Objective Solving Problems by Multiplying and Dividing Integers

Many real-life problems involve multiplication and division of signed numbers.

Example 17

Calculating a Total Golf Score

A professional golfer ﬁnished seven strokes under par for each of three days of a tournament. What was his total score for the tournament?

Solution:

1. UNDERSTAND. Read and reread the problem. Although the key word is

“total,” since this is repeated addition of the same number, we multiply.

2. TRANSLATE.

3. SOLVE:

4. INTERPRET. Check and state your conclusion: The golfer’s total score was or 21 strokes under par.

Work Practice 17

- 21, 3

#

_{1-72 =} - 21

Translate: golfer’s

total = 3

#

1-72

In words: golfer’s total

score = number of

days

#

^score

each day 1-72

PRACTICE 16

Evaluate for and

y = -4.

x = -12 x

y PRACTICE 15

Evaluate xy for and

y = -9. x = 5

PRACTICE 13–14 Divide, if possible.

13. 14. 0

A card player had a score of for each of four games.

Find her total score.

- 12

146

negative 0

positive undeﬁned

Vocabulary and Readiness Check

Use the choices below to ﬁll in each blank. Some choices may be used more than once.

2.5 Exercise Set

1. -21-32 2. 51-32 3. -4192 4. -71-22

5. 81-82 6. -9192 7. 01-142 8. -6102

9. 61-42122 10. -21321-72 11. -11-221-42 12. 81-32132

13. -41421-52 14. -21-521-42

17. -51321-121-12 18. 31021-421-82

15. 101-52102 16. 21-121321-22 Multiply. See Examples 5 through 7.

19. -3² 20. -2⁴ 21. 1-32³ 22. 1-12⁴

23. -5² 24. -4³ 25. 1-22³ 26. 1-32²

Evaluate. See Examples 8 and 9.

27. -24 , 6 28. 90 , 1-92 29. - 30

6 30. 56

- 8 31. - 88

- 11 32. - 32

4 33. 0

14 34. - 13

35. - 10

0 36. 0

- 15 37. 39

- 3 38. - 24

- 12 Objective Find each quotient. See Examples 10 through 14.

Objective Multiply. See Examples 1 through 4.

F O R EXTR A H E LP

1. The product of a negative number and a positive number is a(n) number.

2. The product of two negative numbers is a(n) number.

3. The quotient of two negative numbers is a(n) number.

4. The quotient of a negative number and a positive number is a(n) number.

5. The product of a negative number and zero is . 6. The quotient of 0 and a negative number is . 7. The quotient of a negative number and 0 is .

S E C T I O N 2 . 5 I MULTIPLYING AND DIVIDING INTEGERS

147

Objectives Mixed Practice Multiply or divide as indicated.

39. -12102 40. 01-1002 41. -4132 42. -6

#

43. -9

#

6 44. -121132 45. -71-62 46. -91-52

47. -31-421-22 48. -71-521-32 49. 1-42² 50. 1-52²

51. -10

5 52. -25

5 53. - 56

8 54. -49

55. -12 , 3 56. -15 , 3 57. 41-421-32 58. 61-521-22

59. -301621-221-32 60. -20

#

_1-52

#

_1-32 61. 3

#

1-22

#

0 62. -5142102

63. 100

- 20 64. 45

- 9 65. 240 , 1-402 66. 480 , 1-82

67. - 12

- 4 68. - 36

- 3 69. -1⁴ 70. -2³

71.1-32⁵ 72.1-92² 73. -21321521-62 74. -11221721-32

75.1-12³² 76.1-12³³ 77. -21-221-52 78. -21-221-321-22

79. -42

#

23 80. -56

#

43 81. 25

#

_1-822 82. 70

#

_1-232

95. x = -4and y = -2 96. x = 20and y = -5 97. x = 0and y = -6 98. x = -3and y = 0 Evaluate xy and also for the given replacement values.x

83. a = -4and b = 7 84.a = 5and b = -1 85. a = 9and b = -2

86. a = -9and b = -6 87. a = -5and b = -5 88. a = -8and b = 8 Objective Evaluate ab for the given replacement values. See Example 15.

89. x = 5and y = -5 90.x = 9and y = -3 91.x = -12and y = 0

92. x = -10and y = -10 93.x = -36and y = -6 94. x = 0and y = -5 Evaluate for the given replacement values. See Example 16.x

148

C H A P T E R 2 I INTEGERS AND INTRODUCTION TO VARIABLES

Translating Translate each phrase to an expression. Use x to represent “a number.” See Example 17.

Objective Translating Translate each phrase; then simplify. See Example 17.

99. Find the quotient of - 54and 9. 100. Find the quotient of - 63and -3.

101. Find the product of - 42and -6. 102. Find the product of - 49and 5.

103. The product of - 71and a number 104. The quotient of - 8and a number 105. Subtract a number from -16. 106. The sum of a number and -12 107. - 29increased by a number 108. The difference of a number and -10 109. Divide a number by - 33. 110. Multiply a number by -17.

Solve. See Example 17.

111. A football team lost four yards on each of three consecutive plays. Represent the total loss as a product of signed numbers and ﬁnd the total loss.

112. Joe Norstrom lost $400 on each of seven

consecutive days in the stock market. Represent his total loss as a product of signed numbers and ﬁnd his total loss.

113. A deep-sea diver must move up or down in the water in short steps in order to keep from getting a physical condition called the “bends.” Suppose a diver moves down from the surface in ﬁve steps of 20 feet each. Represent his total movement as a product of signed numbers and ﬁnd the product.

114. A weather forecaster predicts that the temperature will drop ﬁve degrees each hour for the next six hours. Represent this drop as a product of signed numbers and ﬁnd the total drop in temperature.

The graph shows melting points in degrees Celsius of selected elements. Use this graph to answer Exercises 115 through 118.

115. The melting point of nitrogen is 3 times the melting point of radon. Find the melting point of nitrogen.

116. The melting point of rubidium is times the melting point of mercury. Find the melting point of rubidium.

- 1

117. The melting point of argon is times the melting point of potassium. Find the melting point of argon.

- 3

118. The melting point of strontium is times the melting point of radon. Find the melting point of strontium.

- 11

119. During one month Target Corporation posted a reduction in sales of million. If this

continues, what will Target’s sales ﬁgures look like in three months, at the end of the quarter? (Source:

Target Corporation) - $2.1

120. In 2007, General Motors posted a full-year net income of . If the income rate was consistent over the entire year, how much would you expect General Motors’ net income to be for each quarter? (Source: General Motors)

- $38,732 million Melting Points of Selected Elements

ⴚ39

ⴚ70

Mercury Radon Potassium

Degrees Celsius

S E C T I O N 2 . 5 I MULTIPLYING AND DIVIDING INTEGERS

149 Review

Perform each indicated operation. See Section 1.9.

121. In 2005, there were 13,922 new movie titles released on DVD. In 2007, this number of releases on DVD dropped to 12,050. (Source: Motion Picture Association: Worldwide Market Research) a. Find the change in the number of new movie

titles released on DVD from 2005 to 2007.

b. Find the average change per year in the number of new movies released on DVD over this period.

122. In 1987, there were only 27 California Condors in the world. The condors in the wild were captured by the U.S. Fish and Wildlife Service in an aggressive move to rebuild the population by breeding them in captivity and releasing the chicks to the wild.

Thanks to this effort, the condor population increased to approximately 335 birds in 2009.

(Source: Arizona Game and Fish Department) a. Find the change in the number of California

Condors from 1987 to 2009.

b. Find the average change per year in the California Condor population of the period in part a.

127. -87 , 3

Concept Extensions

Mixed Practice (Sections 2.3, 2.4, 2.5) Perform the indicated operations.

Solve. For Exercises 133 and 134, see the ﬁrst Concept Check in this section.

128. -91-102 129. -9 - 10

130. -4 + 1-32 + 21 131. -4 - 15 - 1-112 132. -16 - 1-22

123. 90 + 12² - 5³ 124. 3

#

17 - 42 + 2

#

5² 125. 12 , 4 - 2 + 7 126. 12 , 14 - 22 + 7

133. What is the sign of the product of seven negative numbers?

134. What is the sign of the product of ten negative numbers?

Without actually ﬁnding the product, write the list of numbers in Exercises 135 and 136 in order from least to greatest.

For help, see a helpful hint box in this section.

135. 1-22¹², 1-22¹⁷, 1-52¹², 1-52¹⁷ 136. 1-12⁵⁰, 1-12⁵⁵, 0¹⁵, 1-72²⁰, 1-72²³

137 In your own words, explain how to divide two integers.

138. In your own words, explain how to multiply two integers.

Objectives

Simplify Expressions by Using the Order of Operations.

Evaluate an Algebraic Expression.

Find the Average of a List of Numbers.

Answers

1. 16 2. - 16 3. 108 4. 5

PRACTICE 4 Simplify: - 25

5( -1) PRACTICE 1–3 Find the value of each expression.

3. 3

#

6² - 2⁴ 1-22⁴

150 Examples

Find the value of each expression.

3. 2

#

5² = 2

#

₁₅

#

52 = 2

#

_{25 = 50}

1-32² = 1 - 321 - 32 = 9 The base of the exponent is The base of the exponent is 3.

The base of the exponent is 5.

- 3.

Work Practice 1–3

When simplifying expressions with exponents, remember that parentheses make an important difference.

Only with parentheses around it is the - 3squared.

- 3² means the opposite of 3

#

3, or - 9. 1-32² means 1-321-32 = 9.

1-32² and - 3² do not mean the same thing.

In document Basic Math.pdf (Page 168-173)