This may sound really simple, but I can't get me head around it. I'm looking for a plain English explanation of a simple mathematical operation, if someone can help i'd really appreciate it.

The background is as follows.
If I have a whole number, and multiply it by a fraction, say 100*(1/4), i get a quarter of the whole number - or 25%.

If I divide that whole number by the same fraction, say 100/0.25, I'm saying, if 100 IS a quarter, i'm scaling it up to find out what 100% is... in this case 400.
If I multiply a whole number by 1.25,the answer I get is the whole number PLUS 25%! c nxt post

Question

This may sound really simple, but I can't get me head around it.  I'm looking for a plain English explanation of a simple mathematical operation, if someone can help i'd really appreciate it.

The background is as follows.
If I have a whole number, and multiply it by a fraction, say 100*(1/4), i get a quarter of the whole number - or 25%.

If I divide that whole number by the same fraction, say 100/0.25, I'm saying, if 100 IS a quarter, i'm scaling it up to find out what 100% is... in this case 400.
If I multiply a whole number by 1.25,the answer I get is the whole number PLUS 25%!  c nxt post

mathmate · Answer

I am not sure if this is what you need, but here's my attempt:
This property is called the distributive property of multiplication over addition.
x(1+0.25) = x + 0.25x