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Abacus Maths Tutorial

 
Abacus Maths Tutorial Detail

Performing Genius Addition on the Abacus
Addition on the abacus involves registering the numbers on the beads in the straight-forward left-to-right sequence they are written down in.
Additions
Addition on the abacus involves registering the numbers on the beads in the straight-forward left-to-right sequence they are written down in. As long as the digits are placed correctly, and the carry’s noted properly, the answer to the operation immediately presents itself right on the abacus.
There are 4 approaches to performing additions, each applied to a particular situation. Each of these techniques is explained in tabular form in the sections that follow.
Simple Additions
When performing the addition 6+2, one would move 1 bead from the upper deck down (value = 5) and one bead from the lower deck up (value = 1); this represents 6. Moving 2 beads from the lower deck (in the same column) up (value = 1 * 2 beads = 2) would complete the operation. The answer is then obtained by reading resultant bead positions.


Combined Adding-up And Taking Off
When the original number registered on a rod is smaller than 5, but will become greater than 5 after the addition, one bead from the upper-deck is moved down (added on to the beam) and one or more beads from the lower deck removed from the beam.
When a sum greater than 10 occurs on a certain rod, beads are removed from either or both the upper and lower decks and 1 bead is added to the rod directly to the left. Example: When adding 9 (10-1) to 8, one bead from the lower deck is removed (-1) and one bead from the lower deck on the row directly to the left is added (+10).


Combined Taking-off And Place Advancement
When a sum greater than 10 occurs on a certain rod, beads are removed from either or both the upper and lower decks and 1 bead is added to the rod directly to the left. Example: when adding 9 (10-1) to 8, one bead from the lower deck is removed (-1) and one bead from the lower deck on the row directly to the left is added (+10).

Combined Adding-up, Taking-off And Place Advancement
There are 4 cases when beads are added to the lower-deck, removed from the upper-deck and one bead added to the adjacent rod. Example: When adding 6 (+1-5+10) to 7, one bead is added to the lower-deck, one bead removed from the upper-deck and one bead is added to the left rod (lower-deck).

Performing Genius Subtraction on the Abacus
Subtraction is performed by first registering the minuend and then subtracting, starting from the left, by removing beads from either or both the lower or upper decks.
Genius Subtraction
Subtraction is performed by first registering the minuend and then subtracting, starting from the left, by removing beads from either or both the lower or upper decks. The final bead-positions represent the answer.
Simple Taking-off (Genius Principles)
This is achieved by simply taking off one or more beads from the lower deck, or sometimes both. Example: When subtracting 7 (represented by -5-2= -7) from 9, remove 1 bead from the upper-deck (-5) and 2 beads from the lower deck (-2). The remaining 2 beads represent the result.

Note: The “-” symbol in the Move bead(s) columns represents moving the bead(s) away from the middle beam.
Combined Adding-up And Taking Off (Genius Principles)
When the number of beads in the lower deck is less than the subtracter (the number being subtracted), one or more beads are added in the lower deck and 1 bead is removed from the upper-deck.
Example: When subtracting 4 (+1-5 = -4) from 7 (represented by 1 bead in the upper-deck and 2 beads in the lower deck (less than 4, the subtracter), one bead is added to the lower deck (+1) and 1 bead is removed from the upper-deck (-5) leaving 3 beads, representing the result.

Note: The “+” symbol in the Move bead(s) columns represents moving the bead(s) towards the middle beam; the “-” symbol indicates that the bead(s) should be moved away from the middle beam.

Taking-off From A Rod Of Higher Order And Adding-up (Genius Principles)
When a number on a specific rod is smaller than the subtrahend (4 is the subtrahend when performing 13 - 4; note that in the ones column, the 3 is less than the 4) one bead for the order of tens and one bead from the lower-deck has to be taken off, and one bead from the upper-deck is counted.


Combined Taking-off From A Rod Of Higher Order, Adding-up in the Upper-deck and Taking-off in the Lower-Deck (Genius Principles)
This technique is called for when a number on a specific rod is smaller than the supposed subtrahend [I have no idea what this means], but only in such cases as exemplified by 12 - 6.