–11

–1

–21

ID: A

Name: ________________________ ____

9. Add. (–218) + (+157) + (–162) a. –223 b. –537

ID: A

+537

+223

____ 10. Add. (+9) + (–23) + (+14) + (–10) a. +36 b. –10

+10

+18

____ 11. Add. (–9) + (+27) + (–22) + (–14) a. –18 b. +10

–72

+26

____ 12. The temperature of a town is 18°C. The weather forecast says that the temperature will drop 9°C. Write an expression to find the predicted temperature. What will the temperature be? a. (+9) + (–18); –27°C c. (+18) + (+9); 14°C b. (+9) + (+18); 27°C d. (+18) + (–9); 9°C ____ 13. Rewrite as an addition statement. (+10) – (–14) – (+17) a. (–10) + (+14) + (–17) c. (+10) + (+14) + (–17) b. (–10) + (–14) – (–17) d. (+10) + (+14) – (+17) ____ 14. Which number line model can you use to simplify –5 − (–6)? a.

–5 − (–6) = –1 b.

–5 − (–6) = –11 c.

–5 − (–6) = +1 d.

–5 − (–6) = +11

Name: ________________________

ID: A

____ 15. Use a number line to subtract. (+3) – (–5) a.

(+3) – (–5) = +8 b.

(+3) – (–5) = +8 c.

(+3) – (–5) = –8 d.

(+3) – (–5) = –8 ____ 16. Use a number line to subtract. (–1) – (+3) a.

(–1) – (+3) = –4 b.

(–1) – (+3) = –4 c.

(–1) – (+3) = +4 d.

(–1) – (+3) = +4 ____ 17. Use a number line to subtract. (+9) − (–7) a. –16 b. +16

–2

Name: ________________________

ID: A

____ 18. Write (+58) – (–31) as an addition statement. Then find the sum. a. (+58) + (+31); +89 c. (+58) + (+66); +124 d. (+58) − (+31); +27 b. (+58) − (+66); –8 ____ 19. Subtract. (+2) − (+31) a. –29 b.

–33

+29

+33

____ 20. Subtract. (+8) − (–42) b. a. –34

+34

–50

+50

____ 21. Evaluate. (+9) − (–9) − (–2) a. –2 b. +16

+20

–20

____ 22. Evaluate. (+12) + (+5) − (+4) a. +11 b. –3

+13

____ 23. The highest location in a certain country is 4525 m above sea level. The lowest point in the same country is 192 m below sea level. a) Find the difference of the 2 elevations. b) A city is 2221 m above sea level. Is this elevation closer to the highest point or the lowest point? a. 4717 m; lowest c. 4333 m; highest b. 4333 m; lowest d. 4717 m; highest ____ 24. What is the result of 8 subtract negative 7? a. –1 b. –15

____ 25. Find the result of 6 add negative 8 then subtract negative 5. a. –7 b. 7 c. 3

–3

____ 26. Evaluate. 50 − 32 a. 18

–18

–82

____ 27. Evaluate. 16 − 7 − 6 a. 15

–15

–3

____ 28. Evaluate. −17 + 9 − 7 a. 15 b.

–15

____ 29. Evaluate. 10 − 6 + 7 a. 11

–3

–7

____ 30. Find the missing integer that makes this statement true. 2 − a. 7 b. –11 c. 11

= –9

____ 31. Add brackets to make this an addition statement of integers. –5 – 20 + 13 c. (−5) + (−20) + (+13) a. (–5) − (+20) + (+13) b. (−5) + (−20) + (−13) d. −(+5) − (+20) + (+13) ____ 32. Evaluate. 5 − 10 + (–8) a. +3 b.

–13

–3

Name: ________________________ ____ 33. Evaluate. 4 + (−7) − (−5) a. 2 b.

ID: A

–8

____ 34. Lynn has $169 in her savings account. She withdraws $91, deposits $52, and then withdraws $85. Find the balance of Lynn’s account. a. $397 b. −$59 c. $293 d. $45 ____ 35. Write this sum as a product and evaluate. (–5) + (–5) + (–5) + (–5) a. 4 × (–5); –20 c. 5 × (–5); –25 b. 2 × (–5) + 2(–5); +22 d. (–5) × (–5); –18 ____ 36. Find this product. (+9)(−5) a. –47 b. –45

–43

+81

____ 37. Find this product. (−6)(−8) a. +48 b. +46

+50

+47

____ 38. Find this product. (− 15) × (+11) a. –165 b. –26

–4

+165

____ 39. Find this product. (−8)(+5)(+7) a. –278 b. –281

–40

–280

____ 40. Find this product. (+7)(−3)(+3) a. –21 b. –64

–61

–63

____ 41. Find this product. (+12) × (−4) × (−6) a. +288 b. –288

–36

+36

(+2) × (−6) (+4) − (+16)

(+2) × (+6) (+4) + (+16)

____ 42. Which pair of expressions has the same value? a. (−2) × (+6) b. (−2) × (−6) c. (+16) + (−4) (+4) + (−16)

____ 43. An arctic air current moved into a region where the temperature was originally 25°C. The temperature began to fall at a steady rate of 4°C per hour. What was the temperature after 9 h? a. –7°C b. 36°C c. –11°C d. –15°C ____ 44. A deep-sea diver must descend and ascend in short steps to equalize pressure on his body. Suppose a diver started at 27 m below the water surface and rose in 5 steps of 5 m each. Use an integer to describe his new position in relation to the water surface. a. –2 m b. +2 m c. +25 m d. –25 m ____ 45. Find this product. (− 2) × (− 3) × (− 5) a. –10 b. +13

–30

____ 46. Find this product. (− 2) × (+10) × (+1) × (+11) a. +108 b. –9

–219

–220

Name: ________________________

ID: A

____ 47. Divide. (−42) ÷ (−7) b.

–6

−

1 6

____ 48. Divide. (+50) ÷ (−5) a. +10

–10

+250

–250

____ 49. Divide. (–54) ÷ (+9) a. –6

–8

–5

–1

____ 50. Divide. (+40) ÷ (+8) a. +48

–5

–48

+30

–2

–30

–7

−

1 3

–3

____ 51. Divide. (− 20) ÷ (− 10) a. +2 b. ____ 52. Find this quotient. a.

−

− 84 +12

1 7

____ 53. Find this quotient.

1 6

1 7

+24 −8

1 3

____ 54. A mountain climber is at an elevation of 3640 m. After 5 h, he is at an elevation of 1215 m. Use this formula to find the climber’s vertical speed. Final elevation − Initial elevation Vertical speed = Time a. –2425 m/h b. –728 m/h c. –485 m/h d. –971 m/h ____ 55. One day at 3 p.m., the temperature was −6°C in a city in Alaska. At 10 p.m., the temperature was −20°C. What was the average change in temperature per hour? b. −3°C c. −4°C a. −14°C

−2°C

____ 56. Evaluate. 5 × 7 + 2 a. –4

____ 57. Evaluate. 15 − 40 ÷ 5 a. 7 b.

–5

–185

____ 58. Evaluate. 8 × (−4) ÷ 1 a. –32 b.

–33

–58

–57

____ 59. Evaluate. (–5) × (9 − 7) + (–5) a. –15 b. –14

Name: ________________________

ID: A

____ 60. Evaluate. 8 + (−42) ÷ 7 + 7 × 3 a. 27 b. −1

____ 61. Evaluate. −(−4) + 3(11 − 3) a. 20 b. –28

____ 62. Evaluate. −4 × (−6) − (−24) ÷ (−6) a. 28 b. 0

–8

____ 63. Evaluate. −16 + 18 ÷ (−6) + 7 a. 12 b. –6

–12

____ 64. Write 2 expressions to describe the total area of this figure. Then find the total area of the figure.

a. b. c. d.

8(6) − 2(6); 6 × (8 − 2); area = 36 (8 × 6) + (2 × 6); 6 × (8 + 2); area = 60 6 × 10; (8 + 2) + 6; area = 60 (8 + 6) × (2 + 6); 6 + (8 × 2); area = 60

Short Answer 65. Use a number line to add (+6) + (–6) + (+7) + (–4) 66. An elevator on the 10th floor goes down 9 floors. Then it goes up 19 floors, down 3, and finally up 12. What floor does it end up on? Explain your answer. 67. Add. (–172) + (+257) + (–132) + (+195) 68. Find the missing integer that completes this equation. (–42) = (–13) + 69. Use <, >, or = to complete this sentence. (+10) + (–22)

(–28) + (–11)

70. State if this statement is always, sometimes, or never true. Use examples to explain. “The result of subtracting a positive integer from a positive integer is a positive integer.” 71. State if this statement is always, sometimes, or never true. Use examples to explain. “The result of subtracting a positive integer from a negative integer is a positive integer.” 72. State if this statement is always, sometimes, or never true. Use examples to explain. “The result of subtracting a negative integer from a negative integer is a positive integer.”

Name: ________________________

ID: A

73. State if this statement is always, sometimes, or never true. Use examples to explain. “The result of subtracting a negative integer from a positive integer is a positive integer.” 74. Use a number line to evaluate. (–5) – (–7) 75. Evaluate. (–16) – (–11) + (–6) 76. Evaluate. 20 − 9 − 10 77. Evaluate. 155 − 91 − 106 + 61 78. Draw a number line to evaluate. 6 − 9 + 5 79. Find the missing integer that makes this statement true. –28 − = 52 80. In an experiment, the temperature change was –3°C every 30 min. If the initial temperature was 8°C, what was the temperature after 2 81. Predict the sign of this quotient. (–2) ÷ (+10) 82. Add brackets to make this statement true. (−32) ÷ (−4) ÷ (+2) = +16 83. Add brackets to make each statement true. (−128) ÷ (+8) ÷ (−4) ÷ (+2) = +8 (−128) ÷ (+8) ÷ (−4) ÷ (+2) = +32 (−128) ÷ (+8) ÷ (−4) ÷ (+2) = +128 84. Which resulting integer is greater? (+144) ÷ (−3) × (+8) or (+144) × (−3) ÷ (+8)? 85. Which expression has a value closer to −1? Explain. È ˘ A: 3 × (−7) 2 − 4 × 6 ÍÍÎ 2 − (−4) ˙˙˚ B: (−3) 3 −

(6)(−12)(−3) (−9)

86. Which expression has a greater value? Explain. (−3) 2 + (−9) 2 or (−3 − 9) 2 87. Evaluate. (−4)3 − (+4)3 88. Evaluate. (–8)(–8) + (–5)(6 + 11)

1 h? 2

Name: ________________________

ID: A

89. Evaluate. (–4) + (–4)2 + (–4)3 + (–4)4 90. Find the mean of this set of data. –4, 5, –10, –7, 6 Problem 91. In a board game, 3 players can gain or lose points. Here are the results for 3 games. Game 1

Game 2

Game 3

Player 1

–139

+303

–123

Player 2

+269

–187

–33

Player 3

–170

+127

+169

a) Which player won each game? b) Who had the highest total score after 3 games? What was the score? 92. Describe the signs of the results of adding integers with the same signs and with different signs. 93. Aaron will buy a stock only if it shows an overall increase over the next 3 days. A stock has a daily increase of $30 in the first day, a decrease of $45 in the next day, and an increase of $25 on the third day. Will Aaron buy the stock? Explain. 94. The sum of 3 consecutive integers is –693. Find the integers. 95. The table shows the monthly income and expenses of a new business over 6 months. a) Which months show a profit? Explain your answer. b) Did the business make a profit or loss over the 6 months? Month

Income (I)

Expenses (E)

$258

$335

$287

$367

$427

$330

$359

$314

$333

$383

$504

$449

96. Write the next 3 terms in this pattern. Then write a pattern rule. +3, –1, –5, ... 97. Write add or subtract symbols to make this statement true. (–18) (+39) (–32) = (+53) 98. Find 2 negative integers that have a sum of –11 and a difference of 3. Explain your answer.

Name: ________________________

ID: A

99. x is an integer greater than –45 but less than –20. y is an integer greater than –75 but less than –50. a) What is the greatest possible value of x − y? b) What is the greatest possible value of y − x? Justify your answers. 100. Find a value of n such that (–5) − (–7) > (+9) + (n) 101. A dodecahedron is a solid with 10 faces. You have a blue dodecahedron labelled 1 to 10 and a red one labelled −1 to −10. You roll the 2 dodecahedrons and add the integers that show. a) What is the highest possible sum that will show? Justify your answer. b) How many ways can you get a sum of –6? 102. This table shows the depths reached by a submersible recorded at 15 min intervals. Describe and show the vertical movements of the submersible on a number line. Time (min)

Depth (m)

–9

–12

–5

–6

–4

103. In a board game, the letters of the alphabet are given these integer values. –5

A E I O U

D G L N R S T

–9

B C M P

+11

F H K V W Y

+13

J X

–15

Q Z

Find words from the list below that have: a) the same value b) the least value c) the greatest value d) a value of 0 NUMBER, MULTIPLY, SUBTRACT, QUESTION, QUIZ

104. Jake borrowed $25 from his mother and spent $21. He then earned $22 and spent $15. Does Jake have enough money to repay his mother? Explain. 105. This pattern continues. (–10 + 8), (–11 + 7), (–12 + 6), ... a) Evaluate the first 3 terms in the pattern. b) Write the next 3 terms in the pattern. c) Calculate the sum of the first 6 terms.

Name: ________________________

ID: A

106. Write the next 2 terms in this pattern. Then write a pattern rule. 5, –20, 80, –320, .... 107. Write the next 3 terms in this pattern. Then write a pattern rule. –4, +16, –64, ... 108. A loan for a motorbike requires equal payments of $150 per month for 3 years. a) What is the total amount paid over the 3 years? b) Suppose a down payment of $1000 was made in addition to the monthly payments. What was the total cost of the motorbike? 109. These statements show that product of negative integers could be positive or negative. (−1) × (−1) = +1 (−1) × (−1) × (−1) = −1 (−1) × (−1) × (−1) × (−1) = +1 How can you predict the sign of the product without multiplying? Give 2 another statements that justify your prediction. 110. Explain how you could predict the sign of the product of −8, +9, +7, and −4 without actually multiplying. 111. The product of 3 integers is −24. The sum of the integers is −12. What are the 3 integers? Show your work. 112. Write the next 3 terms in this pattern. Then write a pattern rule. +729, –243, +81, ... 113. Simplify.

−30 +42 −14 × × +14 −7 +10

114. Find 2 integers that make this statement true. ÷ = –1 (+16) ÷ 115. Luther and Nicole were on a hiking trip. They began at an elevation of 139 m above sea level and descended to an elevation of 21 m below sea level in 8 h. a) Write a division expression that can be used to find their average change in elevation per hour. b) Use an integer to represent their average change in elevation per hour. 116. Find the greatest possible negative integer that can be divided completely by −2, −3, −4, −5, −6, or −7. Explain your answer. 117. Write 3 integers such that the sum of the first 2 integers divided by the third integer gives this result: a) 0 b) −1 c) +1 Describe how the 3 integers are related in each case.

Name: ________________________

ID: A

118. Add brackets to make each statement true. 8 + 5 × (−6) − 4 = −82 8 + 5 × (−6) − 4 = −42 8 + 5 × (−6) − 4 = −130 119. I think of a number. I multiply it by 6. I subtract 8. I multiply the result by 3. I subtract 16. The answer is –4. What number did I think of? Justify your answer. 120. Write an expression for each statement and evaluate. a) Divide the sum of –13 and 37 by 6. b) Subtract the square of –10 from the product of 5 and 10. 121. Evaluate each expression. A: (−1) + (−1)2 B: (−1) + (−1)2 + (−1)3 C: (−1) + (−1)2 + (−1)3 + (−1)4 If this pattern was continued, when would you get answers of 0? 122. Describe the steps you would use to evaluate this expression. Then evaluate the expression. 3 + (−8) − (10 + 4) × 2

ID: A

sample test questions on integers Answer Section MULTIPLE CHOICE 1. ANS: STA: 2. ANS: STA: 3. ANS: STA: 4. ANS: STA: 5. ANS: STA: 6. ANS: STA: 7. ANS: STA: 8. ANS: STA: 9. ANS: STA: 10. ANS: STA: 11. ANS: STA: 12. ANS: STA: 13. ANS: STA: 14. ANS: STA: 15. ANS: STA: 16. ANS: STA: 17. ANS: STA: 18. ANS: STA: 19. ANS: STA: 20. ANS: STA:

A 8m22 C 8m22 D 8m22 C 8m22 D 8m22 C 8m22 D 8m22 D 8m22 A 8m22 B 8m22 A 8m22 D 8m22 C 8m22 C 8m22 B 8m22 A 8m22 B 8m22 A 8m22 A 8m22 D 8m22

PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP:

1 DIF: Easy Number Sense and Numeration 1 DIF: Easy Number Sense and Numeration 1 DIF: Easy Number Sense and Numeration 1 DIF: Easy Number Sense and Numeration 1 DIF: Moderate Number Sense and Numeration 1 DIF: Moderate Number Sense and Numeration 1 DIF: Moderate Number Sense and Numeration 1 DIF: Moderate Number Sense and Numeration 1 DIF: Moderate Number Sense and Numeration 1 DIF: Moderate Number Sense and Numeration 1 DIF: Moderate Number Sense and Numeration 1 DIF: Moderate Number Sense and Numeration 1 DIF: Easy Number Sense and Numeration 1 DIF: Easy Number Sense and Numeration 1 DIF: Easy Number Sense and Numeration 1 DIF: Easy Number Sense and Numeration 1 DIF: Easy Number Sense and Numeration 1 DIF: Moderate Number Sense and Numeration 1 DIF: Moderate Number Sense and Numeration 1 DIF: Moderate Number Sense and Numeration

REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY:

9.1 Adding Integers Knowledge and Understanding 9.1 Adding Integers Knowledge and Understanding 9.1 Adding Integers Knowledge and Understanding 9.1 Adding Integers Knowledge and Understanding 9.1 Adding Integers Knowledge and Understanding 9.1 Adding Integers Application 9.1 Adding Integers Application 9.1 Adding Integers Knowledge and Understanding 9.1 Adding Integers Knowledge and Understanding 9.1 Adding Integers Knowledge and Understanding 9.1 Adding Integers Knowledge and Understanding 9.1 Adding Integers Knowledge and Understanding 9.2 Subtracting Integers Knowledge and Understanding 9.2 Subtracting Integers Knowledge and Understanding 9.2 Subtracting Integers Knowledge and Understanding 9.2 Subtracting Integers Knowledge and Understanding 9.2 Subtracting Integers Knowledge and Understanding 9.2 Subtracting Integers Knowledge and Understanding 9.2 Subtracting Integers Knowledge and Understanding 9.2 Subtracting Integers Knowledge and Understanding

ID: A 21. ANS: STA: 22. ANS: STA: 23. ANS: STA: 24. ANS: STA: 25. ANS: STA: 26. ANS: STA: 27. ANS: STA: 28. ANS: STA: 29. ANS: STA: 30. ANS: STA: 31. ANS: STA: 32. ANS: STA: 33. ANS: STA: 34. ANS: STA: 35. ANS: STA: 36. ANS: STA: 37. ANS: STA: 38. ANS: STA: 39. ANS: STA: 40. ANS: STA: 41. ANS: STA: 42. ANS: STA: 43. ANS: STA:

C 8m22 C 8m22 D 8m22 C 8m22 C 8m22 A 8m22 B 8m22 C 8m22 A 8m22 C 8m22 C 8m22 C 8m22 A 8m22 D 8m22 A 8m21 B 8m22 A 8m22 A 8m22 D 8m22 D 8m22 A 8m22 C 8m22 C 8m22

PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP: PTS: TOP:

1 DIF: Moderate Number Sense and Numeration 1 DIF: Moderate Number Sense and Numeration 1 DIF: Difficult Number Sense and Numeration 1 DIF: Easy Number Sense and Numeration 1 DIF: Easy Number Sense and Numeration 1 DIF: Easy Number Sense and Numeration 1 DIF: Easy Number Sense and Numeration 1 DIF: Easy Number Sense and Numeration 1 DIF: Easy Number Sense and Numeration 1 DIF: Moderate Number Sense and Numeration 1 DIF: Moderate Number Sense and Numeration 1 DIF: Moderate Number Sense and Numeration 1 DIF: Moderate Number Sense and Numeration 1 DIF: Moderate Number Sense and Numeration 1 DIF: Easy Number Sense and Numeration 1 DIF: Easy Number Sense and Numeration 1 DIF: Easy Number Sense and Numeration 1 DIF: Easy Number Sense and Numeration 1 DIF: Moderate Number Sense and Numeration 1 DIF: Moderate Number Sense and Numeration 1 DIF: Moderate Number Sense and Numeration 1 DIF: Moderate Number Sense and Numeration 1 DIF: Moderate Number Sense and Numeration

REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY: REF: KEY:

9.2 Subtracting Integers Knowledge and Understanding 9.2 Subtracting Integers Knowledge and Understanding 9.2 Subtracting Integers Application 9.3 Adding and Subtracting Integers Knowledge and Understanding 9.3 Adding and Subtracting Integers Knowledge and Understanding 9.3 Adding and Subtracting Integers Knowledge and Understanding 9.3 Adding and Subtracting Integers Knowledge and Understanding 9.3 Adding and Subtracting Integers Knowledge and Understanding 9.3 Adding and Subtracting Integers Knowledge and Understanding 9.3 Adding and Subtracting Integers Thinking 9.3 Adding and Subtracting Integers Thinking 9.3 Adding and Subtracting Integers Knowledge and Understanding 9.3 Adding and Subtracting Integers Knowledge and Understanding 9.3 Adding and Subtracting Integers Application 9.4 Multiplying Integers Knowledge and Understanding 9.4 Multiplying Integers Knowledge and Understanding 9.4 Multiplying Integers Knowledge and Understanding 9.4 Multiplying Integers Knowledge and Understanding 9.4 Multiplying Integers Knowledge and Understanding 9.4 Multiplying Integers Knowledge and Understanding 9.4 Multiplying Integers Knowledge and Understanding 9.4 Multiplying Integers Thinking 9.4 Multiplying Integers Application

ID: A 44. ANS: STA: 45. ANS: STA: 46. ANS: STA: 47. ANS: STA: 48. ANS: STA: 49. ANS: STA: 50. ANS: STA: 51. ANS: STA: 52. ANS: STA: 53. ANS: STA: 54. ANS: STA: 55. ANS: STA: 56. ANS: REF: TOP: 57. ANS: REF: TOP: 58. ANS: REF: TOP: 59. ANS: REF: TOP: 60. ANS: REF: TOP: 61. ANS: REF: TOP: 62. ANS: REF: TOP:

A PTS: 1 DIF: Moderate REF: 9.4 Multiplying Integers 8m22 TOP: Number Sense and Numeration KEY: Application D PTS: 1 DIF: Moderate REF: 9.4 Multiplying Integers 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding D PTS: 1 DIF: Moderate REF: 9.4 Multiplying Integers 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding A PTS: 1 DIF: Easy REF: 9.5 Dividing Integers 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding B PTS: 1 DIF: Easy REF: 9.5 Dividing Integers 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding A PTS: 1 DIF: Easy REF: 9.5 Dividing Integers 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding C PTS: 1 DIF: Easy REF: 9.5 Dividing Integers 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding A PTS: 1 DIF: Easy REF: 9.5 Dividing Integers 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding C PTS: 1 DIF: Easy REF: 9.5 Dividing Integers 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding C PTS: 1 DIF: Easy REF: 9.5 Dividing Integers 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding C PTS: 1 DIF: Moderate REF: 9.5 Dividing Integers 8m22 TOP: Number Sense and Numeration KEY: Application D PTS: 1 DIF: Moderate REF: 9.5 Dividing Integers 8m22 TOP: Number Sense and Numeration KEY: Application D PTS: 1 DIF: Easy 9.6 Order of Operations with Integers STA: 8m23 Number Sense and Numeration KEY: Knowledge and Understanding A PTS: 1 DIF: Easy 9.6 Order of Operations with Integers STA: 8m23 Number Sense and Numeration KEY: Knowledge and Understanding A PTS: 1 DIF: Easy 9.6 Order of Operations with Integers STA: 8m23 Number Sense and Numeration KEY: Knowledge and Understanding A PTS: 1 DIF: Easy 9.6 Order of Operations with Integers STA: 8m23 Number Sense and Numeration KEY: Knowledge and Understanding D PTS: 1 DIF: Moderate 9.6 Order of Operations with Integers STA: 8m23 Number Sense and Numeration KEY: Knowledge and Understanding D PTS: 1 DIF: Moderate 9.6 Order of Operations with Integers STA: 8m23 Number Sense and Numeration KEY: Knowledge and Understanding D PTS: 1 DIF: Moderate 9.6 Order of Operations with Integers STA: 8m23 Number Sense and Numeration KEY: Knowledge and Understanding

ID: A 63. ANS: REF: TOP: 64. ANS: REF: TOP:

D PTS: 1 DIF: 9.6 Order of Operations with Integers Number Sense and Numeration KEY: B PTS: 1 DIF: 9.6 Order of Operations with Integers Number Sense and Numeration KEY:

Moderate STA: 8m23 Knowledge and Understanding Difficult STA: 8m23 Knowledge and Understanding

SHORT ANSWER 65. ANS: (+6) + (–6) + (+7) + (–4) = +3

PTS: 1 DIF: Moderate REF: 9.1 Adding Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Communication 66. ANS: Find the sum of all the up and down movements of the elevator. (+10) + (–9) + (+19) + (–3) + (+12) = +29 The elevator will be on the 29th floor. PTS: 1 STA: 8m22 67. ANS: +148

DIF: Moderate REF: 9.1 Adding Integers TOP: Number Sense and Numeration KEY: Communication

PTS: 1 STA: 8m22 68. ANS: –29

DIF: Moderate REF: 9.1 Adding Integers TOP: Number Sense and Numeration KEY: Knowledge and Understanding

PTS: 1 DIF: Moderate REF: 9.1 Adding Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Thinking 69. ANS: (+10) + (–22) > (–28) + (–11) PTS: 1 STA: 8m22

DIF: Moderate REF: 9.1 Adding Integers TOP: Number Sense and Numeration KEY: Knowledge and Understanding

ID: A 70. ANS: It is sometimes true. Examples may vary. Sample: (+17) – (+10) = +7 (+10) – (+17) = −7 PTS: 1 DIF: Moderate REF: 9.2 Subtracting Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Communication 71. ANS: It is never true. Examples may vary. Sample: (–17) – (+10) = –27 (–10) – (+17) = –27 PTS: 1 DIF: Moderate REF: 9.2 Subtracting Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Communication 72. ANS: It is sometimes true. Examples may vary. Sample: (–17) – (–10) = –7 (–10) – (–17) = +7 PTS: 1 DIF: Moderate REF: 9.2 Subtracting Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Communication 73. ANS: It is always true. Examples may vary. Sample: (+17) – (–10) = +27 (+10) – (–17) = +27 PTS: 1 STA: 8m22 74. ANS: (–5) – (–7) = +2

DIF: Moderate REF: 9.2 Subtracting Integers TOP: Number Sense and Numeration KEY: Communication

PTS: 1 STA: 8m22 75. ANS: –11

DIF: Moderate REF: 9.2 Subtracting Integers TOP: Number Sense and Numeration KEY: Communication

PTS: 1 STA: 8m22

DIF: Moderate REF: 9.2 Subtracting Integers TOP: Number Sense and Numeration KEY: Knowledge and Understanding

ID: A 76. ANS: 1 PTS: 1 STA: 8m22 77. ANS: 19

DIF: Easy REF: 9.3 Adding and Subtracting Integers TOP: Number Sense and Numeration KEY: Knowledge and Understanding

PTS: 1 STA: 8m22 78. ANS: 6−9+5=2

DIF: Easy REF: 9.3 Adding and Subtracting Integers TOP: Number Sense and Numeration KEY: Knowledge and Understanding

PTS: 1 STA: 8m22 79. ANS: –80

DIF: Moderate REF: 9.3 Adding and Subtracting Integers TOP: Number Sense and Numeration KEY: Communication

PTS: 1 STA: 8m22 80. ANS: –7°C

DIF: Moderate REF: 9.3 Adding and Subtracting Integers TOP: Number Sense and Numeration KEY: Thinking

PTS: 1 STA: 8m22 81. ANS: negative

DIF: Moderate REF: 9.3 Adding and Subtracting Integers TOP: Number Sense and Numeration KEY: Application

PTS: 1 DIF: Easy REF: 9.5 Dividing Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding 82. ANS: È ˘ (−32) ÷ ÍÍÎ (−4) ÷ (+2) ˙˙˚ = +16 PTS: 1 DIF: Moderate REF: 9.5 Dividing Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Thinking 83. ANS: È ˘ (−128) ÷ (+8) ÷ ÍÍÎ (−4) ÷ (+2) ˙˙˚ = +8 È ˘ (−128) ÷ ÍÍÎ (+8) ÷ (−4) ˙˙˚ ÷ (+2) = +32 È ˘ (−128) ÷ ÍÍÎ (+8) ÷ (−4) ÷ (+2) ˙˙˚ = +128 PTS: 1 STA: 8m22

DIF: Moderate REF: 9.5 Dividing Integers TOP: Number Sense and Numeration KEY: Thinking 6

ID: A 84. ANS: (+144) ÷ (−3) × (+8) = −384 (+144) × (−3) ÷ (+8) = −54 (+144) ÷ (−3) × (+8) < (+144) × (−3) ÷ (+8) PTS: 1 DIF: Moderate REF: 9.5 Dividing Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Thinking 85. ANS: Value of A: +3 Value of B: −3 The value of B is closer to −1. PTS: 1 DIF: Moderate REF: 9.6 Order of Operations with Integers STA: 8m23 TOP: Number Sense and Numeration KEY: Communication 86. ANS: (−3) 2 + (−9) 2 = 90 (−3 − 9) 2 = 144 The value of (−3 − 9) 2 is greater. PTS: 1 STA: 8m23 87. ANS: –128

DIF: Moderate REF: 9.6 Order of Operations with Integers TOP: Number Sense and Numeration KEY: Communication

PTS: 1 STA: 8m23 88. ANS: –21

DIF: Moderate REF: 9.6 Order of Operations with Integers TOP: Number Sense and Numeration KEY: Knowledge and Understanding

PTS: 1 STA: 8m23 89. ANS: 204

DIF: Moderate REF: 9.6 Order of Operations with Integers TOP: Number Sense and Numeration KEY: Knowledge and Understanding

PTS: 1 STA: 8m23 90. ANS: −2

DIF: Moderate REF: 9.6 Order of Operations with Integers TOP: Number Sense and Numeration KEY: Knowledge and Understanding

PTS: 1 STA: 8m23

DIF: Moderate REF: 9.6 Order of Operations with Integers TOP: Number Sense and Numeration KEY: Knowledge and Understanding

ID: A PROBLEM 91. ANS: a) Game 1: Player 2 Game 2: Player 1 Game 3: Player 3 b) Player 3; the score was +126 points. PTS: 1 DIF: Moderate REF: 9.1 Adding Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding 92. ANS: Descriptions may vary. Sample: Integers with the same sign: The sum of 2 positive integers is positive. The sum of 2 negative integers is negative. Integers with different signs: To add integers with different signs, find the difference of their number values. The sum has the sign of the integer with the greater number value. PTS: 1 DIF: Difficult REF: 9.1 Adding Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Communication 93. ANS: Yes. (+$30) + (−$45) + (+$25) = +$10 There was an overall increase of $10 over 3 consecutive days. PTS: 1 STA: 8m22 94. ANS: –232, –231, –230 PTS: 1 STA: 8m22

DIF: Difficult REF: 9.1 Adding Integers TOP: Number Sense and Numeration KEY: Communication

DIF: Difficult REF: 9.1 Adding Integers TOP: Number Sense and Numeration KEY: Thinking

ID: A 95. ANS: a) Methods may vary. Sample: Make a table that shows the balance of each month. The 3rd, 4th, and 6th months show a profit. Month

Balance (I − E)

Profit/Loss

−$77

Loss

−$80

Loss

+$97

Profit

+$45

Profit

−$50

Loss

+$55

Profit

b) The business made a profit of $–10 over the 6 months. PTS: 1 DIF: Difficult REF: 9.1 Adding Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Communication 96. ANS: –9, –13, –17 Pattern rule: Start with +3. Subtract +4 each time. PTS: 1 DIF: Moderate REF: 9.2 Subtracting Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Thinking 97. ANS: (–18) + (+39) – (–32) = (+53) PTS: 1 DIF: Difficult REF: 9.2 Subtracting Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Thinking 98. ANS: Find pairs of negative integers that have a sum of –11: −1 and –10, −2 and –9, −3 and –8, ..., and so on. Look for pairs of integers that have a difference of 3: –7 and –4 PTS: 1 DIF: Difficult REF: 9.2 Subtracting Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Communication 99. ANS: a) Subtract the least value of y from the greatest value of x (−21) − (−74) = +53 b) Subtract the least value of x from the greatest value of y (−51) − (−44) = −7 PTS: 1 STA: 8m22

DIF: Difficult REF: 9.2 Subtracting Integers TOP: Number Sense and Numeration KEY: Thinking

ID: A 100. ANS: n is any number less than –7. PTS: 1 DIF: Difficult REF: 9.2 Subtracting Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Thinking 101. ANS: a) The highest possible sum is 10 + (−1) = 9. It is the sum of the greatest positive integer (10) and the greatest negative integer (−1). b) Four ways: (−10) + 4 = −6 (−9) + 3 = −6 (−8) + 2 = −6 (−7) + 1 = −6 PTS: 1 STA: 8m22 102. ANS: Sea level is at 0 m.

DIF: Difficult REF: 9.3 Adding and Subtracting Integers TOP: Number Sense and Numeration KEY: Thinking

PTS: 1 DIF: Difficult REF: 9.3 Adding and Subtracting Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Communication 103. ANS: a) NUMBER and QUESTION have the same value of −14. b) QUIZ has the least value of −40. c) MULTIPLY has the greatest value of +4. d) SUBTRACT has a value of 0. PTS: 1 STA: 8m22

DIF: Difficult REF: 9.3 Adding and Subtracting Integers TOP: Number Sense and Numeration KEY: Knowledge and Understanding

ID: A 104. ANS: No. Explanations may vary. Sample: Calculate the money that Jake has: $25 − $21 + $22 − $15 = $11 Jake has $11 but this is not enough to repay his mother. PTS: 1 DIF: Difficult REF: 9.3 Adding and Subtracting Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Communication 105. ANS: a) −2, −4, −6 b) (–13 + 5), (–14 + 4), (–15 + 3) c) (−2) + (−4) + (−6) + (−8) + (−10) + (−12) = −42 PTS: 1 DIF: Difficult REF: 9.3 Adding and Subtracting Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Thinking 106. ANS: The next 2 terms are: 1280, –5120 Pattern rules may vary. Sample: Start at 5. Multiply by –4 each time. PTS: 1 DIF: Moderate REF: 9.4 Multiplying Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Thinking 107. ANS: The next 3 terms are: +256, –1024, –4096 Pattern rules may vary. Sample: Start at –4. Multiply by −4 each time. PTS: 1 STA: 8m22 108. ANS: a) $5400 b) $6400

DIF: Moderate REF: 9.4 Multiplying Integers TOP: Number Sense and Numeration KEY: Thinking

PTS: 1 DIF: Difficult REF: 9.4 Multiplying Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Application 109. ANS: If the number of negative integers being multiplied is even, then the product is positive. If the number of negative integers being multiplied is odd, then the product is negative. Examples may vary. Sample: The number of negative integers being multiplied is odd: (−1) × (−1) × (−1) × (−1) × (−1) = −1 The number of negative integers being multiplied is even: (−1) × (−1) × (−1) × (−1) × (−1) × (−1) = +1 PTS: 1 STA: 8m22

DIF: Difficult REF: 9.4 Multiplying Integers TOP: Number Sense and Numeration KEY: Communication

ID: A 110. ANS: The sign of the product of (−8)(+9)(+7)(−4) is positive. Explanations may vary. Sample: Since there are 2 negative integers being multiplied, their product will be positive. The product of any number of positive integers is always positive. PTS: 1 DIF: Difficult REF: 9.4 Multiplying Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Communication 111. ANS: Methods may vary. Sample: Find the 3 natural numbers that will multiply to give 24. There are 6 possible combinations. 1, 1, 24; 1, 2, 12; 1, 3, 8; 1, 4, 6; 2, 2, 6; 2, 3, 4 Since the product is negative, 1 or all 3 of the integers are negative integers. (−2)(−4)(−6) = −24 (−2) + (−4) + (−6) = −12 So, the 3 integers are −2, −4, and −6. PTS: 1 DIF: Difficult REF: 9.4 Multiplying Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Thinking 112. ANS: The next 3 terms are: –27, +9, –3 Pattern rules may vary. Sample: Start with +729. Divide by –3 each time. PTS: 1 STA: 8m22 113. ANS: –18

DIF: Moderate REF: 9.5 Dividing Integers TOP: Number Sense and Numeration KEY: Thinking

PTS: 1 DIF: Difficult REF: 9.5 Dividing Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding 114. ANS: Answers may vary. Sample: (+16) ÷ (+4) ÷ (−4) = −1 PTS: 1 DIF: Difficult REF: 9.5 Dividing Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Thinking 115. ANS: È ˘ a) Average change of elevations per hour: ÍÍÎ (−21) − (+139) ˙˙˚ ÷ 8 b) −20 m/h PTS: 1 STA: 8m22

DIF: Difficult REF: 9.5 Dividing Integers TOP: Number Sense and Numeration KEY: Application

ID: A 116. ANS: Explanations may vary. Sample: A number that is divisible by –6 is also divisible by –2 and –3. −4 and −6 are multiples of −2. So, only 1 factor of −2 is needed to ensure divisibility by −4. The greatest possible negative integer is: −(2 × 5 × 6 × 7) = −420 PTS: 1 DIF: Difficult REF: 9.5 Dividing Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Communication 117. ANS: Answers may vary. Sample: È ˘ a) ÍÍÎ (−2) + (+2) ˙˙˚ ÷ (−1) = 0 È ˘ b) ÍÍÎ (−2) + (+3) ˙˙˚ ÷ (−1) = −1 È ˘ c) ÍÍÎ (−3) + (+2) ˙˙˚ ÷ (−1) = +1 In a), the first two integers must be opposites of each other. In b), the sum of the first 2 integers must be the opposite of the third integer. In c), the sum of the first 2 integers must equal the third integer. PTS: 1 DIF: Difficult REF: 9.5 Dividing Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Communication 118. ANS: (8 + 5) × (−6) − 4 = −82 È ˘ 8 + 5 × ÍÍÎ (−6) − 4 ˙˙˚ = −42 È ˘ (8 + 5) × ÍÍÎ (−6) − 4 ˙˙˚ = −130 PTS: 1 DIF: Difficult REF: 9.6 Order of Operations with Integers STA: 8m23 TOP: Number Sense and Numeration KEY: Thinking 119. ANS: Work backwards to find the number. Add 16 to –4 to get 12. Divide 12 by 3 to get 4. Add 8 to 4 to get 12. Divide 12 by 6 to get the original number, 2. PTS: 1 DIF: Difficult REF: 9.6 Order of Operations with Integers STA: 8m23 TOP: Number Sense and Numeration KEY: Communication 120. ANS: (−13) + 37 =4 a) 6 b) 5 × 10 − (−10) 2 = −50 PTS: 1 STA: 8m23

DIF: Difficult REF: 9.6 Order of Operations with Integers TOP: Number Sense and Numeration KEY: Communication

ID: A 121. ANS: A: 0 B: −1 C: 0 If there are an even number of terms in the expression, the answer will be 0. PTS: 1 DIF: Difficult REF: 9.6 Order of Operations with Integers STA: 8m23 TOP: Number Sense and Numeration KEY: Thinking 122. ANS: Methods may vary. Sample: Add 10 + 4 in brackets. 3 + (−8) − (10 + 4) × 2 = 3 + (−8) − 14 × 2 Multiply 14 × 2. 3 + (−8) − 14 × 2 = 3 + (−8) − 28 Add or subtract in order from left to right. 3 + (−8) − 28 = −5 − 28 = −33 3 + (−8) − (10 + 4) × 2 = −33 PTS: 1 STA: 8m23

DIF: Difficult REF: 9.6 Order of Operations with Integers TOP: Number Sense and Numeration KEY: Communication