A Brief Introduction to the Abacus

The abacus is a mechanical aid used for counting; it is not a calculator in the sense we use the word today.

Anatomy & Construction

The standard abacus can be used to perform addition, subtraction, division and multiplication; the abacus can also be used to extract square-roots and cubic roots.

The abacus is typically constructed of various types of hardwoods and comes in varying sizes. The frame of the abacus has a series of vertical rods on which a number of wooden beads are allowed to slide freely. A horizontal beam separates the frame into two sections, known as the upper deck and the lower deck.

abacus image

Abacus Parts: The various parts of the abacus are identified here: the frame, the beam, the beads and rods and the upper and lower decks.

Basics

The abacus is prepared for use by placing it flat on a table or one's lap and pushing all the beads on both the upper and lower decks away from the beam. The beads are manipulated with either the index finger or the thumb of one hand.

Bead Values

Each bead in the upper deck has a value of 5; each bead in the lower deck has a value of 1. Beads are considered counted, when moved towards the beam that separates the two decks.

Counting

After 5 beads are counted in the lower deck, the result is "carried" to the upper deck; after both beads in the upper deck are counted, the result (10) is then carried to the left-most adjacent column.

The right-most column is the ones column; the next adjacent to the left is the tens column; the next adjacent to the left is the hundreds column, and so on. Floating point calculations are performed by designating a space between 2 columns as the decimal-point and all the rows to the right of that space represent fractional portions while all the rows to the left represent whole number digits.


The number: 87,654,321 on the Abacus

Your browser does not support Java.

Abacus Applet: Numeric representation of the number: 87,654,321. If your browser is Java-capable then the applet, above, will identify the parts of the abacus in your browser's status-area as you move your mouse-pointer over it; the beads will move when you click on them and the value of each column will be displayed on the top frame.

Referring to the Figure/Applet above, the third column (from the left), representing the number 8, is counted with 1 bead from the top-deck (value 5) and 3 beads from the bottom-deck (each with a value of 1, totaling 3); the sum of the column (5+3) is 8.

Similarly, the fourth column representing the number 7, is counted with 1 bead from the top-deck (value 5) and 2 beads from the bottom-deck (each with a value of 1, totaling 2); the sum of the column (5+2) is 7.

Technique

Proper finger technique is paramount in achieving proficiency on the abacus. With a Chinese abacus, the thumb and the index finger together with the middle finger are used to manipulate the beads. Beads in lower deck are moved up with the thumb and down with the index finger. In certain calculations, the middle finger is used to move beads in the upper deck.

finger technique

Finger Technique: A Japanese textbook published in 1954 shows the proper technique for moving the beads. It shows the thumb being used to count beads in the lower deck and the index finger being used in all other cases.

With the Japanese version, only the index finger and thumb are used. The beads are moved up with the thumb and down with the index finger. However, certain complex operations require that the index finger move beads up; e.g. adding 3 to 8 (the adding of the three is called Jian Chi Jia Shi which literally means, "subtract 7 add 10").

This Java version of the abacus is a limited simulation of the real device because the fingering technique is completely obfuscated by the mouse. With a real abacus, constant practice is indispensable in achieving virtuosity and calculating speed.

clerk using abacus

The Abacus Today: A store clerk in Beijing, China uses the abacus to settle accounts. (Sep. 1997, courtesy Peter Wouda)

The Abacus Today

The abacus is still in use today by shopkeepers in Asia and "Chinatowns" in North America. The use of the abacus is still taught in Asian schools, and some few schools in the West. Blind children are taught to use the abacus where their sighted counterparts would be taught to use paper and pencil to perform calculations.

One particular use for the abacus is teaching children simple mathematics and especially multiplication; the abacus is an excellent substitute for rote memorization of multiplication tables, a particularily detestable task for young children. The abacus is also an excellent tool for teaching other base numbering systems since it easily adapts itself to any base.

The enduring interest in this ancient device is evident by ever increasing number of visitors to these pages from all around the world.

Last modified: Thu Nov 27 10:37:18 2003

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