 # Where The *** Am I? (Part 2a)

I am aware that, in the previous post, I stated the actual calculation of a Grid Square would be next.  However, that was before it dawned on me that there is a bit of odd math involved in that process and, my intention is to explain the process without advanced tools.

As such, an explanation of one particular process is in order… Modulo Division.

These days, even a crappy spreadsheet application provides a formula for Modulo Division or simply, Mod.  Typically, a spreadsheet formula takes the form of ‘=mod(number, divisor)’.  Many (not all) modern scientific calculators also provide a ‘Mod’ function.

Example:

Modulo division of 7 divided by 3:

Entering ‘=mod(7,3)’ into a spreadsheet cell, returns a value of 1.

This is because with Modulo Division, in this example, the result of the Modulo division of 7 by 3 results in a value of  1.  Visualize it this way, if I have 7 sticks and I can only remove sticks in groups of 3, I can do that 2 times before there will be one stick left over.  Essentially, that is Modulo Division, we only care about the remaining stick (OK, sorry for the first grade math example).

As previously noted, Modulo Division can be done with a push of a button because that, is the magic a spreadsheet or advanced calculator provides.  However, what if you don’t have such tools? Where, did that 1 come from?

Manually dividing 7 by 3, or entering that equation into a regular calculator, should result in a value of 2.333333333.  The number to the right of the decimal point ‘.333333333’ is the the leftover piece, the decimal fraction of dividing one number by another that doesn’t result in a whole number

So, that decimal fraction doesn’t much look like ‘1’, does it?  How do we resolve that?

The first thing we want to do is to remove the whole number value, the integer piece, of the result of dividing 7 by 3, which again, is 2.333333333.  We do this by simply dropping the number to the left of the decimal point, the ‘2’, which is the integer value, resulting from dividing 7  by 3.  This leaves us with 0.333333333.

Now, we take that 0.333333333 and multiply it by our original divisor, ‘3’.

0.333333333 * 3 = … wait for it… ‘1’.  How about that?!

Congratulations!  You just performed Modulo Division!

As always, try it out. Use different values, etc… and have fun.

Keep this process in mind for the next post, because performing Modulo Division is required to calculate a Grid Square!