The Nature of Mathematics, 12th Edition
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Section 5.7 Homework Hints

Problems 1-3
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.
Problem 4
The real numbers a and b are congruent modulo M, is a and b 
differ by a multiple of m.
Problems 5-10
Carry out the arithmetic using a 12-hour clock.  See Examples 1 and 2.
Problems 11-16
Use the definition of congruence. See Example 3.
Problems 17-22
Carry out the given operations and then use the definition of congruence to find the simplified result.  See Examples 1-3.
Problems 23-31
See Examples 5 and 6. If you are working in mod 7 (as in Problem 23a), try each possible value, namely x = 0, 1, 2, 3, 4, 5, and 6. If you are working in mod 5 (as in Problem 23b), try each possible value, namely x = 0, 1, 2, 3, and 4.
Problems 32-33
See Examples 5 and 6, and set up a modulo 7 system.
Problem 34
See Examples 5 and 6, and set up a modulo 24 system.
Problem 35
See Examples 5 and 6, and set up a modulo 10 system.
Problems 36-37
See Examples 5 and 6, and set up a modulo 12 system.
Problems 38-40
See Example 8. The answer for each of these is long. Note that there are 11 properties which need to be checked and verified.
Problems 41-46
See Examples 7 and 8.
Problems 47-52
Follow the problem directions to make an interesting design.  Be creative in coloring the regions to create a potential work of art.

    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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