I'm an individual that learns by understanding the concept or
reasoning behind what ever is presented. Therefore math was always an
issue for me.  I could regurgitate the rules and apply formulas, but I
never 'got' it, if you know what I mean.  So my question is about
fractions...

  Why do equivalent fractions show themselves to be such when you
multiply the denominator by the numerator of each other??  (2/3 is
equivalent to 40/60) What is the core Principal that shows this to be
true??  What is the reason behind this fractional truth??

  Things only become real to me once I UNDERSTAND the principal of
things..  and for me at least, math was never taught as reason.. 
always as rules...  Kinda like Dad saying "Because I said so..." 
Never sunk in...  I need the truth behind the rule.

Any (non-zero) number divided by itself is exactly 1 .
So for example 20/20 is 1 .

If you take 2/3 * 20/20  it is still 2/3 so
2/3 = (2/3) * (20/20) = (2*20)/(3*20) = 40/60 
Much algebra consists of rewriting the same value in a way that will
turn out more convenient.

Multiplying parts of fractions by each other is sometimes required for addition.
1/3  + 1/4 can be expressed as a number of twelths if you multiply both (by 1
to keep the values unchanged).

4/12 + 3/12 = 7/12 .

Thank you!!  Finally, a simple reason why equivalent fractions are
equivalent.  Any idea where I can go to get more basic principlas for
early math??  I have similar questions from that general area of
math...  Fractions, percents and decimals.

Thank you again for the answer!

Ok, another rule I don't get....  Why do you move the decimal 2 places
to the right when changing a decimal to a percent...  And the reverse
also??  Why when changing back?

When expressed as a fraction, percents must have a denominator of 100.  

Moving the decimal point two places is a shortcut to the long version
of conversion between decimals and fractions.  Moving two decimal
places to the right is the shortcut to multiplying by 100 and moving
two decimal places to the left is the shortcut to dividing by 100.

So you have 56%
When expressed as a fraction, it becomes 56/100

Then to express that fraction as a decimal:
56 divided by 100 = .56

The shortcut would be to see 56 as 56.00 and then move the decimal
point two places to the left to get .56

Then to turn it back into a fraction...

You have .56 * 100 = 56

The basic rule for moving decimal points is that when you multiply or
divide by any power of 10 (meaning any number where 1 is the first
digit and is followed by various amounts of zeros), you simply move
the decimal point in the required direction the same number of places
as there are zeros.

Examples:

.56 * 100000 = 56000
5.6 divided by 10000 = .00056

Mathematically 2/3 is equivalent to 4/6, but they are not the same
thing, the first expression tells you that you have 2 parts of a
3-parts-divided object and the second says that you have 4 parts of a
6-parts-divided object.
The denominator is giving you information that you do not miss in real
life problems.