How to use an Abacus to Speed up Solving Math Problems

The abacus is a counting tool, used to help speed up mathematical calculations, and has been in use since ancient times. An abacus consists of beads strung on wires that run across a wooden frame. This device may seem archaic in today’s world because the advancement of technology has given us calculators and modern computers but the abacus is still in use today. It is still used by some merchants in Asia and school children in Japan are still taught how to use the abacus as part of their regular curriculum. It can also be used by individuals who are blind and cannot see the display on a calculator.

To use an abacus you must first understand its layout. The modern soroban (Japanese abacus) consists of several columns each containing four beads with a crossbar above them containing a single bead that represents five units. The single unit beads are known as earth beads and the beads above the crossbar which represent five units are called heaven beads. The extreme right of the abacus contains the smallest units. For example if you are working with whole numbers only, the value of the beads in right column is one unit. If using decimal places, this row can represent a tenth of a unit, a hundredth, etc. If we assume that the right-most row is a single unit, then the row immediately to the left of it would be tens which is followed by hundreds, thousands, and so on. To represent the number 27 on the abacus you would slide up two earth beads from the ten column, two earth beads from the one column, and finally the heaven bead above the crossbar in the one column.

The first step to utilizing the abacus is the clear it out. You do this by sliding all the beads downwards so that none of the beads are raised. You let gravity do the work for you simply by tilting the abacus towards yourself before laying it on a flat surface. Addition and subtraction are very simple operations to perform with an abacus. The most important concept is that when using the abacus you work from left to right. This allows you to easily add and subtract numbers the way they are read. If you wish to perform the calculation 142+156, you would set the abacus to the number 142 then add one bead in the hundreds column, five beads in the tens column and 6 beads in the ones column.

When there aren’t enough beads in a column to perform the addition or subtraction a system using complementary numbers is implemented. The complementary numbers in respect to 10 are pairs of numbers that equal 10 when added together such as 6 and 4. When doing a problem like 5 + 6 you would set the abacus to 5 but that leaves only 4 beads in the column. Instead of adding 6 you subtract its complement which is four and then you carry the ten. Subtract four beads from the five in the one column and you are left with a single bead. You then add one bead to the ten column and you are left with the answer which is 11 of course. To do subtraction you merely add the complement instead of subtracting it and you would subtract one bead from the tens column instead of adding one. More advanced abacus techniques include multiplication and subtraction.

Through practice you can become very efficient with an abacus. Some have even been able to perform calculations with an abacus faster than someone using a modern calculator. This is because of the principle of mechanization. Mechanization means we want to use as little mental power as possible when using the abacus. The purpose is for the human to operate the device and allow the device to do the calculation. In this way, the process of using the abacus requires very little thought from the operator allowing one to use it in a very fast and efficient manner. This makes the abacus a great tool for teaching young children arithmetic. There is also a system of mental arithmetic that utilizes a mental abacus to do calculations. The abacus continues to prove its worth even in the modern world where technology appears to have long surpassed the usefulness of the abacus.