How to Do Division on the Abacus in Easy Steps

Updated on September 8, 2018
Tim Truzy info4u profile image

Tim Truzy is a rehabilitation counselor, educator, and former dispatcher from North Carolina.

Before starting any arithmetic problem, clear (set) the abacus to zero.
Before starting any arithmetic problem, clear (set) the abacus to zero. | Source

The Abacus is a Fabulous Tool for Performing Arithmetic

The abacus is a fascinating tool which has been used by mankind for a very long period of time to conduct a variety of math tasks. Practically all math problems can be solved with the proper knowledge of moving the beads manually on the device. Although not normally used in many Western nations for finding mathematical solutions, the abacus is still a reliable counting tool. By applying the learning senses (touch, hearing, and sight), a person can eventually become proficient with the abacus.

I have years of experience working with the abacus. This includes instructing students with visual impairments on the correct way to apply the counting tool for solving arithmetic problems. I’ve also worked with long-time masters of the abacus to sharpen my skills. Below is a technique for working with division problems with four or more digits in the equation on the abacus. Now, bring your abacus to rest, like in the photo above, and we will soon begin working with division on the fabulous counting device.

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{{Things to Know Before Performing Division on the Abacus

  1. Issues relevant to zero and multiplication wit the abacus should be known. Terms associated with the abacus should be thoroughly understood as well. Concepts and terms which should be understood include: set or clear, payback, keeping balance, one for the abacus, and at rest.
  2. By the time division is attempted, a person should have performed multiplication, subtraction, and addition problems with the abacus, including equations with four digits or greater. A person should be comfortable with the various steps in these mathematical processes as well. This is because in order to do division with the abacus, subtraction and multiplication are fundamental functions which occur when solving equations.
  3. A person should be able to place (set) any numerical value on the abacus with the limitation only being the number of columns of beads available. He/she should be comfortable with mentally dividing the counting tool, such is done in multiplication. Likewise, he/she should recognize not having to mentally “split” the device when solving addition and subtraction equations. Finally, the words associated with division should be firmly understood, including: quotient, divisor, remainder, and dividend.

 Division problems are placed on the abacus in a different way. The abacus in this photo reads: 308 divided by 7.
Division problems are placed on the abacus in a different way. The abacus in this photo reads: 308 divided by 7. | Source

Preparing to Carry out Division with the Abacus

Realizing division is the opposite function of multiplication is essential when working with an abacus. Fundamentally, division is subtraction done repeatedly. When performing division, we must think of the abacus as being split into two sections which helps in understanding these concepts. This will help us in finding the solution (quotient). Thinking of the counting tool as having two sections should be a familiar cognitive task since multiplication requires the same way of approaching the counting tool.

The photo above shows an abacus with the equation: 308\7. The dividend 308 uses the hundreds, tens, and ones rows on the right side of the device. The divisor 7 is placed on the far left on the abacus. This is how we set division problems on the counting tool.

Let's do Some Division

  • First, the number 7 doesn’t go into the number 3, unless we are dealing with decimals, which is beyond the scope of this article. Therefore, we move over to include the zero in 308. Now, we divide 30 by 7.
  • Next, we understand that 30 can be divided by 7 four times. Immediately to the left of the 3 (on the fourth column) we place the four and leave it there. (This should give us an indication the answer will be in the forties.)
  • Now, we multiply. 7 x 4 to reach 28. Or We think: 7 x 40 to get 280.
  • We subtract 280 from 308, leaving us with 28 still occupying the tens and ones’ columns. Your partial answer should resemble the photo.

This is an abacus showing the divisor 7, the partial quotient 4 and the number 28.
This is an abacus showing the divisor 7, the partial quotient 4 and the number 28. | Source
  • Now, we divide the remaining 28 by 7. You place the next 4 immediately beside the first 4. Your answer should occupy the fourth and third columns. Clear the remaining 28.
  • Our answer will be 44, which is shown in the photo below.
  • If you examine the answer carefully, you will notice that 44 takes up the fourth and third columns. If you check your work through multiplication, you would be able to determine that the answer would be in the hundreds. You should be able to get 308 when you multiply 7 x 44.
  • Now, bring your abacus to rest.

This abacus is showing the quotient 44.
This abacus is showing the quotient 44. | Source
The abacus shows 459\62 in this photo.
The abacus shows 459\62 in this photo. | Source

Let's do a Division Problem with a Remainder

  1. Set the division problem: 459 divided by 62.
  2. Remember: The number 459 is set on the hundreds, tens, and ones columns on the right side of the counting tool. 62 is placed on the left side of the abacus. The equation should look like the photo above.
  3. Now, look at the first number in the divisor: 6, or 6 tens.
  4. We know that 6 goes into 45 7 times. We place the seven beside 459, then multiply 7 x 6 to get 42.
  5. We then subtract: 42 from our dividend. Or we subtract 420 from 459 for a result of 39.
  6. We still have another number left in the divisor: 2. We want to multiply the 7 by that number.
  7. Multiply: 7 x 2 to get 14. Subtract this number from 39.
  8. You will notice 25 is still on the ones and tens column. This is your remainder.
  9. Now, clear the divisor. Your answer should look like the photo below.
  10. You should have a quotient of 7 with a remainder of 25 on the counting tool. After you have examined your answer, bring your abacus to rest. You have successfully completed two division problems.

Remainders will appear after the quotient is found in the columns on the right hand side of the abacus. This abacus shows the quotient 7 with a remainder of 25.
Remainders will appear after the quotient is found in the columns on the right hand side of the abacus. This abacus shows the quotient 7 with a remainder of 25. | Source

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Was this a new technique for carrying out division on the abacus for you?

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Exploring Different Types of the Counting Device

  • Indeed, there are different types of abaci. For this article and others I have written, I used the Cranmer abacus. This counting tool can be purchased through vendors such as the American Printing House for the Blind in Louisville, KY. It is a favorite of students with visual impairments and Teacher of the Visually Impaired (TVI) training programs.
  • Yet, there are Japanese abaci, called soroban, which utilize the base ten system. The Chinese suanpan uses a base sixteen system. Regardless of the abacus you decide to work with to perform arithmetic, the tactile, auditory, and visual senses must be applied to perfect your skill.
  • Without question, there are even digital abaci available. But these apps can hinder development of the crucial skill of mental visualization. Physically manipulating the beads helps with memorizing various steps. Applying all of the learning senses through regular practice is essential for becoming proficient with the abacus.

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    • Tim Truzy info4u profile imageAUTHOR

      Tim Truzy 

      2 days ago from U.S.A.

      Hi, Nell,

      It's o.k. You jumped in on a more difficult topic when using the abacus. If you visit my page, you can read the other articles which have built up to working with these concepts. Start with the one called: "How to Count to 99 on the Abacus." Then, I have one on subtraction and multiplication. If you are able to locate an abacus like the Cranmer, that would be helpful too.

      Remember: the abacus is focused on the tactile sense and it helps to have one near.

      You are neither stupid nor lacking the ability to master the abacus. It's just a matter of having experience using it. That's why I tried to include as many photos as possible to help people.

      Nevertheless, I appreciate your comment, and if you pick up an abacus and want some assistance or have questions, let me know.

      Much respect and admiration,

      Tim

    • Nell Rose profile image

      Nell Rose 

      3 days ago from England

      LOL! laughing my head off at my own stupidity here! I was scratching my head while mumbling, 'okay 7 goes by the...3? What? what on earth does it mean? I will stick to writing, but interesting stuff! LOL!

    • Tim Truzy info4u profile imageAUTHOR

      Tim Truzy 

      3 months ago from U.S.A.

      Thanks for your comment, Jo. The great thing about the abacus is that it could still be used for developing numerical concepts. Just playing with counting the beads can help the child understand such concepts as quantity (How many objects represent 3? How many equal four? And so on.)

      I'm sure she is a bright child and can grasp the abacus. After all, she is related to you, a very skilled writer and dedicated soul.

      Thanks again for taking the time to read this article.

      Much respect and admiration,

      Sincerely,

      Tim

    • jo miller profile image

      Jo Miller 

      3 months ago from Tennessee

      Thanks, Tim. I've never really learned much about the abascus but have usually just known it as a toy for my children and grandchildren. My granddaughter has one sitting on her desk. I wonder if she really knows how to use it.

    • Tim Truzy info4u profile imageAUTHOR

      Tim Truzy 

      3 months ago from U.S.A.

      Thanks, Sean. Your comment means much to me. Later I will visit some of your articles.

      Sincerely,

      Much respect and admiration,

      Tim

    • Sean Dragon profile image

      Ioannis Arvanitis 

      3 months ago from Greece, Almyros

      Oh! How many talents do you have, my brother! Speechless!

      God bless your talents!

      Sean

    • Tim Truzy info4u profile imageAUTHOR

      Tim Truzy 

      3 months ago from U.S.A.

      Not a problem, Eric. Thanks for the comment. Keep up your great work on the West side and I'll be sending my prayers your way from the East.

      God bless you.

      Sincerely,

      Tim

    • Ericdierker profile image

      Eric Dierker 

      3 months ago from Spring Valley, CA. U.S.A.

      So cool Tim. That together abacus stuff is really fun. We are right behind you.

    • Tim Truzy info4u profile imageAUTHOR

      Tim Truzy 

      3 months ago from U.S.A.

      Thanks, Pamela. Your comment is valued and precious. I've read enough of your articles to know that if you decide to do something, Pamela will achieve.

      If you want any reference material, if you acquire an abacus, please, let me know. It's fun to own one of these devices. My wife and I take them with us to the grocery store when we shop. She hides her smartphone during those trips.

      People look at us as we add the cost of things and then the sales tax. We just smile.

      Thanks again for your comment. May your day be peaceful and rewarding.

      Much respect and admiration,

      Sincerely,

      Tim

    • Tim Truzy info4u profile imageAUTHOR

      Tim Truzy 

      3 months ago from U.S.A.

      It's all right, Eric. I appreciate your feedback and thoughtful words. By the way, this is pretty poetic, my friend:\

      "Food preparation and cooking

      Deep in depth one word work

      Virtual interaction

      Action without seeing

      Action without hearing

      Touching communication without speaking and,

      The art of words in a picture"

      You are indeed a poet, Eric. Quite a master with words. Not only that, you strive to live the words you write.

      Thanks again.

      May your weekend be blessed.

      Much respect and admiration,

      Sincerely,

      Tim

    • Pamela99 profile image

      Pamela Oglesby 

      3 months ago from Sunny Florida

      Tim, I have never used an abacus, but I was fortunate as I learned math without too many problems. I do remember using flash card for multiplication, and I can still do it in my head thank goodness. I think the abacus would have made it easier.

      This was a very interesting article, and I would like to own an abacus to try it out. It seems to easily help anyone with all the math problems. Thanks for this new information.

    • Ericdierker profile image

      Eric Dierker 

      3 months ago from Spring Valley, CA. U.S.A.

      Thank you Tim, called the number but wrong time zone ;-) I am working on a concept, not yet a program of any sorts. More like mental machinations with some goals.

      I am all about doing blind stuff and balance stuff and mature crawling, and playing catch with our "other" hand. So take that as a disclaimer.

      I believe we all could do much better fruitfully and kind of intensely getting in the groove with parts not used.

      I think Carb Diva and Ann Art are folks I want to work with though they are quite busy. And I need a poet artist with words.And I have a virtual reality 3D type fellows. I also think that making seeing folks blind and hearing folks deaf should be helpful.

      Food preparation and cooking

      Deep in depth one word work

      Virtual interaction

      Action without seeing

      Action without hearing

      Touching communication without speaking and,

      The art of words in a picture

      I think these notions go for our youngsters and our oldsters. Development to dementia. I believe that the untapped centers are more important than even the positive tapped sources of comprehension.

      I am working on a hub on it and would hope folks would be critical and lay out downfalls from funding to plain stupidity.

      Sorry to take too much of your time from your loved ones.

    • Tim Truzy info4u profile imageAUTHOR

      Tim Truzy 

      3 months ago from U.S.A.

      Hi, Eric,

      Great question. The best source I recommend to parents for finding an abacus is our own governmental nonprofit organization. This organization is devoted to creating braille books, large print text, and books in audio. It is the American Printing House for the Blind located in Kentucky.

      Their toll free number is: (800) 223-1839.

      The American Printing house for the Blind (APH) also has websites where you can check out more of their products. They are leaders in innovation for people with vision loss. My students use the Cranmer abacus, which is not that expensive. Although there are other sources for finding the counting tool, APH seems to respond the quickest from what parents have told me.

      Thanks again for your question. I hope this helps.

      Sincerely,

      Much respect,

      Tim

    • Ericdierker profile image

      Eric Dierker 

      3 months ago from Spring Valley, CA. U.S.A.

      Tim I have to get one super cheap. Any suggestions. My son used to do finger abacus method. Now that is to slow for him. When a kid can smirk when asked to do 133 divided by 7. I forget, something about integers.

      But I fully believe that as in my undergraduate work that, numbers are the basis for all logic.

      Therefor we need an abacus and will learn it with our eyes closed.

    • Tim Truzy info4u profile imageAUTHOR

      Tim Truzy 

      3 months ago from U.S.A.

      Thanks, Flourish,

      You are right. I call multiplication and division two siblings. Without understanding one you can not prosper in doing the other on the abacus.

      Thanks for your comment.

      Much respect and admiration to another skilled and aware writer who always has something interesting to say in her work,

      Sincerely,

      Tim

    • Tim Truzy info4u profile imageAUTHOR

      Tim Truzy 

      3 months ago from U.S.A.

      Hi, Eric,

      The abacus is one of those older technologies that we have forgotten somewhat as a culture. But people with vision loss love the device. I've taught one of my fully sighted nieces who was having trouble grasping arithmetic to use her fingers like an abacus to count and do multiplication. Some excelled afterwards.

      Some people need more tactile methods to grasp mathematical concepts. One size doesn't fit all. We are in a competitive world, and a teacher has to be flexible, trying different approaches with children, much like you do from what I've read of your innovative approaches.

      That's why I enjoy the abacus.

      Thanks for your comment.

      Much respect and admiration,

      Sincerely,

      Tim

    • FlourishAnyway profile image

      FlourishAnyway 

      3 months ago from USA

      Wow, this emphasizes the need to learn those multiplication tables and be snappy about the answers.

    • Ericdierker profile image

      Eric Dierker 

      3 months ago from Spring Valley, CA. U.S.A.

      What an interesting deal here. Thanks.

    • Tim Truzy info4u profile imageAUTHOR

      Tim Truzy 

      3 months ago from U.S.A.

      Division is probably the most challenging of the basic mathematical processes. This article presents a way to use the abacus for division based on techniques I have worked with to make it easier. I have written other articles on subtraction, addition, and multiplication for the abacus. Maybe this will be useful to you, reader.

      Thanks for reading and commenting.

      Sincerely,

      Tim

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