Math Concepts

Best Way to Use an Abacus for Basic Math Operations

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25 November 2020

 1 Introduction 2 How to perform counting on an Abacus? 3 How to use an Abacus for Addition? 4 How to use an Abacus for Subtraction? 5 How to use an Abacus for Multiplication? 6 Conclusion 7 Frequently Asked Questions (FAQs) 7 External References

Introduction

Have you ever wondered how people used to solve mathematical problems before the invention of a calculator or the computer?

If you are thinking they always used to carry a pen and paper, then you are mistaken.

For centuries, people in Asia have used the Chinese calculator “suanpan,” also known as an abacus.

It is a simple calculating device that consists of a rectangular wooden frame divided by a horizontal bar into the upper and lower sections.

There is a series of vertical wires to which 7 beads are attached (two in the upper row and five in the lower row) which extends from top to bottom of the frame.

The two beads in the upper row have a value of five, and the five beads in the lower row have a value of one each.

The wires represent the powers of 10. A traditional abacus consists of 13 wires in order to represent very large numbers. Chinese abacuses are designed to allow for hexadecimal computation.

You can check the below video for a simple introduction to the abacus:

How to perform counting on an Abacus?

Each bead in the lower row, as stated, is of value 1.

After 5 lower beads are counted, the result is "carried" to the upper row.

After both the upper beads in the upper row are counted, the result (i.e. 10) is then carried to the left-most adjacent column.

The right-most column represents the units column; the next adjacent column to the left is the tens column, and so on.

How to use an Abacus for Addition?

Once you have learned how to count Beats 1 abacus, the first operation that we can learn in addition. There are various strategies that can be applied while learning addition.

• The 10 Strategy

For example, if we have to add 9+6, we will enter 6 and 9 in the first two columns. Then moved from 6 to 9 so that 9 becomes 10 and 6 becomes 5.

So now we can easily operate 10+5=15. Once your child masters this strategy on an abacus, you can make them try doing it mentally.

• The Two 5s Strategy

For example, if we have to add 6+7, we will enter 6 and 7 in the first two wires. The two 5s will make it 10, and we will remain with three beads. Now performing 10+3=13 is easy.

This strategy works in problems where the two numbers being added are more than five.

Suppose we have to add 65+89. Students will have to represent 89 on an abacus.

The first wire from the right will have 9 and the second wire will have 8. Start with the first wire and add 5 to 9.

This will result in 14. Keep the digit 4 and pass on 1 to 8, thereby making it 9.

Now perform 9+6 which will result in 15. So, the actual result will be 154.

How to use an Abacus for Subtraction?

The next operation which you will learn is, how to use an abacus in a step-by-step method to perform subtraction?

Subtraction is just the reverse process of addition. All you need to do is borrow the digits from the previous column instead of carrying them over. For example, if you want to subtract 867 from 932.

1. After entering 932 in the abacus, start subtracting column by column from the left. If you subtract 8 from 9 you will receive 1, so you will leave a single bead in the hundreds place.

2. Now move to the tens place. You can't subtract 6 from 3, so you will have to borrow 1 in the hundreds place leaving it with 0. Now you have to subtract 6 from 13 making it 7.

3. Now move on to the unit's place. Repeat the process. Because you cannot subtract 7 from 2 you have to borrow 1 from the tens place, which will convert 7 present in the tens place into 6. Now subtract 7 from 12 so you will obtain 5.

4. So our final answer will be 932 - 867 = 65.

A regular practice will make things easier to perform. Abacus is like training for the mind. Therefore, it requires patience and regular training.

How to Use Abacus for Multiplication?

Now let's move on to the most important basic mathematical operation which is multiplication. How to multiply with an abacus?

1.  In order to multiply small numbers, for example, 6×4, we can ask the students to follow the process of addition. All they have to do is enter 6 in four different wires.

Then follow the strategy of five, as mentioned above. So now they have to perform 5+5+5+5 = 20 and 1+1+1+1 = 4. Finally, they will have to add 20+4 = 24.

Well, but the above-mentioned strategy can only be utilized in case of numbers that are small. There may be situations wherein the student confronts large numbers. In those cases, we will follow a different approach.

1. For example, if you're multiplying 34×12.

Step 1 - Assign one letter into each column. So it will become "3", "4", "X", "1", "2", and "=".

This makes us feel the first six wires. Leave the rest of the columns to the right as it is for the answer.

Remember, “X” and “=” will be represented by blank columns.

Step 2 - Multiply 3 with 1 and then 3 with 2. Next, you will multiply 4 with 1 and then 4 with 2.

Understand the pattern. This is the part which we will apply for all kinds of numbers.

Step 3 - Record the results of the products in the correct order. Start recording the first product i.e. 3x1 = 3 in the seventh wire.

Next, 3×2 = 6, record it after the column in which you recorded 3 i.e. eighth wire.

Step 4 - When you multiply 4x1, add the result i.e. 4 to the previous multiplication which we did i.e. 3×2 = 6. Now 4+6 becomes 10.

Carry one to the seventh wire which was 3 and now it becomes 4 and the eighth wire becomes 0.

Step 5 - Perform the last multiplication which is 4×2 = 8. Recorded in the ninth wire. So our answer is 408.

Conclusion

The above mentioned were some of the most basic operations which can be performed using an abacus.

An abacus is a tool that can also be used for performing higher-level calculations and operations.

There are designated abacus videos and classes that are available on various platforms, both online and offline.

With such strong benefits of using an abacus, more and more schools are imparting this training and education, especially in the lower classes.

Therefore, we encourage you to start understanding the basic fundamentals of an abacus.

If you liked this post, feel free to share it with your friends who can also benefit from learning abacus.

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!

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 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

How to use an abacus?

It is a simple device used for counting, much beneficial for the visually impaired, once you

know the basics of counting on an abacus, you can easily perform various operations on it .

Following are the basic steps to be followed:

• Assign each column a place value.
• Start counting with the beads in the lower row.
• Complete the "4/5 exchange.
• Repeat the pattern for the higher numbers.

How to learn abacus?

We can easily learn abacus. Start with learning the basic structure and bead placement of the Abacus. Then you can move on to learn the basic operations of Abacus.

External References

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