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Numbers and Operations Chapter Questions

1. Draw a Venn Diagram showing the Number System

2. Explain what absolute value represents.

3. Create an owing money example for comparing two negative numbers.

4. Explain how you can use absolute value to add rational numbers.

5. Why can rational number subtraction problems be turned into addition problems?

6. Why are the rules for multiplying and dividing rational numbers the same?


Numbers and Operations Chapter Problems

Addition, Subtraction and Integers

Classwork

1. Name 5 integers.

2. Name 5 numbers that are rational but not integers.

3. What is the opposite of 20?

4. What is the opposite of -13.5?

5. Find:

a. │-12│

b. │ │

c. │-47.27│

d. │ │

6. Which numbers have the number given as their absolute value?

a. 150

b. 75.47

c. 14½

d. 1250.3

7. How would you explain to a new student how to find the absolute value of -10 and +10?

8. Place the appropriate inequality symbol between the following pairs of numbers:

a. 3 -7

b. -8.75 -10.3

c. 12 -11

d. 7½ 7½

e. -4 0

f. 0

9. Draw a number line and mark and label points for these numbers: 4.3, -7, 5, 0, -2.7, 1.8, -4.1

10. Draw a number line and mark and label points for these numbers: -15.1, 0, , 4, -3.8, -1.2, 9

3

125

7

511

3.5

2

17


Homework

11. What is the opposite of -50?

12. What is the opposite of 11.3?


14. What is the opposite of -7.98?

15. Find:

a. │9

213 │

b. │-35.74│

c. │-55│

d. │3½ │

16. Which numbers have the number given as their absolute value?

a. 72

b.

c. 155.35

d. 2500

17. How would you explain to a new student how to find the absolute value of 27.8 and -27.8?

18. Place the appropriate inequality symbol between the following pairs of numbers:

a. 25 -25

b. -30.3 -30.3

c.

d. -99.8 -100.1

e. -5.75 0

f. 0 -1

19. Draw a number line and mark and label points for these numbers: 15.2, -3½ , 0, , -9, 7.8, 11

20. Draw a number line and mark and label points for these numbers: -9.25, 1, 0, -3, 9.5, -1,

4

128

5

215

5

215

3

112

3

18


Addition and Subtraction of Integers

Classwork

21. Show the addition problem on a number line, and give the answer.

a. 4 + 2

b. 4 + (-2)

c. -4 + 2

d. -4 + (-2)

e. -4 + 4

22. Decide whether the statements below are always true, sometimes true, or always false. Give

examples to support your answer.

a. The sum of two positive numbers is a positive number.

b. The sum of a negative number and a positive number is a positive number.

c. The sum of two negative numbers is a negative number.

23. Show the subtraction problem on a number line, and give the answer.

a. 3 – 5

b. 3 – (-5)

c. -3 – 5

d. -3 – (-5)

e. -3 – (-3)

24. Write three addition problems that have a sum of 5.

25. Write three addition problems that have a sum of -7.


Homework

27. Show the addition problem on a number line, and give the answer.

a. -6 + (-4)

b. -6 + 4

c. 6 + 4

d. 6 + -4

e. 6 + -6

28. Show the subtraction problem on a number line, and give the answer.

a. 7 – 2

b. 7 – (-2)

c. -7 – 2

d. -7 – (-2)

e. -7 – (-7)





Multiplication and Division of Integers

Classwork

32. Show and solve the following multiplication problems on a number line:

a. 3(3) =

b. 2(-3) =

c. 5(-2) =

33. (7)(-2) =

34. (8)(-3) =

35. (-8)(7) =

36. (6)(8) =

37. (3)(-7) =

38. (1)(7) =

39. (0)(-9) =

40. Show the following division problems on a number line:

a. 10 ÷ 2 =

b. -12 ÷ 3 =

c. -9 ÷ 3 =

41. -45 ÷ 5 =

42. 56 ÷ 8 =

43. -12 ÷ -6 =

44. 7 ÷ -7 =

45. -9 ÷ 1 =

46. -6 ÷ -6 =

47. 0 ÷ -4 =

48. -18 ÷ -9 =

49. 27 ÷ 9 =

Homework

50. Show and solve the following multiplication problems on a number line:

a. 2(3) =


b. 3(-2) =

c. 4(-3) =

51. (-1)(-8) =

52. (1)(-2) =

53. (-7)(8) =

54. (9)(1) =

55. (-6)(3) =

56. (2)(-5) =

57. (0)(-5) =

58. (7)(-3) =

59. (-8)(-2) =

60. 5 ÷ -1 =

61. 24 ÷ 4 =

62. -3 ÷ -3 =

63. 0 ÷ 3 =

64. -10 ÷ 2 =

65. -6 ÷ 3 =

66. -40 ÷ -8 =

67. -4 ÷ 2 =

68. -25 ÷ -5 =

Addition and Subtraction of Rational Numbers

69. Explain the absolute values approach to solving a problem adding and positive and a negative

number.

70. Find the sum.

a. 2.3 + (-4.8) =

b. -6 + 4 =


c. -10.9 + (-10.9) =

d. -8.23 + 8.23 =

e. -3 + 0 =

f. =

g. -7 + 10 =

h. -40.32 + (-25) =

i. + (-110) =

j. During a football game the Hawks lost 5 yards due to a penalty and 6 yards from a

quarterback sack. Write and solve an expression that represents the situation.

k. Isaiah is scuba diving 30 feet below sea level. If he ascends 25.8 feet, what is his new

position?

l. Joe’s bank account statement stated he had $-250.30 in his account. If Joe deposited $100

on Friday and then later took out $27.25, what is his balance in his bank account?

m. A store has 40 IPads Wednesday morning. On Wednesday, it sells18 IPads. On Thursday it

sells 10. Friday the store receives another shipment of 30 IPads. Write an addition problem

that represents the number of IPads the store has at the end of the day on Friday. Then

solve.

71. Write three different addition problems that have a sum of:

a. 15

b. 42

c. -27

d. -3

Homework

72. Explain the absolute values approach to solving a problem adding two positives or two negatives.

73. Find the sum.

a. -7 + 2 =

b. -2.3 + (-4.8) =

c. -1 + 8 =

d.

e. -7 + 7 =

f. 0 + (-8.95) =

g. -5.86 + 1 =

h. -9.3 + (-9.3) =

i. 11.5 + (-98.5) =

j. -34.8 + (-82.6) =

k. A car left home and traveled 78.2 miles South on Highway 92. The car then traveled 75.9

miles North (back toward home) on the same Highway. How far is the car from home?

l. A scuba diver is 3 meters below sea level. If the diver descends another 8 meters, what is

the scuba diver’s position?

)2

14(

3

25

5

525

)7(3

15


m. A hole was dug 53 4

5 feet under ground. The construction workers then dug 61

2

5 further down.

How deep is the hole?

n. Grace received $200 for her birthday on Saturday. Later that day she bought a dress for

$88.30 and shoes for 52.50. On Sunday morning gave her a late birthday present of $30.

Write an addition expression that represents how much money Grace has on Sunday. Then

solve.

74. Write three different addition problems that have a sum of:

a. -12

b. 5

c. -20

d. 33

Turning Subtraction into Addition

Classwork

75. Decide whether the statements below are always true, sometimes true, or always false. Give

examples to support your answer.

a. The difference when a negative number is subtracted from a positive number is a negative

number.

b. The difference when a negative number is subtracted from a negative number is a negative

number.

76. Convert the following subtraction problems into addition problems, then find the sum.

a. 12 – (-2)

b. -5.8 – (-2.9)

c. -12 – 3

d. 10.75 – 14

e.

f. -2½ – 5

g. 5.6 – (-4.72)

h. -100 – (-99)

i. -30.6 – 30.6

j. 45 - (-45)

k. -175 – 30

77. Write three subtraction problems that have a difference of:

a. 4

b. 17

c. -19

d. -2

Homework

78. Convert the following subtraction problems into addition problems, then find the sum.

a. -5 – (-4) =

)2

17(

8

315


b. -11.9 – 5.1 =

c. -3 – 5 =

d. -7.2 – (-2) =

e. =

f. 3.12 – (-3.12) =

g. -2.4 – (-2.4) =

h. 7 – (-10) =

i. 9 – (-2½ ) =

j. 50 – (-25) =

k. -35.7 – 20.4 =

l. -100 – 99 =

79. Write three subtraction problems that have a difference of:

a. 14

b. -22

c. -9

d. 23

Adding and Subtracting Rational Numbers Review

Classwork

80. 3.8 + (-8.5) =

81. 6 – (-4) =

82. (-9) – (-4) =

83.

84. -4.6 – (-2.6) =

85. -4 -10 =

86.

87. -2 -7.8 =

88. -9 + 10 =

89. 8.65 + (-10) =

90. 2 – (-10.3) =

3

19

4

15

3

15

5

27

7

25

7

46


91.

92.

93. 4½ + 1½ =

94. 0 – (-3.8) =

95. -8 – (-2) =

96. -5 + (-6) =

97.

98. -41.3 + 53.2 =

99.

100. -88.88 – (-44.44) =

101.

102. 38 + (-64) =

103. 38 – (-64) =

104. -5 – 21 =

105. The hottest temperature ever recorded in Houston, Texas was 104 degrees. The coldest it has

ever been is 30 degrees below zero. How many degrees difference is between the hottest and

coldest recorded temperature?

106. Find the difference between the top of a house 55.12 feet above sea level and a coral reef 20.34

feet below sea level.

)4

12(

4

38

8

310

8

15

)2

128(

4

352

)5

194(

5

214

4

121

8

571


107. John owed his friend $7. For his birthday John received 10 dollars. After paying his friend back,

how much money will John have?

108. Henry spent $32.44 on a shirt and another $45 on a tie. Write and solve a subtraction equation

that represents the situation.

109. The temperature in the morning was -3 degrees. By the afternoon the temperature dropped 23

degrees. What is the temperature in the afternoon?

110. After Enrico withdrew $90 from his bank account, his balance was $354. Write a subtraction

expression to show your balance before Enrico’s withdrawal. Solve.

Homework

111. -8 + 6 =

112. -3.5 – 6.8 =

113. -8.3 – (-2.75) =

114.

115. -1 + (-3) =

116.

117. -6.9 + (-1.4) =

118. 3.9 + (-6.5) =

119.

120.

121. 2.4 – (-1.8) =

122. -1 – 8 =

123. -10 + 10 =

124. 4½ – 9 =

125. -2.9 + 1.24 =

)3

210(

3

17

)7

26(

7

41

)6

22(

6

22

)4

18(

4

15


126. 7 – (-7) =

127. -7 + 4 =

128. 33.8 – (-58.4) =

129. 25 + (-49) =

130.

131. 49 + (-69) =

132. 0 – (-92) =

133. -15.6 + 73.9 =

134. -60 – (-58) =

135. 50 -76 =

136. The hottest ever recorded temperature in New Jersey was 110 degrees. The coldest it’s ever

been was 34 degrees below zero. How many degrees difference is between the hottest and coldest

recorded temperature?

137. Find the difference between the top of a basketball hoop 10.10 feet above the ground and the

end of the pole 3 feet under ground.

138. Tara’s bank account showed -14.56 on her statement. She withdrew another 60 dollars from her

account that same day. After the withdrawal what will Tara’s bank account statement show?

139. Tony went to an orchid with his family to pick apples. Throughout the day, Tony collected 14

apples. His brother then took 5 apples and then Tony dropped 3. Write and solve an addition

equation to represent how many apples Tony has at the end of the day.

140. Mike earned $32 mowing his neighbor’s yard. Mike also owed his brother $40. Write and solve

an equation that shows Mike’s money situation.

141. During a football game the Giants gained 15 yards on one play. The next play the quarterback

was sacked and loss 6 yards. During these two plays how many yards did the Giants loos or gain?

142. The temperature at 3 a.m. was 7 degrees. By 12 p.m. the temperature dropped 19 degrees.

What was the temperature at 12 p.m.?

4

355

4

151


Multiplying Rational Numbers

Classwork

143. (-2.5)(-2.1) =

144. (8.5)(-9.4) =

145. (-4.79)(-1) =

146. (-7.12)(8) =

147. (8.45)(-6) =

148. (1.001)(-1.1) =

149. (-9.75)(-5) =

150. (4.21)(-9.2) =

151. (1)(-5.786) =

152.

153.

154.

155.

156.

157.

158. (-33)(-13) =

159. (-77)(4) =

160. (20)(-40) =

)2

16(

3

15

)3

11(

4

12

)0(8

57

)4

14(

5

26

)10(8

116

)8

415(3


Homework

161. (-5.21)(-5.3) =

162. (-9.12)(-7) =

163. (-5.8)(3.1) =

164. (4.87)(-1) =

165. (4.4)(4.4) =

166. (-2.86)(9.2) =

167. (9.3)(-9.3) =

168. (-6.2)(-9.1) =

169. (6.34)(2) =

170.

171.

172.

173.

174.

175.

176. (-10)(45) =

)4

34(

5

16

)3

25(

5

14

)51(5

262

)60(3

213

)6

18(

2

136

)80(8

34


Dividing Rational Numbers

Classwork

177. 3.5 ÷ -0.5 =

178. -5.525 ÷ 8.5 =

179. -63.84 ÷ -9.12 =

180. -36.9 ÷ 9 =

181. 6.6 ÷ -3.3 =

182. -40.8 ÷ -5.1 =

183. -1.63 ÷ -1.63 =

184. 0 ÷ -13.24 =

185. -61.992 ÷ 7.2 =

186.

187.

188.

189.

190.

191.

192. -4230 ÷ -90

)4

36(

4

120

)4

16(

4

156

)8

34(

4

126

)5

44(15

)4

313(

2

127

)2

14(26


Homework

193. 49.2 ÷ -8.2 =

194. -78.72 ÷ 6 =

195. -2.4 ÷ -4 =

196. 0.128 ÷ 3.2 =

197. -1.53 ÷ 51 =

198. -1.92 ÷ -1.92 =

199. 6.64 ÷ -8

200. 57.6 ÷ -8 =

201.

202.

203.

204.

205.

206. 20÷ -6 =

207. -212 ÷ -53 =

208. 4050 ÷ 75 =

)4(5

35

)3

23(

3

214

)8

18(

8

324

)8

34(35

)4

12(

2

15


Converting Rational Numbers to Decimals

Classwork

Convert each Rational Number to Decimal Form.

209.

210.

211.

212.

213.

214.

215.

Homework

Convert each Rational Number to Decimal Form.

216.

217.

218.

219.

220.

221.

222.

Exponents Classwork 223. (-8)2 224. -82 225. -73 226. (-7)3 227. -54 228. (-5)4

Homework 229. (-9)2 230. -92 231. -43 232. (-4)3 233. -64 234. (-6)4

9

4

6

16

8

321

11

2

4

311

8

56

3

14

6

5

9

14

8

715

11

7

4

323

8

32

6

25


Numbers and Operations Unit Review PMI 7th Grade Name ________________________

Multiple Choice– Choose the correct answer for each question. No partial credit will be given.


a) 5

b) -5

c) 0

2. What is │231

4│?

a) 231

4

b) -231

4

c) 0

3. What is │-7│?

a) 7

b) -7

c) 0

4. -11 -10

a) > b) = c) <

5. -20.0 -19.9

a) > b) = c) <

6. -9 -9 ¼

a) > b) = c) <

7. Convert the subtraction problem into an addition problem. 10 – (- 5)

a) -10 + 5

b) -10 + (-5)

c) 10 + 5

d) 10 + (-5)

8. Convert the subtraction problem into an addition problem. 8.75 – 4.3

a) -8.75+ 4.3

b) -8.75 + (-4.3)

c) 8.75 + 4.3

d) 8.75 + (-4.3)


9. Name the two numbers that have 10 as their absolute value _________________

In 17-18, use a number line to illustrate the given problem.

10. -6 + 7

11. 9 + -3

12. Convert the fraction into a decimal. Show all work.

92

9

13. Mike had a balance of $175 in his bank account at the start of the week. He withdrew $65.00 on

Monday, $43.25 on Wednesday, and $56.45 on Thursday. On Friday he deposited $165.30.

At the end of the week, does Mike have more or less money in his savings account than he

had at the beginning of the week?

How much more or less?

Show all of your work to support your answers.

14. In the first quarter of the game, the Giants gained 5 yards, lost 13 yards, gained 2 yards, gained 6

yards and, unfortunately, lost 12 yards in their final play.

Use a number line to depict the Giants’ activity in the first quarter.

Use addition only to illustrate the Giants’ activity in the first quarter.

What was the net yardage for the Giants in the first quarter?

15. The temperature varied greatly throughout the evening. Mary’s bug farm cannot survive if the

temperature falls below 32°C at any time. The evening temperature was consistently 62 degrees, until

a storm passed through the town. The temperature dropped 24°, dropped another 5°, rose 2°,

dropped 11°, and rose 9°.

Illustrate the temperature changes throughout the night using only addition

What was the lowest temperature of the night?

Did the bug farm survive the night? Explain your answer.


Answer Key

1. For example: 3, 4, 5, -2, -2

2. For example: ½, -3/4, 0.4, √5, π

3. -20

4. 13.5

5.

a. 12

b.

c. 47.27

d.

6.

a. -150, 150

b. -75.47, 75.47

c.

d. -1250.3, 1250.3

7. Answers will vary.

8.

a. 3 ˃ -7

b. -8.75 ˃ -10.3

c. 12 ˃ -11

d. =

e. -4 ˂ 0

f. 0 ˂

9. Order on number line:

-7, -4.1, -2.7, 0, 1.8, 4.3, 5


-15.1, -3.8, -1.2, 0, 4, 7 , 9

11. 50

12. -11.3

13. -2

14. 7.98

15.

a.

b. 35.74

c. 55

d.

16.

a. -72, 72

b.

c. -155.35, 155.35

d. -2500, 2500

17. Answers will vary.

18.

a. 25 ˃ -25

b. -30.3 = -30.3

c. -15 = -15

d. -99.8 ˃ -100.1

e. -5.75 ˂ 0

f. 0 ˃ -1


-9, -3 , 0, 7.8, 11, 12 , 15.2


-9.25, -8 , -3, -1, 0, 1, 9.5

21.

a. 6

b. 2

c. -2

d. -6

e. 0

22.

a. Always true

b. Sometimes true

c. Always true

23.

a. -2

b. 8

c. -8

d. 2

e. 0

24. Answers will vary



27.

a. -10

b. -2

3

125

7

511

2

114,

2

114

2

17

2

17

3.5

2

1

132

9

2

13

4

128,

4

128

5

2

5

2

2

1

3

1

3

1


c. 10

d. 2

e. 0

28.

a. 5

b. 9

c. -9

d. -5

e. 0




32. a. 9

b. -6

c. -10

33. -14

34. -24

35. -56

36. 48

37. -21

38. 7

39. 0

40.

a. 5

b. -4

c. -3

41. -9

42. 7

43. 2

44. -1

45. -9

46. 1

47. 0

48. 2

49. 3

50.

a. 6

b. -6

c. -12

51. 8

52. -2

53. -56

54. 9

55. -18

56. -10

57. 0

58. -21

59. 16

60. -5

61. 6

62. 1

63. 0

64. -5

65. -2

66. 5

67. -2

68. 5


70.

a. -2.5

b. -2

c. -21.8

d. 0

e. -3

f. -10

g. 3

h. -65.32

i. -5

j. -5 + -6= -11

k. -4.2

l. -77.55

m. 40+ (-10)+ (-18) + 30 = 42



73.

a. -5

b. -7.1

c. 7

d. -1

e. 0

f. -8.95

g. -4.86

h. -18.6

i. -87

j. -117.4

k. 2.3 miles

l. -11

m. 115 feet deep

n. $89.20


75.

a. Always false

6

1

3

2


b. Sometimes true

76.

a. 12 + 2 = 14

b. -5.8 + 2.9 = -2.9

c. -12 + (-3) = -15

d. 10.75 + (-14) = -3.25

e.

f. -2½ + (-5) = −71

2

g. 5.6 + 4.72 = 10.32

h. -100 + 99 = -1

i. -30.6 + (-30.6) = -61.2

j. 45 + 45 = 90

k. -175 + (-30) = -205


78.

a. -5 + 4 = -1

b. (-11.9) + (-5.1) = -17

c. -3 + (-5) = -8

d. -7.2 + 2 = -5.2

e. 51

4+ (−9

1

3)= −4

1

12

f. 3.12 + 3.12 = 6.24

g. -2.4 + 2.4 = 0

h. 7 + 10 = 17

i. 9 + 2½ = 111

2

j. 50 + 25 = 75

k. -35.7 + (-20.4) = -56.1

l. -100 + (-99) = -199


80. -4.7

81. 10

82. -5

83. 2

84. -2

85. -14

86. 1

87. -9.8

88. 1

89. -1.35

90. 12.3

91. 11

92. -15

93. 6

94. 3.8

95. -6

96. -11

97. 24

98. 11.9

99. 108

100. -44.44

101. -50

102. -26

103. 102

104. -26

105. 134

106. 75.46

107. 3 dollars

108. -32.44 – 45 = -77.44

109. -26

110. 354 – (-90) = 444

111. -2

112. -10.3

113. -5.55

114. -31

3

115. -4

116. 76

7

117. -8.3

118. -2.6

119. 0

120. 3

121. 4.2

122. -9

123. 0

124. -4

125. -1.66

126. 14

127. -3

128. 92.2

129. -24

130. -4

131. -20

132. 92

8

77)

2

17(

8

315

15

1

7

2

2

1

4

1

5

3

8

3

2

1

2

1


133. 58.3

134. -2

135. -26

136. 144

137. 13.1

138. -45.44

139. 14 + (-5) + (-3) = 6

140. 32 – 40 = -8

141. 9 yards gained

142. -12 degrees

143. 5.25

144. -79.9

145. 4.79

146. -56.96

147. -50.7

148. -1.1011

149. 48.75

150. -38.732

151. -5.786

152. 34

153. -3

154. 0

155. 27

156. 161

157. -46

158. 429

159. -308

160. -800

161. 27.613

162. 63.84

163. -17.98

164. -4.87

165. 19.36

166. -26.312

167. -86.49

168. 56.42

169. 12.68

170. -29

171. 23

172. -3182.4 or -3182

173. -820

174. -298

175. -350

176. -450

177. -7

178. -0.65

179. 7

180. -4.1

181. -2

182. 8

183. 1

184. 0

185. -8.61

186. 3

187. 9

188. -6

189. 3

190. -2

191. 5

192. 47

193. -6

194. -13.12

195. 0.6

196. 0.04

197. -0.03

198. 1

199. –0.83

200. -7.2

201. 1

202. 4

203. -3

204. -8

205. 2

206.

207. 4

208. 54

209. 0.

3

2

5

1

4

1

2

1

20

9

5

4

5

2

12

1

8

1

9

7

5

2

9

4

3.3

44


210.

211. 21.375

212.

213. -11.75

214. 6.625

215.

216.

217.

218. 15.875

219.

220. -23.75

221. 2.375

222.

223. 64

224. -64

225. -343

226. -343

227. 625

228. -625

229. 81

230. -81

231. -64

232. -64

233. 1296

234. -1296

Unit Review Answer Key

1) B

2) A

3) A

4) C

5) C

6) A

7) C

8) D

9) 10, -

10

10)

11)

12) .922

13) More, $0.60

14) 5 + (-13) + 2 + 6 + (-12), -12 yards

15) 62 + (-24) + (-5) + 2 + (-11) + 9

Lowest temp in the night was 24 degrees. The bug farm did not survive the night since

the temp did drop below 32 degrees at one point.

616.6

18.0

33.4

383.0

11.4

366.0

33.5

http://www.google.com/imgres?q=number+line&hl=en&gbv=2&biw=1600&bih=684&tbm=isch&imgrefurl=http://www.mathematic.ws/&tbnid=VfMMsMGGLn23uM&docid=A9BhNb1Kq0x14M&ved=0CEcQhRYoAA&ei=ogfpT6bMH8zG0AGbtfm3DQ&dur=3353

http://www.google.com/imgres?q=number+line&hl=en&gbv=2&biw=1600&bih=684&tbm=isch&imgrefurl=http://www.mathematic.ws/&tbnid=VfMMsMGGLn23uM&docid=A9BhNb1Kq0x14M&ved=0CEcQhRYoAA&ei=ogfpT6bMH8zG0AGbtfm3DQ&dur=3353

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