# Homework Hints 5-7

[tippy title=”Problems 1-3″]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.[/tippy]

[tippy title=”Problem 4″]Problem 4
The real numbers a and b are congruent modulo m, is a and b differ by a multiple of m.[/tippy]

[tippy title=”Problems 5-10″]Problems 5-10
Carry out the arithmetic using a 12-hour clock. See Examples 1 and 2.[/tippy]

[tippy title=”Problems 11-16″]Problems 11-16
Use the definition of congruence. See Example 3.[/tippy]

[tippy title=”Problems 17-22″]Problems 17-22
Carry out the given operations and then use the definition of congruence to find the simplified result. See Examples 1-3.[/tippy]

[tippy title=”Problems 23-30″]Problems 23-30
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.[/tippy]

[tippy title=”Problems 31-32″]Problems 31-32
See Examples 5 and 6, and set up a modulo 7 system.[/tippy]

[tippy title=”Problem 33″]Problem 33
See Examples 5 and 6, and set up a modulo 24 system.[/tippy]

[tippy title=”Problem 34″]Problem 34
See Examples 5 and 6, and set up a modulo 10 system.[/tippy]

[tippy title=”Problems 35-36″]Problems 35-36
See Examples 5 and 6, and set up a modulo 12 system.[/tippy]

[tippy title=”Problems 37-40″]Problems 37-40
See Example 8. The answer for each of these is long. Note that there are 11 properties which need to be checked and verified.[/tippy]

[tippy title=”Problems 41-46″]Problems 41-46
See Examples 7 and 8.[/tippy]

[tippy title=”Problems 47-52″]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.[/tippy]

### 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/