Fractions!

Problem
=======

ok the problem has changed to an entirely diffrent kind of beast

i am having problems with basic math principles i guess

the problem i had in the previous question was when u have to divide 2
by 1 and 3/4 i was ariving at the answer of 1 and 8/3 witch was rong

i took the problem and devided 2 by 1 and 3/4 in the comp calculator
and got 1.375 witch comes out to 1 and 3/8 i dont know what i did rong
in my equation compared to the calculators answer

i dont need to know how to solve the geometry problem nemore i need to
figure out how to sovle the problem with in it

Problem
=======

Well, I dunno about this "calculator" stuff :-)

answer = divide 2 by 1-3/4

       = 2 / 1-3/4

       = 2 / 7/4

       = 2 * 4/7

       = 8/7

       = 1-1/7 ("one and one seventh") 

To do that, I used two very handy things that have stuck with me since
high school - they're even handy when designing spacecraft orbits,
calculating airflow over wings, and fixing a triple batch of pancakes
that calls for 1-1/4 cups of some messy crap.

First handy thing
=================

Convert 2-3/4 to a single fraction in the form x/y

First, imagine a picture of it:

  3
2 - 
  4

Take the 4 and slide it up over to the 2, and multiply them: 4 * 2
is 8.

Then take that answer, 8, and slide it up over to the three and add
them: 8 + 3 = 11.

Now we've slid the numbers around till we have one number, 11, over the
other number, 4.  The answer is

11
--
4

Second handy thing
==================

Say you have to divide 2 by 3/4.  @!#$

2 / 3/4 is THE VERY SAME THING as 2 * 4/3

When you're dividing by a funky fraction, multiply by its reciprocal
because that's 10000 times easier.  What's the reciprocal of 3/4?
It's 4/3.

And to find 2 * 4/3, 

    4
2 * -
    3

Slide the 2 up over to the 4 and multiply them, which gives you 8.
There, you have one number over the other:

8
-
3

Third handy thing
=================

Yeah, I said there were two.  Here's the script I run through to do
this.  It takes about half a second to DO, but it takes at least 119
words to EXPLAIN.

Reduce 8/3 to "x and mumble thirds".

Start with the 3.  3 times 1 is 3.  That's less than 8, so try the
next one.  3 times 2 is 6.  That's less than 8, so try the next one.
3 times 3 is 9.  Too far.  Back to 3 times 2.  TWO.  That's the x in
"x and mumble thirds".  Remember it and continue by saying the phrase
"TWO and ..."

3 times 2 is 6.  8 - 6 is 2.  TWO.  Continue your phrase "... TWO ..."

Then look at the number on the bottom: THREE.  Finish your phrase
"... THIRDS".

So when you're done you've said "Two and two thirds", which happens to
be the right answer.