# Using an Abacus/Close-up of the eastern abacus

## Description of the Eastern abacus

An abacus consists of the following parts made of wood, bamboo, metal, plastic, etc.:

• A rectangular frame.
• The frame supports a variable (odd) number (from 9 to 27) of rods parallel to its shorter sides along which the beads are strung.
• A bar or beam, parallel to the longer sides of the frame, divides the abacus and the rods into two desks: a narrower upper one, the Heaven , and a wider one below, the Earth.
• Beads of the upper region of the rods (the upper beads) to which a value of 5 is assigned when they are activated.
• Beads of the lower region of the rods (the lower beads) to which a value of 1 is assigned when they are activated.
• Some modern abacos may include a reset button to return the beads to their inactive position (see below).
• Modern abacuses also usually present some type of unit rod marks every three rods to facilitate the alignment of numbers as well as the reading of them. They are convenient for abacus with a high number of rods (17-27) but are not essential. For some it is a nuisance.

The beads are considered inactive while they are separated from the central bar or beam. The abacus in the following figure has been reset or cleared and all of its beads are inactive. All bars can be considered to have been filled with zeros.

 0 0 0 0 0 0 0 0 0 0 0 0 0

When we move the beads towards the central bar we consider them active and then they acquire the assigned value 5 (the upper ones) or 1 (the lower ones). This is what allows us to represent numbers. With a modern 4 + 1 abacus we can form exactly the ten digits from 0 to 9 necessary to perform calculations with decimal numbers, and these digits have a unique representation.

 0 1 2 3 4 5 6 7 8 9

But with a traditional 5 + 2 abacus, and using the suspended bead, we can represent numbers up to 20 on each rod.

 0 1 2 3 4 5 5 6 7 8 9 10
 10 11 12 13 14 15 15 16 17 18 19 20

Note the use of the suspended bead for numbers from 15 to 20. Also note that the numbers 5, 10 and 15 can be represented in two different ways: using the fifth lower bead or not. This fact may be used to simplify addition and subtraction operations a bit. If you are interested in the details of use of a traditional abacus consult the book: Traditional Abacus and Bead Arithmetic

## Resetting the abacus

After finishing a calculation and before starting a new one, it will be necessary to reset the abacus to its cleared state.

• If your abacus has a reset button, simply press it and you will have your abacus ready for new use.
• With a modern Japanese style abacus (soroban, with biconical beads) this is achieved in a very fast and effective way. Simply tilt the abacus towards you until all the beads drop to their lowest position and return the abacus to its usual position on the table. Then use the nail of your right index finger to push the top beads upward with a flick of your finger from left to right just above the center beam.
• With a traditional Chinese style abacus (suanpan with ellipsoidal beads) the above maneuver may not work properly, but if the abacus is large enough there is another procedure that represents a small skill challenge interesting in itself:
• Take the abacus with both hands by the short sides of the frame and tilt it towards you about 45 degrees until the beads fall down.
• From that position and without moving your forearms, force a sharp rotation to the abacus to the horizontal position with a twist of the wrists. If the axis of rotation defined by your wrists passes through the highest of the lower beads, the centrifugal force will drive the upper beads to their inactive position.
• Put the abacus back on the table.
You will probably need some time to perfect this technique.
• Finally, if all of the above fails, as a last resort you can use the fingers of your hand like a broom to sweep the beads into their inactive position.

Until late 19th century Japan, no ancient author ever bothered to write how beads should be handled; but surely the technique was transmitted orally.

To begin with, let's say that modern abacuses are so light that you need to hold them with your left hand to stabilize them and prevent them from shifting on the table when handling the beads. This could have disastrous consequences if that displacement induces the movement of other beads than the ones we want to move. By comparison, other traditional abacos are so heavy that they remain stable on their own, allowing you to use your left hand for other purposes, such as following a list of numbers in a ledger. Furthermore, you can use the abacus as a paperweight to stabilize a stack of invoices, etc.

And yet, in some countries it is taught to manipulate the beads using both hands. But we will use only the right hand for this purpose.

### Which fingers to use

For modern abacuses with a rod length of approximately 6 cm (2.4 inches) it is recommended to use two fingers: the thumb and the index finger of the right hand.

• Use your index finger to move the upper beads up and down and to move the lower beads down.

But some very experienced masters only use the index finger...

For larger traditional abacuses, three fingers should be used: thumb, index and middle finger of the right hand.

• Use your middle finger to move the upper beads up and down.

### Combined mouvements

When the operation affects both upper and lower beads, try to follow the rules in the table below. Some movements can be done simultaneously and others must be done in rapid succession in the order indicated.

Combined mouvements of upper and lower beads
To move →

and ↓

Lower beads Up Do it simultaneously Do it simultaneously

### Exercises

• Enter digits 1 to 9 from left to right anywhere on your abacus (modern or traditional) using the above rules.
 1 2 3 4 5 6 7 8 9
then, clear them from left to right also using the above rules.
• Enter three or more consecutive sixes from left to right and wipe them in rapid succession from left to right.
Write caption here!
A B C
6 6 6
This exercise should be repeated daily a few times until you are able to do it almost without looking at the abacus.

Next Page: Addition and subtraction | Previous Page: Basic concepts
Home: Using an Abacus