By Jerome E. Kaufmann, Karen L. Schwitters
Starting ALGEBRA employs a confirmed, three-step problem-solving approach--learn a ability, use the ability to resolve equations, after which use the equations to resolve program problems--to maintain scholars considering construction abilities and reinforcing them via perform. this straightforward and simple strategy, in an easy-to-read layout, has helped many scholars seize and follow primary problem-solving abilities. The conscientiously based pedagogy contains studying ambitions, certain examples to enhance suggestions, perform workouts, an in depth number of problem-set routines, and well-organized end-of-chapter studies and tests. also, the fresh and uncluttered layout is helping retain scholars interested by the recommendations whereas minimizing distractions. difficulties and examples reference a huge array of themes, in addition to occupation components similar to electronics, mechanics, and healthiness, displaying scholars that arithmetic is a part of daily life. additionally, as prompt through the yank Mathematical organization of Two-Year schools, many simple geometric recommendations are built-in within the book's problem-solving units. The text's source package--anchored through more desirable WebAssign, a web 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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Additional info for Beginning Algebra (Available 2010 Titles Enhanced Web Assign)
7)(8) 62. (Ϫ6)(9) 63. (Ϫ5)(Ϫ12) 64. (Ϫ7)(Ϫ14) For Problems 101–104, ﬁnd the value of 65. 14(Ϫ9) 66. 17(Ϫ7) the given values for F. 67. (Ϫ11)(Ϫ14) 68. (Ϫ13)(Ϫ17) 69. (Ϫ15)(Ϫ15) 70. (Ϫ18)(Ϫ18) 101. F ϭ 59 102. F ϭ 68 103. F ϭ 14 104. F ϭ Ϫ4 5 Divide Integers 73. Ϫ42 Ϫ6 74. Ϫ72 Ϫ8 75. 96 Ϫ8 76. Ϫ91 7 78. 1Ϫ482 Ϭ 1Ϫ32 81. 1Ϫ722 Ϭ 18 82. 1Ϫ702 Ϭ 5 80. 102 Ϭ 1Ϫ72 6 Simplify Numerical Expressions Involving Integers For Problems 83 –92, simplify each numerical expression. 85. 1Ϫ32 1Ϫ82 ϩ 1Ϫ92 1Ϫ52 87.
28 Chapter 1 Basic Concepts of Arithmetic and Algebra EXAMPLE 5 Simplify 19(Ϫ26 ϩ 25). Solution For this problem, we are better off not applying the distributive property but simply adding the numbers inside the parentheses and then ﬁnding the indicated product. Thus 19(Ϫ26 ϩ 25) ϭ 19(Ϫ1) ϭ Ϫ19 ▼ PRACTICE YOUR SKILL Simplify Ϫ19(Ϫ34 ϩ 34). EXAMPLE 6 ■ Simplify 27(104) ϩ 27(Ϫ4). Solution Keep in mind that the distributive property enables us to change from the form a(b ϩ c) to ab ϩ ac, or from ab ϩ ac to a(b ϩ c).
EXAMPLES 115 is divisible by 5, because 5 is divisible by 5. 172 is not divisible by 5, because 2 is not divisible by 5. 36 Chapter 1 Basic Concepts of Arithmetic and Algebra Rule for 9 A whole number is divisible by 9 if and only if the sum of the digits of its base-10 numeral is divisible by 9. EXAMPLES 765 is divisible by 9, because 7 ϩ 6 ϩ 5 ϭ 18 and 18 is divisible by 9. 147 is not divisible by 9, because 1 ϩ 4 ϩ 7 ϭ 12 and 12 is not divisible by 9. 4 Find the Greatest Common Factor We can use the prime factorization form of two composite numbers to conveniently ﬁnd their greatest common factor (GCF).