Question 976753
<pre>
We are learning how to make a whole number look exactly like a mixed
number with a whole part and a fraction part, so that we can subtract
from it.  


1. We are borrowing 1 from the 3, leaving 2, and then breaking the
1 that we borrowed into 2 halves.


{{{matrix(4,3,
  3, ""="",2&2/2,
-1/2,""="",-1/2,
"---","","---",
  "","", 2&1/2)}}}

2. We are borrowing 1 from the 3, leaving 2, and this time we are breaking 
the 1 that we borrowed into 3 thirds.

{{{matrix(4,3,
  3&1/3, ""="",2&3/3,
-1/3,""="",-1/3,
"---","","---",
  "","", 2&2/3)}}}

3. We are borrowing 1 from the 3, leaving 2, and this time we are breaking 
the 1 that we borrowed into 6 sixths.

{{{matrix(4,3,
  3, ""="",2&6/6,
-5/6,""="",-5/6,
"---","","---",
  "","", 2&1/6)}}}

We can always borrow 1 from the whole number, then break the 1 that we 
borrow from the whole number into any of these that we need in order to
be able to subtract a fraction from it:

2 halves, 3 thirds, 4 fourths, 5 fifths, 6 sixths, 7 sevenths, etc., etc.

That is, we can write the whole number:

{{{4}}} as {{{3&5/5}}} or as {{{3&7/7}}} or even {{{3&73/73}}}, whatever we need
it to be written as, so we can subtract a fraction from it.

{{{58}}} as {{{57&9/9}}} or as {{{57&78/78}}} or even {{{57&9999/9999}}}, whatever we 
need it to be written as, so we can subtract a fraction from it.


Edwin</pre>