Abacus has been in use for more than 5000 years in various forms. However, in today’s competitive world, where sometimes correctness of one extra question and fraction of second makes all the difference between success and failures, having all the required information about Abacus and learning how to use an abacus has become increasingly important. Mindbuilder training provides Abacus classes in Dubai at its Karama Center in order to assist in achievement of above objective. This article provides the basic information about abacus and its use while subsequent articles deals with the basic operations such as addition, subtraction, multiplication and division operation through use of Abacus.
Difference between Suan-pan (Chinese Abacus) and Soroban (Japanese Abacus) were discussed in article about History of Abacus. All future articles about use of abacus shall be based on use of Japanese Soroban.
Essential Information about Abacus and its use
The Soroban abacus is best suited for a Base-10 numbering system. In Base-10 numbering system, each of the rod works as a placeholder and represents a value between 0 and 9.
In the Japanese Soroban with 1/4 configuration, in each of the rod, there is one bead above the beam called as the Heaven bead and four beads are below it, called as the Earth Beads. The Heaven Beads represents a value of 5 and each of the earth beads has a value of 1.
The value of any bead is ten times the value of the bead lying on its immediate right and one tenth of the value of the bead which lies to its immediate left.
If you carefully observe the beam, you’ll find a dot marking placed on the intersection of beam and rod on every third rod. The rods marked with such dots are called unit rod. Any one of such rods marked with dots can be designated to carry the unit number placeholder depending on the choice of the operator of the Abacus and his convenience.
However, it is usual practice to choose unit rod, just to the right of center on the soroban. Decimals are represented on the right side of the unit rod. If we are dealing with large numbers, we can choose the unit rod more on the right side and in case we are dealing with decimal numbers with larger number of significant digits we can choose it more towards the left side.
These dots also acts as markers by use of which, the larger numbers can be quickly and conveniently recognized.
How to use an Abacus
The beads are considered counted when they are moved towards the divider separating the upper and lower decks.
Setting numbers on an Abacus
While setting up numbers on an Abacus, you are advised to make use of only the thumb and your index fingers to manipulate the position of beads on the abacus. The thumb is used only to move the earth beads up toward the beam and all other type of movements are carried out by the use of the index finger ( such as moving all earth beads down and all heaven beads up & down).
In order to set numbers on the abacus, the operator slides the beads in upward or downward direction to make the beads touch the beam. Bringing up one earth bead and making it touch the beam gives the concerned rod a value of 1. If we move three earth beads up and make them touch the beam will give that particular rod a value of 3. To give a value of 5 to the rod, all the earth beads are cleared (moved away from the beam) and the heaven bead is moved downwards to touch the beam. Placing together one heaven bead and two earth beads will set a value of 7 and so on.
In Fig shown below from left to right, the numbers on single rods show 1, 3, 5, 7 & 9. Designating rod F as the unit rod, the soroban on the right shows the number 42,386 on rods B, C, D, E and F.
Clearing an Abacus
First operation to be carried out on abacus before using it is called as clearing the Abacus. To clear or empty the abacus, it is placed flat on the table or other surface in front of you. Then you are required to then tilt the frame toward you, whereby the gravity will pull all the beads down.
By this operation all the earth beads have been cleared and are away from the beam. Again, place the abacus back onto the table. Right index finger is used and moved in a sweeping motion from left to right between top of the beam and bottom of heaven beads forcing the heaven beads to move away from the beam. During this operation the abacus is held by the left hand. As a result of this action, none of the rods carry any value. What we get now, as a result of above operation is known as a Cleared Frame.
Two Important General Rules
We shall now study two general rules which are essential for quickly and easily solving any addition and subtraction problem with the Soroban abacus.
- Always work from Left to Right: Fundamental to good Soroban technique is the rule always work from left to right. This is against the practice, we are accustomed to, while doing the pen and paper calculations, but is very important in using an abacus. It’s one of the Soroban’s biggest advantages. It allows us to solve mathematical problems with great agility and speed, in part, because numbers are added and subtracted in exactly the same way we read and hear them.
- Finding Complement: Second, the Abacus operator must be familiar with how to find complementary numbers, specifically, always with respect to 10. The value or the number that should be added to the original number to make the result of addition as 10 is the number’s complement. For example, the complement of 7, with respect to 10, is 3 and the complement of 6, with respect to 10, is 4.
In competent hands, an abacus is a very powerful and efficient calculating tool. Much of its speed while calculating with abacus is result of use of mechanization, where we minimize mental work as much as possible and to perform the physical task of adding and subtracting beads mechanically, without thought or hesitation, which in a way leads to a process of thoughtlessness.
Finding Complementary numbers is a technique to achieve above objective.