Problem Solving with Abacus



Mathematics for many is a scary subject right from their childhood. They dread numbers and this may continue even when they are in college. Mathematics is considered "better" as agreed by the teacher who said it was not a killer. As a human anything abstract is always difficult to understand and become friends with. And, numbers certainly are abstract. Moreover, with multiple formulae and arithmetic operations makes it challenging for many. The best solution to get over the math phobia at an early age is if one could transform numbers from abstract to something tactile that can be visualized and be touched. Here we will discuss one such method.

I am sure you have heard of the ancient Chinese / Japanese calculating device Abacus.  This certainly is one instrument that gives the numbers an image that a child can feel and visualize.

Abacus, as you know, has a wooden frame, divided horizontally by a fixed bar and has the odd number of vertical rods with beads in the upper and lower deck. These beads represent numbers and facilitate calculating from single-digit to numerous digits numbers. It also allows the use of all the arithmetic operation. One can even solve roots. The kids can virtually see numbers in the image of the bead position. The numbers are no more abstract.

Let us see how an abacus can be used for doing calculations.

1. The basic use of an abacus

For using an Abacus as a calculating device, a child has to be trained in the basics of the Abacus and its methods of calculation. There are certain techniques and methods that one has to learn to be able to use the Abacus proficiently. This requires training and rigorous practice. Once done a child would be able to calculate a series of multiple digits numbers mentally by using a mental Abacus (The child can visualize an Abacus and do the calculations).

There are operating methods that have to be mastered by undergoing training for being able to use the arithmetic applications correctly. This is a gradual process starting from simple addition, subtraction, multiplication and division.

2. Addition and Subtraction on Abacus

Before starting to calculate on Abacus the child has to understand the instrument itself. Either the middle rod or the rearmost rod on the left of the Abacus is considered as the unit rod and subsequent rods moving to the left would be units, tens, Hundreds and so on so forth doing the sums, one can calculate to tens of millions place value. Once the basic structure and the value of each bead starting from the unit rod are understood the child would now be ready to start with the simple addition of a single digit. The upper deck of the Abacus has only one bead and has a numeric value of 5, while the lower deck has 4 beads with the numeric value of each being one. Any bead when it touches the horizontal bar attains the value.

For example, if we have to add 1 + 2,  we move one bead on the unit rod from the lower deck towards the Horizontal bar.

Next, to add 2 we will move 2 beads on the unit rod towards the Horizontal bar. Now three beads are touching the Abacus, you get a value of 3.

The sums are done starting from the unit's rod and moving the left rod as tens and so on. The similar method of solving from left to right is applied for doing addition and subtraction.

3. Multiplication on Abacus

Let us explain how to do multiplication on Abacus. Let us understand this through a sum.  Say you have to multiply 5 with 2, We will set 5 on the extreme left and 2 on the extreme right of the abacus. Now 2 times 5 is 10, so we will place 0 on the unit rod and 1 on the 10’s rod. This process can be followed for the multiplication of any number of digits.  If it is a multiplication of 2 digits, the result of the first digit multiplication will be put on the unit rod need to be on the 10’s rod. The result of the 2nd digit will be put on the 10’s rod and need be on the 100’s rod. The final position will give the perfect multiplication.

There are several companies giving training for Abacus. Among the very popular company is Mastermind Abacus. They have a program with a lot of technological advancements but maintaining the sanctity of the traditional Abacus method calculation.

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