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Guides for the addition:

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

If (V+Di)<10 and V<5, add 5 and subtract
(5-V) to the i
th position :
  • One; lower five, cancel four.
  • Two; lower five, cancel three.
  • Three; lower five, cancel two.
  • Four; lower five, cancel one.
If (V+Di) >= 10 and V >= 5 , add 1 to the i+1
position, subtract 5 and add (V-5) to i position:
  • Six; raise one, cancel five, forward ten.
  • Seven; raise two, cancel five, forward ten.
  • Eight; raise three, cancel five, forward ten.
  • Nine; raise four, cancel five, forward ten.

If (V+Di)>=10, add 1 to the i
+1 position
and subtract (10-V) from the i
th position:
  • One; cancel nine, forward ten.
  • Two; cancel eight, forward ten.
  • Three; cancel seven, forward ten.
  • Four; cancel six, forward ten.
  • Five; cancel five, forward ten.
  • Six; cancel four, forward ten.
  • Seven; cancel three, forward ten.
  • Eight; cancel two, forward ten.
  • Nine; cancel one, forward ten.

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