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Guides for the subtraction:

There are guides that make the subtraction with the abacus much more easier. At the following
guides, the first number indicates the number to be subtracted from another which is already placed
on the abacus, and the rest tells how to proceed. To cancel five means to take away (subtract) from
the same column 5 hypobeads or one altobead. To cancel ten means to take away (subtract) from the
next left column 1 hypobead. To return means to move up hypobeads or to move down altobeads
(add) depending on how much to return in the same column.
Given a number D with n digits (Dn, Dn-
1, ..., D2, D1), to subtract digit V at the ith digit position from Di:

If (Di-V)>=0 and V<5, subtract 5 and
add (5-V) from i
th position:
  • One;cancel five, return four.
  • Two; cancel five, return three.
  • Three;cancel five, return two.
  • Four; cancel five, return one.
If (Di-V)<0 and V>5, subtract 1 from i+1 position,
add 5 and subtract (V-5) to ith position:
  • Six; cancel ten, return five, cancel one.
  • Seven; cancel ten, return five, cancel two.
  • Eight; cancel ten, return five, cancel three.
  • Nine; cancel ten, return five, cancel four.

If (Di-V) < 0, subtract 1 from i
+1 position
and add (10-V) to ith position:
  • One; cancel ten (i.e. take
    away one hypobead on
    the left column), return nine.
  • Two; cancel ten, return eight.
  • Three; cancel ten, return even.
  • Four; cancel ten, return six.
  • Five; cancel ten, return five.
  • Six; cancel ten, return four.
  • Seven; cancel ten, return three.
  • Eight; cancel ten, return two.
  • Nine; cancel ten, return one.

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