The One and the Only ONE

So if you can't use 0 to solve a multiplication problem, what is there that sort of "disappears" when you multiply or divide?  There is only one answer to that.  The answer is one, and one is the answer.

Here are the facts in algebraic expressions:

1*A = A

A/1 = A

A/A = 1

There you have it, the secret to "higher math".  Well, not really, but it helps a lot in problem solving.

Remember how you can rearrange multipliers?  Well that is where "reciprocals" come in.  Stated with variables that looks like this:

A/B x B/A = 1.

Got that? It looks better with pencil and paper, but my scanner is asleep right now.

Anyway, "A over B" times "B over A" equals "1".

It works out to something like this:

A*B/B*A
= A/A * B/B
= 1 x 1
= 1

Funny how that works out, huh?

Now we can use this unique upright integer to solve a problem.

Solve for A:

3A = 9
3A/3 = 9/3

Let's redo that second line:

(3/3)*A = 9/3
1*A = 3
A = 3

I really do need to get a scratch pad for Windows.  Or Something.

Anyway, here is what I know so far:

A+B = B+A
A-0 = A
A-A = 0
A/A = 1
A*1 = A
and
A*B = B*A
A/B x B/A = 1

Aren't I smart?


Well?

Perhaps I need to check to see if my hat is getting tight.

Tomorrow: Strange Facts about Exponents