Getting it togeher

First, I know that mathematics is the purest of sciences.  The basic truths of math cannot be altered.  Surprisingly there are not as many truths as one might think.

First out, though we can make assumptions -- like working in base 10 or base 2 (binary) -- using "algebra" with variables works in whatever number system that is used.  Algebra is  just basic problem solving, balancing an equation.

The Equal sign about says it all -- you have to be "fair" to both sides of the equation.  That has great applications in "real life," but I'll get to that later.

But let us start with the first thing we know.  I will be using letters in place of numbers (called variables) because it does not matter what number you use, the answer will be the same in these equations.

WORKING TOGETHER

A + B = B + A.  

This cannot be denied. When adding things together, it doesn't matter which direction you go.

It comes in handy when adding a lot of numbers together.  Order doesn't matter, so you can regroup so you get to numbers you can work with more easily.  Most people like 10 and 5, so here is an example:

8 + 7 + 1 + 2 + 3
= 3 + 7 + 2 + 8 +1
= 10 + 10 + 1 = 21

A x B = B x A.

Multiplication is just shortcut addition.  In the example above we find 10+10.  That means we have two tens, or 2*10.  So, the direction doesn't matter, and you can group any way you want to.

4 x 8 x 7 x 2 x 3 x 11
= 7x3 x 2x4 x 8x11
= 21 x 8 x 88.
= 21 x 704
= 14080 + 704 = 14,784

Yeah, I know, a student might need scratch paper to see what I did there, but basically, I used arithmetic the old fashioned way.

Next: Working with Nothing - aka Zero