You know what I mean? The fancy math stuff that makes you feel like a genius when you solve for ‘X’. But let’s be real here, who has time to learn all these complicated formulas and theorems? Not me, that’s for sure!

But hey, modular arithmetic is actually pretty cool. It’s basically math with a twist instead of dealing with regular numbers like 12 or 345, we work with numbers in a cycle. For example, if you have the number 7 and want to find its equivalent in a cycle of 6 (because that’s what we’re working with), you would do some fancy math stuff called ‘modulo division’.

So let’s say you divide 7 by 6 using modular arithmetic. The answer is…drumroll please…1! That’s right, the remainder when dividing 7 by 6 in a cycle of 6 is 1. And that’s where things get interesting.

One of the coolest properties of modular arithmetic is called ‘congruence’. It basically means that if two numbers are equivalent (or congruent) in a certain cycle, they will have the same remainder when you divide them by that number. For example, 12 and 60 both have a remainder of zero when divided by 36 using modular arithmetic. That’s because 12 is divisible by 36 with no remainder (which means it has a remainder of zero), and so does 60!

Another property that’s worth mentioning is ‘addition’. When you add two numbers in a cycle using modular arithmetic, the result will be equivalent to adding their remainders. For example, if we have the numbers 12 and 35 (in a cycle of 60), we can find their sum by finding the remainder when each number is divided by 60:

– The remainder for 12 is 12 (because it’s already divisible by 60)
– The remainder for 35 is 45 (when you divide 35 by 60, the result is 0.58 with a remainder of 45)

So to find their sum using modular arithmetic, we add those remainders: 12 + 45 = 57. And that’s our answer! The final number will have a remainder of 57 when divided by 60 (which is equivalent to the result you would get if you added 12 and 35 using regular arithmetic).

Now, multiplication. When we multiply two numbers in a cycle using modular arithmetic, we find their product and then take the remainder when that product is divided by our cycle number. For example:

– If we have the numbers 12 and 35 (in a cycle of 60), we can find their product by multiplying them together: 12 * 35 = 4,200
– The remainder when dividing 4,200 by 60 is 80. So the result of our multiplication using modular arithmetic would be 80 (which is equivalent to the product you would get if you multiplied 12 and 35 using regular arithmetic).

And that’s it! Those are just a few of the cool properties of modular arithmetic. It might seem complicated at first, but once you get the hang of it, it can be pretty fun to play around with. So next time someone asks you about math, don’t run away embrace your inner ‘mathlete’ and try out some modular arithmetic!