How to Use an Abacus for Counting, Adding, Subtracting & Multiplying

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June 13, 2020

Reading Time: 6 minutes

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 deck and five in the lower deck) which extends from top to bottom of the frame. The two beads in the upper deck have a value of five, and the five beads in the lower deck 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.

 

How to perform counting on an abacus?

Each bead in the lower deck, as informed, is of value 1. After 5 beads are counted, the result is "carried" to the upper deck. After both the beads in the upper deck 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 an 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.

 

  • Adding Bigger Numbers

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 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.

 

(2) 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 the 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.

 

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. But that was kept out of the scope of the article. There are designated abacus videos and classes that are available on various platforms, both online and offline. We highly recommend our students enroll themselves in these classes so that they can understand more about how an abacus works and how to read an abacus. Towards the end of the article, we would like to answer the final question which relates to what is the importance of learning abacus. Besides all the dramatic improvement in the ability to calculate, learning an abacus is also beneficial because:-

  • It improves the proficiency of students in a difficult subject like mathematics. With regular practice on abacus and visualization, the child becomes more capable to perform mathematical calculations mentally.

  • It boosts the concentration and memory of the students. Various researchers have claimed that Abacus generates a positive effect on the mindset of a child.

  • It enhances the logical understanding of children to carry out the mental calculations.

  • It also helps to improve the numerical memory of the child.

 

Summary

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 all our readers to start understanding the fundas of an abacus.

Cuemath is an online platform that teaches your child one of the most difficult school subjects, mathematics. Our highly qualified and trained teachers are always on the edge of helping each and every student with all the doubts. They follow a step-by-step manner to make students understand the nuances of a particular problem. There are different levels of assignments that are provided to students which helps them for regular practice. Along with everything, regular follow-up sessions and feedback sessions also take place in order to clear the understanding of students. We are also available through an application which is present on both the Android and the iOS platform. This maths gym app helps our students to develop their mental skills and abilities through various games and puzzles. We are ready to provide each and every support required for your child's better future. Come, join Cuemath for a new beginning.

  
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