The Nature of Mathematics, 12th Edition
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Section 5.6 Homework Hints

    Problems 1-4
    There are many problems throughout the text labeled IN YOUR OWN WORDS. Just relax; do not be afraid to give your opinion. For the most part, these questions do not have "right" or "wrong" answers. You should spend about five minutes in answering each of these questions.
    Problems 5-6
    You can find these definitions in the text.
    Problems 7-8
    See Figure 5.16.
    Problems 9-12
    See Example 1. Use your calculator or division. Be sure to write down exactly what you see with your calculator display. If you see, 8.1111111111, for example, note the pattern and write 8.1 with an overbar over the one.
    Problems 13-20
    See Example 2.
    Problems 21-25
    Review the order of operations (Section 1.3); remember parentheses first, then multiplications and divisions (left to right), and finally additions and subtractions (left to right).
    Problems 26-31
    See Examples 3 and 4 as well as the commutative, associative, and distributive properties introduced in Section 5.1.
    Problems 32-35
    Use the table given on the cover to find results.
    Problems 36-44
    See Example 5. Verify each of the following properties separately: Closure, associative, identity, and inverse.
    Problems 45
    Parts a and b are fairly straightforward.
    For part c, check the closure, associative, identity, inverse, and commutative properties for both operations. Then check the distributive property for X over *. This is a total of eleven different properties which much be satisfied, shown in Example 5.

    Note: Homework Hints are given only for the Level 1 and Level 2 problems.

    However, as you go through the book be sure you look at all the examples in the text. If you need hints for the Level 3 problems, check some sources for help on the internet (see the LINKS for that particular section. As a last resort, you can call the author at (707) 829-0606.

    On the other hand, the problems designated "Problem Solving" generally require techniques that do not have textbook examples.

    There are many sources for homework help on the internet.

    Algebra.help
    Here is a site where technology meets mathematics. You can search a particular topic or choose lessons, calculators, worksheets for extra practice or other resources.
    http://www.algebrahelp.com/

    Ask Dr. Math
    Dr. Math is a registered trademark. This is an excellent site at which you can search to see if your question has been previously asked, or you can send your question directly to Dr. Math to receive an answer.
    http://mathforum.org/dr/math/
    Quick Math
    This site provides online graphing calculators. This is especially useful if you do not have your own calculator.
    http://www.quickmath.com/

    The Math Forum @ Drexel
    This site provides an internet mathematics library that can help if you need extra help. For additional homework help at this site, click one of the links in the right-hand column.
    http://mathforum.org/

    Mathematics Home Page
    Access the Clemens and Alcuins Library of CSB/SJU and find one of the world's best collections of mathematical internet sites.
    http://library.csbsju.edu/rqs.phtml?subject_id=32

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