By Jerome E. Kaufmann, Karen L. Schwitters
Kaufmann and Schwitters have outfitted this text's attractiveness on transparent and concise exposition, various examples, and ample challenge units. This conventional textual content continually reinforces the subsequent universal thread: study a ability; perform the ability to aid remedy equations; after which practice what you've realized to resolve program difficulties. this easy, undemanding method has helped many scholars clutch and follow primary challenge fixing talents invaluable for destiny arithmetic classes. Algebraic rules are built in a logical series, and in an easy-to-read demeanour, with out over the top vocabulary and formalism. The open and uncluttered layout is helping preserve scholars fascinated about the suggestions whereas minimizing distractions. difficulties and examples reference a large variety of subject matters, in addition to profession components akin to electronics, mechanics, and well-being, displaying scholars that arithmetic is a part of lifestyle. The text's source package--anchored via better WebAssign, an internet homework administration tool--saves teachers time whereas additionally supplying extra support and skill-building perform for college kids outdoor of sophistication.
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Extra info for Algebra for College Students (9th Edition)
4 ϭ 0 Subtracting Real Numbers We can describe the subtraction of real numbers in terms of addition. ” In other words, every subtraction problem can be changed to an equivalent addition problem. Consider the following example. 3 7 1 7 1 7 2 5 (d) Ϫ Ϫ aϪ b ϭ Ϫ ϩ ϭ Ϫ ϩ ϭ Ϫ 8 4 8 4 8 8 8 7 1 (d) Ϫ Ϫ aϪ b 8 4 14 Chapter 1 • Basic Concepts and Properties It should be apparent that addition is a key operation. To simplify numerical expressions that involve addition and subtraction, we can first change all subtractions to additions and then perform the additions.
48. 50. 2 • Operations with Real Numbers 3 4 51. aϪ ba b 4 5 53. 3 1 Ϭ aϪ b 4 2 1 4 52. a b aϪ b 2 5 85. 6) 5 7 54. aϪ b Ϭ aϪ b 6 8 87. 6) For Problems 55 – 94, simplify each numerical expression. (Objective 7) 19 86. 8) 88. 6) 89. 9) 90. 5) 55. 9 Ϫ 12 Ϫ 8 ϩ 5 Ϫ 6 56. 6 Ϫ 9 ϩ 11 Ϫ 8 Ϫ 7 ϩ 14 57. Ϫ21 ϩ (Ϫ17) Ϫ 11 ϩ 15 Ϫ (Ϫ10) 91. 2 3 5 Ϫa Ϫ b 3 4 6 58. Ϫ16 Ϫ (Ϫ14) ϩ 16 ϩ 17 Ϫ 19 1 3 1 92. Ϫ Ϫ a ϩ b 2 8 4 1 1 7 59. 7 Ϫ a2 Ϫ 3 b 8 4 8 1 2 5 93. 3a b ϩ 4a b Ϫ 2a b 2 3 6 3 1 3 60. Ϫ4 Ϫ a1 Ϫ 2 b 5 5 10 3 1 3 94.
Finally, let’s consider the product of two negative integers. The following pattern using integers helps with the reasoning. 4(Ϫ2) ϭ Ϫ8 3(Ϫ2) ϭ Ϫ6 2(Ϫ2) ϭ Ϫ4 1(Ϫ2) ϭ Ϫ2 0(Ϫ2) ϭ 0 (Ϫ1)(Ϫ2) ϭ ? To continue this pattern, the product of Ϫ1 and Ϫ2 has to be 2. In general, this type of reasoning helps us realize that the product of any two negative real numbers is a positive real number. Using the concept of absolute value, we can describe the multiplication of real numbers as follows: Multiplication of Real Numbers 1.