By Marvin L. Bittinger, David J. Ellenbogen, Barbara L. Johnson
The Bittinger Graphs and versions sequence is helping readers study algebra via making connections among mathematical recommendations and their real-world functions. plentiful purposes, lots of which use actual info, provide scholars a context for studying the maths. The authors use various instruments and techniques—including graphing calculators, a number of techniques to challenge fixing, and interactive features—to have interaction and inspire all kinds of rookies.
Read or Download Elementary and Intermediate Algebra: Graphs and Models, 4th Edition PDF
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Additional info for Elementary and Intermediate Algebra: Graphs and Models, 4th Edition
It is neither prime nor composite. Try Exercise 9. Every composite number can be factored into a product of prime numbers. Such a factorization is called the prime factorization of that composite number. Student Notes EXAMPLE 3 When writing a factorization, you are writing an equivalent expression for the original number. Some students do this with a tree diagram: SOLUTION # 9 ⎫ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎭ 36 = 2 # 2 # 3 # 3 All prime We first factor 36 in any way that we can. One way is like this: 36 = 4 # 9.
5 - 11 48. - 3 -4 51. - 125 11 - 25 52. - 14 17 TW 85. Is the absolute value of a number always positive? Why or why not? TW 86. How many rational numbers are there between 0 and 1? Justify your answer. TW 87. Does “nonnegative” mean the same thing as “positive”? Why or why not? List in order from least to greatest. 89. - 23, 4, 0, - 17 88. 13, - 12, 5, - 17 90. 5 56. 12 Ú t 94. ƒ - 8 ƒ ! Aha 66. ƒ - 25 ƒ 95. ƒ 23 ƒ ƒ - 23 ƒ Solve. Consider only integer replacements. 96. ƒ x ƒ = 7 97. 66 = 23, express each of the following as a ratio of two integers.
All numbers, except zero, have reciprocals. For example, the reciprocal of 23 is 23 because 23 # 3 2 1 9 = 6 6 9 9 = 1; the reciprocal of 9 is because 9 # = = 1; and the reciprocal of 41 is 4 because 41 # 4 = 1. 1 9 Reciprocals are used to rewrite division using multiplication. Division of Fractions To divide two fractions, multiply by the reciprocal of the divisor: c a d a , = # . b d b c S E CT I O N 1. 3 EXAMPLE 7 SOLUTION Divide: 1 3 , . 2 5 Note that the divisor is 3 1 5 1 , = # 2 5 2 3 5 = .