By Lewis Hirsch; Arthur Goodman
ISBN-10: 0534494897
ISBN-13: 9780534494896
ISBN-10: 0534999727
ISBN-13: 9780534999728
ISBN-10: 0534999794
ISBN-13: 9780534999797
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Example text
57 Ϫ 82 Ϫ 31 65. Ϫ23 Ϫ 41 Ϫ 62 66. Ϫ49 Ϫ 26 Ϫ 33 67. 100 Ϫ 83 Ϫ 45 Ϫ 24 68. 225 Ϫ 56 Ϫ 97 Ϫ 115 69. 52 Ϫ (Ϫ38) Ϫ 67 70. 89 Ϫ (Ϫ27) Ϫ 62 71. Ϫ246 Ϫ 327 Ϫ (Ϫ542) 72. Ϫ561 Ϫ 412 Ϫ (Ϫ678) Subtracting Integers 29 In Exercises 73–84, evaluate the given expression. 73. 9 Ϫ 5 и 4 Ϫ 2 74. 7 Ϫ 3 и 5 Ϫ 1 75. 9 Ϫ 5(4 Ϫ 2) 76. 7 Ϫ 3(5 Ϫ 1) 77. 9 Ϫ (5 и 4 Ϫ 2) 78. 7 Ϫ (3 и 5 Ϫ 1) 79. ͉6 Ϫ 2͉ Ϫ ͉2 Ϫ 6͉ 80. ͉10 Ϫ 7͉ Ϫ ͉7 Ϫ 10͉ 81. ͉2 Ϫ 6͉ Ϫ (2 Ϫ 6) 82. ͉7 Ϫ 10͉ Ϫ (7 Ϫ 10) 83. ͉Ϫ4 Ϫ 3 ϩ 2͉ Ϫ 4 Ϫ 3 ϩ 2 84. ͉Ϫ8 ϩ 6 Ϫ 5͉ Ϫ 8 ϩ 6 Ϫ 5 85.
We can state them algebraically as follows: Associative Properties Associative Property of Addition a ϩ (b ϩ c) ϭ (a ϩ b) ϩ c Associative Property of Multiplication a(bc) ϭ (ab)c As with the commutative properties, the associative properties do not pertain to subtraction or division. For example, 10 Ϫ (5 Ϫ 2) 10 Ϫ 3 7 (10 Ϫ 5) Ϫ 2 5Ϫ2 3 36 Ϭ (6 Ϭ 3) 36 Ϭ 2 18 (36 Ϭ 6) Ϭ 3 6Ϭ3 2 In words, the commutative property says that we can reorder within a sum or a product, while the associative property says that we can regroup within a sum or a product.
That is, 0 ᎏᎏ ϭ 0 8 Keep in mind that 20 ᎏᎏ ؍5 4 because 5 и 4 ؍20. because 0 и 8 ϭ 0 and 0 ᎏᎏ ϭ 0 Ϫ4 because 0 и (Ϫ4) ϭ 0 In general, we have 0 ᎏᎏ ϭ 0 n for all integers n not equal to 0 What happens when we try to divide by 0? There are two cases to consider. If we try to divide 0 into a nonzero number—say, for example, 5—we cannot get an answer. 5 Multiplying and Dividing Integers 35 If ᎏ50ᎏ is going to be equal to some number, say m, then it must follow that m и 0 ϭ 5. But we know that any number times 0 is equal to 0, so it is impossible to get 5.
Understanding elementary algebra with geometry : a course for college students by Lewis Hirsch; Arthur Goodman
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