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Stupid Arithmetic Tricks

On Wed, Mar 27, 2002 at 08:08:40PM -0600, David Starner wrote:
> I take you've never worked in a deli or bakery or some other place where
> the average person has to do math. My cow-orkers were surprised that I
> could add up the price for 3 $.69 pieces of chicken in my head.
> And, honestly, when I tried adding that up in my head, I got it wrong
> the first time. It's not like adding up long strings of two digit
> numbers in the head is a well-honed skill among most people.

You're using (IMO) the wrong technique.  Your brain is not a pencil and
paper, so don't try to make it work that way.  My approach to doing that
kind of problem in my head is something like:

.69 three times, eh?
Well, that's 70 3 times, minus 1 cent 3 times.
Now, 7 times 3 is 21, and I know where the decimal point goes.  So $2.10.
Now take back the three-cent overage.
10 minus 3 is 7.
So, $2.07.

If you need to be careful, you can validate your result just by doing
the "ones" digit of the original multiplication.  We know that nine
times three is 27, and my answer ends in a seven, so I can be reasonably
sure I did it correctly.

Here's another stupid math trick I once came up with.

If I'm given a long column of one or two-digit numbers to add up (on
paper), I go down the ones column and strike out all complementary pairs
that add up to 10, e.g., 1 and 9, 2 and 8, 3 and 7, etc.  For each pair
that I strike out, I make a tally mark or just keep track mentally.
Odds are you won't be left with very many digits to add up.  So you do
that, carry the one if need be, and then add your tally marks to what
you're carrying.  So if I struck off 4 complementary pairs that add up
to 10 and I was carrying a one, I'm now carrying a 5.  You can then
repeat this process for the tens column.  In theory this works for
arbitrarily long numbers, but with numbers > 99 paper space becomes a
concern.  This technique is much, much faster than manually adding each
digit to the one below.  At least in my experience...

Now, since you can probably mop the floor with me when it comes to diff
eq's, I'll defer to yours as the greater mathematical talent.  I thought
I was pretty good at math until I hit that brick wall.  I phear people
who can look at one and "just know" which solution technique to apply.

G. Branden Robinson                |      It doesn't matter what you are
Debian GNU/Linux                   |      doing, emacs is always overkill.
branden@debian.org                 |      -- Stephen J. Carpenter
http://people.debian.org/~branden/ |

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