Stimulating Understanding of Computational science through Collaboration, Exploration, Experiment, and Discovery for students with Hearing Impairments
a collaboration of the Shodor Education Foundation, Inc., Eastern North Carolina School for the Deaf, Barton College, the National Technical Institute for the Deaf, and Interpreters, Inc.

For Teachers!

Modular Mathematics

What is Modular Mathematics? 
Think about division. Do you remember what a remainder is? Think about 10 divided by 4. 10 divided by 4 is 2 with a remainder of 2. The remainder is the part left over. Working with a number in mod is like looking only at the remainders. The number you divide by is your mod. For example, let 10 be your number and 4 be your mod. 10 in mod 4 is 2. 

There is another way to think about modular mathematics. Think about a clock. What time is it an hour after 12? 1 comes after 12 on a clock. That is because a
clock is similar to mod. After a certain number you start back at the beginning. On a clock you start over at 1 after 12. In mod 4 you start over at 0 every time you have a 4.

What about negative numbers? 
In modular math, every negative number has a positive number that is equal to it. For example, imagine that it is 12:00. You want to know what time it was an hour ago. An hour is 1 but since it's in the past we are talking about -1 hour. You wouldn't say -1 hour ago. Instead you say 11:00. This is going backwards from 12. That is how negatives work in modular math. 

Where do we use Modular Mathematics? 
Modular Math is used frequently. An example is how they tell time in the military. In the military 01:00 is 1 am, 02:00 is 2 am, and so on until 12:00 is 12 pm. 1 pm is not written as 01:00 because that is 1 am. 1 pm is 13:00. If someone refers to 15:00 they mean 15-12, 3 pm. Subtracting 12 to get a number that is on our watches is using modular math. 

Modular math is also used in cryptography. Cryptography is a way to change regular messages into secret messages. It is similar to a code, but not the same! 

Developed by
The Shodor Education Foundation, Inc.

Copyright © 1999-2001 by The Shodor Education Foundation, Inc.

This project is supported, in part, by the National Science Foundation Opinions expressed are those of the authors and not necessarily those of the National Science Foundation.