Modular Mathematics

What time is it 4 hours after 9:00? It is 1:00. How did you figure that out? Look at a clock or a watch. Start at the 9 and count around 4 numbers. Where do you finish? You stop at the 1. This is called counting on a clock or counting in mod. Your mod is how many numbers are on your clock. What mod are the clocks that you use? They are probably mod 12. There is one difference between mod and our clocks. When working in mod 12 we never use the number 12. Instead of using 12 we use a 0. 12 and 0 are the same thing in mod 12.

Let's make our own clocks. Get a piece of circle paper from your teacher. In the first circle draw the face of a normal clock. Now, erase the number 12 and put 0 there instead. Try the following problems using your clock. Write the problems and their answers on your own paper.

1) 20 (mod 12) = ?
2) 5 (mod 12) = ?
3) 16 (mod 12) = ?

Now, let's try different mod clocks. Use your second circle to make a clock with only 7 numbers on it. 0 should be at the top. 1 through 6 should go in order around the outside.

4) What is your new mod? Why?
5) What is 9 in mod 7?
6) What is 12 in mod 7?

Try these other problems by drawing clocks in the other circles.

7) What is 5 in mod 3?
8) What is 10 in mod 9?
9) What is 7 in mod 2?

1. introduction

3. positive