By Jerome E. Kaufmann, Karen L. Schwitters
Make math a snap with undemanding ALGEBRA. utilizing daily language and plenty of examples, Kaufman and Schwitters enable you practice algebra techniques and ace the try out. And if tutoring is on your destiny, with this variation you get forty hours of unfastened tutoring every week via own teach with SMARTHINKING, the stay on-line tutoring application that connects with you with an algebra professional who has a duplicate of your textbook. Plus, you will get the robust web-based iLrn Homework application that makes your assignments a breeze. Get the grade you will have with basic ALGEBRA
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144 59. 120 60. 84 61. 135 62. 98 For Problems 63 –74, ﬁnd the greatest common factor of the given numbers. 63. 12 and 16 64. 30 and 36 65. 56 and 64 66. 72 and 96 67. 63 and 81 68. 60 and 72 69. 84 and 96 70. 48 and 52 Rule for 5 71. 36, 72, and 90 72. 27, 54, and 63 A whole number is divisible by 5 if and only if the units digit of its base-ten numeral is divisible by 5. ) 73. 48, 60, and 84 74. 32, 80, and 96 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.
For example, 3 ϩ 1Ϫ42 ϭ 1Ϫ42 ϩ 3 because of the commutative property for addition. For Problems 13 –30, simplify each numerical expression. Don’t forget to take advantage of the properties if they can be used to simplify the computation. 1. 317 ϩ 82 ϭ 3172 ϩ 3182 13. 1Ϫ18 ϩ 562 ϩ 18 14. Ϫ72 ϩ [72 ϩ 1Ϫ142] 2. 1Ϫ921172 ϭ 171Ϫ92 15. 36 Ϫ 48 Ϫ 22 ϩ 41 16. Ϫ24 ϩ 18 ϩ 19 Ϫ 30 17. 12521Ϫ1821Ϫ42 18. 1221Ϫ7121502 19. 1421Ϫ1621Ϫ921Ϫ252 20. 1Ϫ2211821Ϫ1221Ϫ52 21. 371Ϫ42 Ϫ 582 22. Ϫ461Ϫ73 Ϫ 272 23. 591362 ϩ 591642 24.
You may ﬁnd these models helpful. ■ Subtraction of Integers The following examples illustrate a relationship between addition and subtraction of whole numbers. 7Ϫ2ϭ5 because 2 ϩ 5 ϭ 7 9Ϫ6ϭ3 because 6 ϩ 3 ϭ 9 5Ϫ1ϭ4 because 1 ϩ 4 ϭ 5 20 Chapter 1 Some Basic Concepts of Arithmetic and Algebra This same relationship between addition and subtraction holds for all integers. 5 Ϫ 6 ϭ Ϫ1 Ϫ4 Ϫ 9 ϭ Ϫ13 Ϫ3 Ϫ 1Ϫ72 ϭ 4 8 Ϫ 1Ϫ32 ϭ 11 because 6 ϩ 1Ϫ12 ϭ 5 because 9 ϩ 1Ϫ132 ϭ Ϫ4 because Ϫ7 ϩ 4 ϭ Ϫ3 because Ϫ3 ϩ 11 ϭ 8 Now consider a further observation: 5 ϩ 1Ϫ6 2 ϭ Ϫ1 5 Ϫ 6 ϭ Ϫ1 and Ϫ4 Ϫ 9 ϭ Ϫ13 and Ϫ4 ϩ 1Ϫ9 2 ϭ Ϫ13 and Ϫ3 ϩ 7 ϭ 4 Ϫ3 Ϫ 1Ϫ7 2 ϭ 4 8 Ϫ 1Ϫ3 2 ϭ 11 and 8 ϩ 3 ϭ 11 The previous examples help us realize that we can state the subtraction of integers in terms of the addition of integers.