Mathematics

Complete Guide: How to multiply two numbers using Abacus?

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13 November 2020                

Read time: 5 minutes

Introduction

Can you imagine our world if numbers do not exist? How difficult would it 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.

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

So throughout history, calculating larger numbers has been difficult, especially for the typical uneducated merchant. In that scenario, the idea of the abacus was born.

The abacus is a timeless computing tool that is still applicable in today’s classrooms.

Solving problems on an abacus is a quick mechanical process compared to modern-day multifunctional calculators.

After learning the necessary counting procedures and memorizing a few simple rules, students can use the abacus to solve various problems.

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 involved 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.

History of Abacus: Chinese Abacus, Japanese Abacus, Russian Abacus

The abacus is a window into the past, allowing users to carry out all operations in the same manner as it is done for thousands of years

. Moreover, the device provides students in today’s classrooms with alternatives to paper-and-pencil procedures that let them explore calculations in a more hands-on manner, which also contributes to the overall development of students.

For more detailed information on the history of Abacus, check Abacus History


How to count numbers on Abacus?

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.

Another example, consider adding 8 and 4. The process begins by registering 4 on the unit rod H,

Abacus multiplication process

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 multiplication process 2

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

Abacus multiplication process -3

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.


How to perform Multiplication on Abacus?

Multiplication problems are more complicated than addition and subtraction but can be easily computed with the help of the Soroban abacus.

Before students can complete multiplication problems, they must first be familiar with multiplication tables through 1 to 9.

Registering the multiplicand and the multiplier is the most critical step in the process. This ensures the one's value of the product falls neatly on the unit rod.

As an example, let’s consider the multiplication problem 36 × 4, with multiplicand 36 and multiplier 4.

We begin by placing our finger on unit rod H and count left one rod for every digit in the multiplier (1 position to rod G) and one rod for each digit in the multiplicand (2 positions to rod E).

Next, register 36 on rods E and F. Then place 4 on rod B. This leaves enough space to help students distinguish the multiplicand from the multiplier.

Abacus Multiplication : Multiplier and multiplicant

Performing multiplication on the abacus involves only the addition of partial products.

Our first step is multiplying 6 by 4 and adding the partial product on the two rods, GH, to the right of the multiplicand. Since we’ve accounted for the 6, we reset rod F to zero.

Abacus Multiplication : resetting to zero

A similar process is followed to multiply 30 by 4. Its product, 120, is added to rods EFG.

Since we’ve accounted for the 30 in our calculation, we reset rod D to zero. This leaves the final product, 144, on rods FGH.

Once addition is mastered, the reader is encouraged to try multiplication problems involving carrying, such as 36 × 9.

Abacus Multiplication

Solving division problems on the Soroban abacus mirrors familiar paper-and-pencil calculations.


Summary

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.

Performing basic operations like multiplication on an abacus involves and develops a child's mind.

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

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

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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.


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