ASL
What is Modular Mathematics?
Modular math is similar to division. Think about division. Do all numbers divide evenly? No, they do not. What happens when a number does not divide evenly? A remainder is left over. For example, 9 divided by 4 is 2 with a remainder of 1. Modular mathematics uses these remainders. Consider our example 9 divided by 4. Our number is 9 and 4 is called our mod. The mod is the number that we divide by. What is 9 in mod 4? The answer is our remainder. 9 in mod 4 is equivalent to 1.
ASL
Is there an easier way?
There is another way to think about modular math. What time is it three hours after 11:00? It is 2:00. Why did you say 2:00 instead of 14:00? You said 2:00 because you know to continue past the 12 to the 1 on the clock. This is similar to modular math. Draw the face of a clock. Instead of using the number 12 put a zero. Put your finger on 0. Move your finger clockwise (starts to the right) to the next number as you count. Count to 14. Where do you stop? You should stop at 2. What is your mod on this clock? Your mod is how many numbers are on your clock. It is 12 (remember to count 0). What is 14 in mod 12? 14 is 2 in mod 12.
ASL
Why do we use 0 instead of 12?
First remember that the numbers on our mod clock are remainders. Think about dividing by 12. What remainders are possible when you divide by 12? 12 divided by 12 gives you a remainder of 0. 13 divided by 12 gives you a remainder of 1. 14 divided by 12 gives you a remainder of 2. Are there any numbers that give you a remainder of 12? No, there are not. Why is this true? What is 12 divided by 12? 12 divided by 12 is 1 remainder 0. This is why we use 0 for 12.
