# How to Do Subtraction Using the Abacus With Easy Steps

*Tim Truzy is an expert instructor in the use of the abacus. He has taught adults and children in the use of the counting tool.*

## The Usefulness of the Abacus

The abacus is a counting tool which has been put to work by humans over many centuries to perform various arithmetic tasks. By manipulating beads on the abacus with the proper knowledge, almost all math problems can be solved. People can find the answer to multiplication, division, subtraction, and addition problems using the abacus. Today, it is still used by merchants, vendors, and the average person where calculators or pen and paper are not readily available. I have taught techniques for using the counting device to students with vision loss, and I’ve applied the helpful tool in aiding my students with grasping numerical concepts. In addition, I’ve used the abacus for years, receiving my training from masters of the counting tool. Below is a method for working with the abacus to carry out subtraction problems.

## Let's Get Started

- When you look at the abacus, you immediately notice it has rows of four beads beneath a dividing bar. Above the bar, you will see that there are rows of only one bead. To begin, we must make sure the rows of beads are pushed away from the dividing bar as far as they can go. This gives us the value of zero. We say the abacus is “resting at zero.” The picture at the beginning of the article shows an abacus “at rest.
- Next, the abacus works on the base-ten system. This is a system of counting common in most parts of the world. For this reason, from right to left with the rows of beads below the dividing bar, we count: ones, tens, hundreds, thousands, etc.
- For example, if you push the four beads on the first row up to the dividing bar, you have “placed” the number 4 on the abacus. Now, bring the abacus to rest.
- Now, if you push the four beads on the second row up to the bar, you have “placed” 40 on the abacus. It continues on in this manner. Now, bring the abacus to rest.
- In addition, above the dividing bar, the numbers indicate 5 in varying values. For instance, pull down the bead in the first row to the dividing bar. You have placed 5 on the abacus. Now, bring the abacus to rest. Now, pull down the bead above the dividing bar on the second row. You have placed 50 on the abacus. Bring the abacus to rest.
- Finally, if you were to continue doing this, the next bead above the dividing bar on the third row would represent 500, then the next 5,000, and so on. Here is some more information about working with the abacus which is important:

## Terms to Know

- Borrow – This process occurs when you subtract a smaller number from a greater one. For example: we borrow 6 from the equation which reads: 10 – 6.
- Pay back – In the above example of 10 – 6, we would have to “pay back” 4 to the abacus. Remember: You always want to keep balance on the abacus; we seek to keep the base-ten counting schemes in mind at all time.
- Place or set – This action occurs when you move beads to the dividing bar to represent a numerical value. Place and set can be used interchangeably.

## Now, let’s Work Some Math.

- Our math problem is: 100 - 50.
- Begin by placing 100 on the abacus like shown in the photo.
- Now, we want to take 5 ten’s from 100.
- We know the tens column is showing “0” tens. This means we need to “borrow” 5 ten’s from the 100 column because it is a greater number.
- Because we borrowed 5 tens, we have to “pay back” the abacus 5 tens. (Remember: the abacus works on the principles of the base-ten system.)
- We do this by pulling down the bead representing 50, and “clearing” the bead representing 100 on the third row. This gives us the answer of 50, like shown in the photo. Now, you can bring the abacus to rest.

## Let's Do Another Problem

- This time, our subtraction equation is: 100 – 33.
- Begin by placing 100 on the abacus like you did before.
- Now, this time, we want to subtract 3 tens, but there are no tens showing on the device. This means we will have to borrow 30 from 100, or 3 ten’s from 100.
- We know when we borrow 3 tens; we will have to pay back 7 tens. We place 70 on the abacus.
- The number 70 is represented by the 50 bead on the second row with two ten beads beneath it.
- Now, we need to borrow 3 ones from 70 because no ones are showing on the device.
- We push a ten bead back to its starting location, and then we payback 7 ones in the ones column.
- Our answer will read: 67. It should look like the picture.

You have successfully carried out two problems on the abacus in subtraction. You may bring the counting tool to rest. Congratulations!

## Benefits of the Abacus for Aiding a Young Child with Counting and Subtraction Concepts

Besides the benefit of assisting a young child with understanding mathematical concepts, the abacus can provide further advantages to a child who has not received training in the use of the counting tool. Without any exposure to the techniques of using the abacus, a young child can count the beads. Depending on the child’s numerical knowledge, he/she can slide the beads back and forth from a set position. A child should be able to set all of the beads, one by one, recognizing the abacus has all of the beads in a set position.

Be sure a child can count the beads before you try to help him/her comprehend subtraction. Here are some less obvious ways in which a child benefits from working with the abacus:

## Areas in which a Young Child Benefits from Working with the Abacus

- Enhancing Fine Motor skills: Manipulating beads on the abacus will help a child further develop fine motors skills. Such skills are useful for later in life when the child may play an instrument, learn to write by hand, type, or work with tools. Improving fine motor skills involve developing small muscle groups, such as in the fingers, through practiced coordination with the brain and nervous system.
- Improving the Tactile Sense: Working with the abacus will help the child focus on the sense of touch. Development of the tactile sense is essential if the child will become a Braille reader. However, even children who will not read the medium can benefit later in life in fields such as engineering and various design professions by utilizing their sense of touch when working with the abacus.
- Mental Visualization: The ability to mentally think about what must happen is enhanced through the use of the counting tool. Mental visualization is crucial in many areas of life. The abacus helps users focus on step by step analysis of a problem, preparing the child to engage in critical thinking.

## simple Method to Introduce a Child to subtraction with the Abacus

- First, have the child set all of the beads on the counting tool, like shown in the photo. Have the child count the beads one at a time, aloud if necessary.
- Next, ask the child to tell you how many beads are set on the abacus. (In the abacus used in the photo, the number would be 65 beads.)
- Now, have the child move a given number of beads back to the starting position. For this example, let’s say the young person moved four beads.
- Now, ask the child how many beads are left. If he/she has to count, allow it.
- When the child gives you the correct answer, give him/her a positive response.
- Say to the child: “Now, we know that when you take away 4 from 65, you will have 61.” Or: “We know now that 65 – 4 = 61.”
- Vary how you express the answers about subtraction. This assists the child in comprehending the same idea can be expressed with different words.
- Finally, try this simple method again using a different number of beads.
- When you think the child understands what you are communicating about subtraction, use other examples. For instance, you may want to try subtraction with pennies, spoons, books, etc. The child must be able to transfer the knowledge gathered from working with the abacus to other situations to build his/her mathematical abilities.

## Comments

**Tim Truzy (author)** from U.S.A. on June 07, 2018:

The abacus is a complex tool subject to many approaches for doing math. In the articles I've written, I've presented one approach which is very "proper" because once it is mastered, the answers are always correct. Enjoy exploring the counting tool.

Sincerely,

Tim

**Tim Truzy (author)** from U.S.A. on March 12, 2018:

I created this article along with one about addition to help people understand that the abacus is not a strange tool and is a powerful source for developing numerical concepts. I went more into the history of the abacus in my article: "How to Count to 99 On the abacus." I simply wanted to demonstrate a method I developed over time from working with masters of the counting device. One of my instructors was from India and the other was from Spain.

Thank you for reading this article. Your comments are apreciated and valued.

Sincerely,

Tim

**Ioannis Arvanitis** from Greece, Almyros on March 11, 2018:

The period 2700–2300 BC saw the first appearance of the Sumerian abacus. So it is the ancestor of today's computers. There is a great amount of wisdom saved in Avax (the Greek name)!

My Brother Tim, I am so glad for the respect you show to the ancient knowledge! It is important not to forget where we have been.

Thank you for sharing this knowledge.

Keep on your noble work.

God Bless you

Sean