Worksmart said:
I understand the logic of what you're saying, mathematically.
But I'm not explaining myself well. The sale price is in B3, $27.50. How
does typing a 1 in the formula tell Excel that this represents the price?
Well, __mathematically__, the answer is derived from the following
rule:
a*(b+c) = a*b + a*c
Therefore, B3*(1+F9) is "27.50 plus 8.25% of 27.50" because it is the
same as B3*1 + B3*F9 -- and because B3 contains the sale price and F9
contains the sales tax rate, as your previous posting indicated you
understand.
And to reiterate the answer to the subject line of your posting, when
you write 8.25%, it is simply an alternative to writing 0.0825, which
is what Excel actually uses.
If I put a 2 in the formula, it doubles the price. How is Excel making this
connection?
Because B3*(2+F9) is B3*2 + B3*F9.
But beware: that is not the correct way to add the sales tax to double
the price. The correct way would be: 2*B3*(1+F9), which is the same
as 2*B3 + 2*B3*F9. The sales tax must be computed based on twice the
price.
The lightbulb for this is not on yet
That seemed quite clear from the start, so I tried to avoid a
mathematical explanation. If I may take one last stab at a
non-mathematical explanation....
How does typing a 1 in the formula tell Excel that this represents the price?
It doesn't. In the expression B3*(1+F9), "this thing" (1) is the value
of whatever is to the left of the asterisk ("*") -- subject to the
rules of order of operations, which you said you understand. Only the
human knows that B3 contains the sale price and F9 contains the sales
tax rate (percentage).
Perhaps I confused you by skipping a step. Excel translates B3*(1+F9)
into "this thing (B3) plus F9 times this thing (B3)". Alteratively, to
put it in the same terms that you have been using throughout this
thread: B3*(1+F9) means "this thing (the sale price in B3, $27.50)
plus the sales tax rate in F9 (8.25%) times this thing (the sale price
in B3, $27.50)".
As to why a*(b+c) = a*b + a*c, it is simply something that we must
accept as fact. In mathematics, it is called an axiom: a rule that
was demonstrated to be true long ago and never needs to be proved
again.
But if B3*(1+F9) is still impossible to gronk, simply rewrite it as B3
+ B3*F9. Hopefully the meaning of that will be obvious to "the other
person".