Mathematics

Complete Guide: Learn how to count numbers using Abacus now!

2.2k views

17 November 2020                

Read time: 5 minutes

Introduction

Have you ever wondered how people managed without an important device like Calculators centuries ago?

As you can imagine, it would be quite difficult 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 more significant 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.

Abacus is a tool that can be used to calculate — Add, Subtract, Multiply & divide, apart from being able to do other arithmetic functions and Brain activation.

In this article, you will learn how Abacus is used for simple counting.

Abacus Blogs
How to use an Abacus Discover Addition and Subtraction using Spike Abacus
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 Abacus Basics

A Brief Journey Of Abacus through time

According to written text, Counting tables have been used for over 2000 years dating back to Greeks and Romans. 

 The normal method of calculation in Ancient Greece and Rome was done by moving counters on a smooth board or table suitably marked with lines or symbols to show the ‘places.’

The origin of the portable bead frame abacus is not well-known. It was thought to have originated out of necessity for traveling merchants.

Some historians give the Chinese credit as the inventors of bead frame abacus, while others believe that the Romans introduced the abacus to the Chinese through trade.

Today the abacus lives in rural parts of Asia and Africa and has proven to be a handy computing tool.

The widely used abacus throughout China and other parts of Asia is Known as Suanpan. It has five unit beads on each lower rod and two ‘five-beads’ on each upper rod.

The modern Japanese abacus, known as a Soroban, was developed from the Chinese Suan-pan.

The Russian abacus, the Schoty, has ten beads per rod and no dividing bar. The Soroban abacus is considered ideal for the base-ten numbering system, in which each rod acts as a placeholder and can represent values 0 through 9. 


How to count numbers on Abacus?

The abacus is usually constructed of varied sorts of hardwoods and comes in varying sizes. The frame of the abacus features a series of vertical rods on which a variety of wooden beads are allowed to slip freely.

A horizontal beam separates the frame into two sections, referred to as the deck and, therefore the third deck.

Abacus Counting : parts of abacus lower deck and upper deck

Preparing The Abacus: The abacus is ready to be used ("zeroed") by placing it flat on a table and pushing all the beads on both the upper and lower decks far away from the beam by sliding the thumb along the beam.

Abacus counting: zeroing the abacus

Bead Values: Each bead within the deck features a value of 5; each bead within the third deck features a value of 1.

Beads are considered counted when moved towards the Beam— the piece of the abacus frame that separates the 2 decks.

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

Abacus counting: Bead Values on abacus

The right-most column is the ones column; subsequent adjacent to the left is that the tens column; subsequent adjacent to the left is that the hundreds column, and so on.

Floating-point calculations are performed by designating an area between 2 columns because the decimal-point and every one of the rows to the proper of that space represents fractional portions while all the rows to the left represent integer digits.

The third column (from the left), representing the amount 8, is counted with 1 bead from the top-deck (value 5) and three beads from the bottom-deck (each with a worth of 1, totaling 3); the sum of the column (5+3) is 8.

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

On each rod, the Soroban abacus has one bead in the upper deck, known as the heaven bead, and four beads in the lower deck, known as the earth beads.

Each heaven bead in the upper deck has a value of 5; each earth bead in the lower deck has a value of 1.

Once it is understood how to count using an abacus, it is straightforward to find any integer for the user. 

There are two general rules to solve any addition and subtraction problem with the Soroban abacus.

  • The operator should always solve problems from left to right. 
  •  The operator must be familiar with how to find complementary numbers, specifically, always with respect to 10 

The value added to the original number to make 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. For example, consider adding 8 and 4. The process begins by registering 4 on the unit rod H,

Abacus Bead values while counting on abacus

Because the sum of the two numbers is greater than 9, subtraction must be used. We subtract the complement of 8 - namely 2 - from 4 on rod H and add 1 bead to tens rod G. 

Abacus Bead values : subtracting on abacus

This leaves us with 1 bead registered on rod G (the tens rod) and 2 beads on rod H (the unit rod)

Abacus Bead values

This rule remains the same regardless of the numbers used. 

As we all know, subtraction is the opposite operation of addition. Thus, when subtracting with the Soroban abacus, we add the complement and subtract 1 bead from the next highest place value.

Using Abacus for Visually Impaired Children

Parents of many children with visual impairments are familiar with "talking calculators" and understand how their child can use this adaptive device to aid him/her in doing math problems.

However, there is an ancient device they may not be aware of that is very important for their child to be able to use. This device is an abacus and is an adaptation of the Japanese abacus.

Most of you have seen an abacus somewhere in your life, but you may never have used one.

For the child with a visual impairment the abacus is comparable to the sighted child's pencil and paper, and should be considered a fundamental component of his math instruction.

Just like his sighted peers, the VI student should also learn to use a calculator.

Total reliance on the calculator should be avoided, however, because

  • the calculator does not allow a child to learn problem-solving skills.
  • the VI child will not have a "backup" plan when the battery goes dead.
  • children who are deafblind and who may not be able to hear the voice of a talking calculator may also benefit from using an abacus.

How to Use the Counting Method

Similar to Chisenbop (a system of using fingers for calculating), the counting method uses rote counting as beads are moved toward or away from the horizontal counting bar of an abacus.

As compared to other methods of calculating on the abacus (synthesis, direct/indirect, secrets, number partners), the counting method involves only four processes.

Consequently, this method is best for students with visual and multiple impairments who would benefit from using an abacus.

These students will probably learn the four processes more easily than the many steps needed to complete calculations with other methods

To be successful using the counting method, students should be capable of rote counting and have the knowledge of the concepts "one more than" and "one less than."

 

Abacus Counting Method

4/5 exchange = exchanging a 5-bead for four beads set in the same column

Example: When you have four beads set and need to add one more, you set the 5-bead above the bar in the same column as you clear the four beads and count "one."

0/9 exchange = exchanging beads equaling the amount of nine for a 1-bead in the column to the immediate left

Example: When you have the amount of nine set and need to add one more, you set a 1-bead in the column to the immediate left as you clear the nine and count "one."

49/50 exchange = exchanging beads equaling the amount of 49 for a 5-bead in the same column in which the four beads are set

Example: When you have the amount of 49 set and need to add one more, you set the 5-bead in the same column in which the four beads are set as you clear the 49 and count "one."

99/100 exchange = exchanging beads equaling the amount of 99 for a 1-bead in the column to the immediate left

Example: When you have the amount of 99 set and need to add one more, you set a 1-bead in the column to the immediate left as you clear the 99 and count "one."

These exchanges are reversed for subtraction and can occur in any column on the abacus.


Simple addition and subtraction

Given below are some examples to explain how to solve problems of addition and subtraction.

Simple addition is performed on the abacus by counting the beads for the first number and then counting the beads for the number to be added.

For example, to solve 1 + 2, you would first move up a bead in the lower deck to represent 1, and then move up 2 beads from the lower deck.

The beads will then represent the number 3, which is the solution to 1 + 2.

If counting during addition results in a value greater than 10 on any wire, then “carrying” is accomplished by clearing beads from the upper and lower deck of the current wire and moving one bead up from the lower deck on the wire to the left.

Simple Addition

Simple Addition of two numbers using abacus

Simple Subtraction

Subtraction is done on the abacus by counting out the first number and then clearing beads that represent the second number.

For the problem 9 – 6, you would move down one bead in the upper deck and move up four beads in the lower deck to represent the number 9.

Then you would move down 1 bead from the upper deck and move up one bead from the lower deck to subtract 6. The resulting beads represent the number 3, which is the solution to 9 –6.

Simple Subtraction of two numbers using Abacus



Downloadable PDF

Here are some additional points that talk about how to count numbers using Abacus now!. To view them click on the Download button.

📥

Learn how to count numbers using Abacus now!

Download

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, the abacus is taught to early school goers as it has been seen that it helps subtends have a better understanding of numbers.

So, let’s recapitulate

  • The abacus instrument is durable

  • The abacus can be used to help young children learn numerical concepts.

  • It helps in developing the skills at correctly manipulating beads on the counting tool.

  • It builds an understanding of mathematical processes such as division, multiplication, subtraction, and addition. 

Below are some blogs related to Abacus that will develop your understanding further:

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 Abacus Basics

About Cuemath

Cuemath, student-friendly mathematics and coding platform, conducts regular Online Live Classes for academics and skill-development, and their Mental Math App, on both iOS and Android, is a one-stop solution for kids to develop multiple skills.

Check out the fee structure for all grades and book a trial class today!


Frequently Asked Questions (FAQs)

What is an Abacus?

An Abacus is a manual aid for calculating, which consists of beads that can be moved up and down on a series of sticks or strings within a usually wooden frame. The Abacus itself doesn't calculate; it's merely a device for helping a human being calculate by remembering what has been counted.

Where was the Abacus invented?

The type of Abacus most commonly used today was invented in China around the 2nd century B.C. However, Abacus-like devices are first attested from ancient Mesopotamia around 2700 B.C.!

Where was Abacus first used?

The Abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool used in the ancient Near East, Europe, China, and Russia, centuries before the adoption of the written Arabic numeral system. The exact origin of the Abacus is still unknown.

What are the advantages of learning how to use an Abacus?

Mathematical skills lay a secure foundation for higher classes. 

Abacus education improves the skills of

  • Visualization (photographic memory)

  • Concentration 

  • Listening Skills

  • Memory, Speed

  • Accuracy

  • Creativity

  • Self Confidence

  • Self-Reliance resulting in Whole Brain Development

Is it good for children to use an abacus?

Yes, an abacus is an excellent tool for teaching children basic math. The different senses involved in using an abacus, like sight and touch, can also reinforce the lessons


External References


GIVE YOUR CHILD THE CUEMATH EDGE
Access Personalised Math learning through interactive worksheets, gamified concepts and grade-wise courses
Learn More About Cuemath