# Read e-book online Elementary and Intermediate Algebra: Graphs and Models, 4th PDF 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.

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Additional info for Elementary and Intermediate Algebra: Graphs and Models, 4th Edition

Example text

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 = . 