Math & Beyond

The Complete Guide to the Abacus

12th Oct '2018 views8 mins read

13 November 2020

Read time: 5 minutes

Introduction

As one can imagine, how difficult it would be to count without numbers. There was a time when written numbers did not exist. The earliest counting device would have been the human fingers or toes.

But for greater or bigger numbers, people would depend upon natural resources available to them, such as pebbles, seashells, etc.

The abacus is the most ancient calculating device known. It has endured over time and is still in use in some countries.

The Abacus is a Latin word meaning sand tray. The term originated with the Arabic ‘abq’, which refers to dust or sand. In greek, this becomes ‘abax’ or ‘abakon’ meaning a tablet.

The abacus was used as a counting tool before the advent of the Arabic numeral system.

Merchants and traders needed to maintain an inventory of the goods they bought and sold. When the Hindu-Arabic number system came into use, abaci ( plural of abacus) were adapted for place-value counting.

Abacus Blogs
Abacus Anatomy & Construction Abacus History
Abacus Level I Abacus Level II
Abacus Counting Abacus Techniques
Abacus Addition Abacus Subtraction
Abacus Multiplication Abacus Division
Negative Numbers in Abacus How to Use an Abacus for Counting, Adding, Subtracting & Multiplying

What is an Abacus?

An abacus or a counting board consists of a wooden frame, rods, and beads. Each rod represents a different place value—ones, tens, hundreds, thousands, and so on.

Each bead represents a number, usually 1 or 5, and can be moved along the rods. Addition and subtraction can easily be performed by moving beads along the wires of the abacus.

The beads that slide along a series of wires or rods set in a frame to represent the decimal places. The standard abacus can be used to perform addition, subtraction, division, and multiplication. It can also be used to extract square-roots and cubic roots.

The beads are manipulated with either the index finger or the thumb of one hand. The abacus is typically constructed of various types of hardwoods and comes in varying sizes.

The abacus frame has a series of vertical rods on which a number of wooden beads are allowed to slide freely. A horizontal beam separates the structure into two sections, known as the upper deck and the lower deck.

One could call it a precursor to the modern-day calculator. Merchants commonly used it in Europe and the Arabic world. Even today, in the modern world of computers and calculators, it is used by traders, merchants, etc. in many parts of the world. It is still used to teach the basics of arithmetic to children.


A brief history of Abacus

It is the most primitive form of a calculating device, invented somewhere between 300 and 500 B.C.. The exact date of the origin of the abacus is unknown.

The first written information about the abacus survived to the present, is from the Greek historian Herodotus (480-425 B.C.), who mentioned also, that the ancient Egyptians used abacus.

The oldest abacus survived to the present day, is so-called Salamis abacus. It is believed to have been found on Salamis, a Greek island, in 1899, hence the name. It was used by the Babylonians around 300 b.c.e.

Salamis Abacus

Drawings of people using counting boards have been found dating back to the same time period.

There is evidence that people were using abacuses in ancient Rome (753 b.c.e.–476, c.e.). A few hand abacuses from that time have been discovered.

They have slots with beads in them that can be moved back and forth in the slots similar to counters on a counting board. They resemble the Chinese and Japanese abacuses, suggesting that the use of the abacus spread to many parts of the world from Greece and Rome to China, Japan, and Russia.

The Chinese called it the Suanpan. Not much is known of its early use, but rules on how to use it emerged in the thirteenth century.

The Japanese abacus is called the Soroban which was not used widely until the seventeenth century. The Soroban is still in use today. The Japanese have yearly examinations and competitions in computations on the Soroban.

The Russians called it the Schoty. Not much is known about how it came to be used in Russia.

To learn more about the diverse history of the Abacus, click Abacus: A brief history from Babylon to Japan.


Abacus Basics

For many of us, Mathematics is the subject we love to hate. Having said that, calculations and numbers are part of our everyday lives.

Abacus learning makes the calculation process easy and interesting.

An abacus has beads that slide on rods.

  • The column on the far right is for ones (1,2,3,...)
  • The next column is for tens (10,20,30,...)
  • The next column is for 100s (100,200,300,...) etc

The most common abacus is split into two basic rows:

There are two beads in the top row, and five beads in the bottom one. The top row is worth 5 of the bottom row

Example

 

 

7 can be made using one bead on the top row, and 2 beads from the bottom row, because 5 + 2 = 7.


Abacus Counting

First, make sure each column in the top row has one or two beads per row and each column in the bottom row has four. While starting, all of the beads should be up in the top row, and down in the bottom row. The beads in the top row represent the number value 5 and each bead in the bottom row represents the number value 1.

Abacus details

Each column of beads represents a "place" value”. So, the farthest column on the right would be the "ones" place (1-9), the second farthest the "tens" place (10-99), the third farthest the hundreds (100-999), and so on.

To count a digit, push one bead to the "up" position. "One" would be represented by pushing a single bead from the bottom row in the farthest column on the right to the "up" position, "two" by pushing two, etc.

It is easier to use one’s thumb to move the beads in the top row, and the index finger to move the beads in the bottom row.

To learn more about Abacus Counting, check out Abacus Counting.

Abacus Adding

To add 1234 and 5678, enter 1234 on the abacus by pushing up four beads in the ones place, three in the tens place, two in the hundreds place, and one in the thousands place

The first numbers to be added are the 1 and the 5 from the thousands place, moving the single bead from the top row of that column down to add the 5, and leaving the lower bead up for a total of 6. Likewise, to add 6 in the hundreds place, move the top bead in the hundreds place down and one bead from the bottom row up to get a total of 8.

Since adding the two numbers in the tens place will result in 10, you'll carry over a 1 to the hundred place, making it a 9 in that column. Next, put all the beads down in the tens place, leaving it zero.

In the ones column, you'll do essentially the same thing. Eight plus 4 equals 12, so you'll carry the one over to the tens place, making it 1. This leaves you with 2 in the one's place.

Now if you count your beads you get the answer. You're left with a 6 in the thousands column, a 9 in the hundreds, a 1 in the tens, and a 2 in the ones: \(1,234 + 5,678 = 6,912.\)

To learn more about Addition on Abacus, check out Complete Guide: How to add two numbers using Abacus?

Subtracting

Here we reverse the process. Borrow digits from the previous column instead of carrying them over. If you are subtracting 867 from 932, enter 932 into the abacus, start subtracting column-by-column starting on your left.

Eight removed from nine is one, so a single bead is left up in the hundreds place.

In the tens place, you can't subtract 6 from 3, so you'll borrow the 1 in the hundreds place (leaving it zero) and subtract 6 from 13, making it 7 in the tens place (the upper bead up and two lower beads).

Do the same thing in the ones place, "borrowing" a bead from the tens place (making it 6) to subtract 7 from 12 instead of 2.

There should be a 5 in the ones column: \(932 - 867 = 65\).

Similarly, multiplications and divisions can be done. All it requires is a concentration and counting ability.

To learn more about subtraction on Abacus, check out Complete Guide: How to subtract two numbers using Abacus?.

Abacus Techniques

As mentioned earlier the thumb and the index fingers play a very prominent role in mastering the abacus. The abacus is used in many countries even today and an efficient method to achieve proficiency in arithmetic. With a Chinese abacus, the thumb and the index finger together with the middle finger are used to manipulate the beads.

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. The techniques remain more or less the same.

To learn more about Abacus Techniques, check out Abacus Techniques


Summary

Despite the abacus being ancient in its origin, it is still in use today. It has been a boon for the visually challenged as learning placement value, and other calculations can be done by touch. In many countries abacus is taught to early school goers as it has been seen that it helps subtends have a better understanding of numbers. You can also check out further blogs on Abacus below.

Abacus Blogs
Abacus Anatomy & Construction Abacus History
Abacus Level I Abacus Level II
Abacus Counting Abacus Techniques
Abacus Addition Abacus Subtraction
Abacus Multiplication Abacus Division
Negative Numbers in Abacus How to Use an Abacus for Counting, Adding, Subtracting & Multiplying


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Frequently Asked Questions (FAQs)

What is an abacus?

It is a counting frame used for mathematical calculations. It is the oldest calculating device known to mankind and was discovered by the Babylons around 300 B.C.

Where was Abacus first used?

The abacus was first discovered by the Babylons in 300 B.C. but it also has traces of being used during ancient times near east, China, Japan, and Europe.

What are the advantages of using an abacus?

Removes the fear of mathematics by making arithmetic calculations easier. It is also said to improve one’s concentration, Listening Skills, Memory, Speed, and accuracy, among other things.

Who invented the abacus?

Many study's have shown that no one in particular has made the abacus but many believe it was made in China. An adapted abacus, invented by Tim Cranmer, called a Cranmer abacus is still commonly used by individuals who are blind. A piece of soft fabric or rubber is placed behind the beads so that they do not move inadvertently.



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