The Nature of Mathematics, 12th Edition
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Section 4.1 Homework Hints

Problems 1-7
These discussion problems are designed to make sure you understand the basic ideas of a numeration system. Remember, the particular systems are not as important as the ideas and properties of numeration systems.
Problems 8-13
See Example 1. Take each symbol separately, find it's value, and then find the sum of the values of the given symbols.
Problems 14-17
See Example 3. Roman numbers include the subtractive property, so as you read from left to right, add the value of each numeral unless its value is smaller than the value of the numberal to its right. Some problems (such as Problems 24-27) include a bar over some of the symbols; remember that the bar means multiply the value of those symbols by 1,000.
Problems 18-21
See Examples 5 and 6. Don't forget that the position is important in the Babylonian numeration system.
Problems 22-23
These are not exactly like any of the examples; convert all the numbers to decimal form, and then answer the question.
Problems 24-25
Look for patterns; Problem 24 is straightforward, but Problem 25 is tricky.
Problems 26-31
Look at Example 2; remember that the Egyptian system is repetitive.
Problems 32-37
Look at Example 4. Start with the larger Roman numerals.
Problems 38-43
Look at Example 7; remember that the Babylonian numeration system is repetitive.
Problems 44-49
See Example 2. Treat these problems as puzzles and have fun with them!
Problems 50-55
There is no example to match these problems.  Remember the subtractive property when doing these problems.

    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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