How to Do Division on the Abacus in Easy Steps
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.
Which one of these mathematical processes have you performed on the abacus?
Things to Know Before Performing Division on the Abacus
- Issues relevant to zero and multiplication with 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.
- 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.
- 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.
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.
- 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.
Let's do a Division Problem with a Remainder
- Set the division problem: 459 divided by 62.
- 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.
- Now, look at the first number in the divisor: 6, or 6 tens.
- We know that 6 goes into 45 7 times. We place the seven beside 459, then multiply 7 x 6 to get 42.
- We then subtract: 42 from our dividend. Or we subtract 420 from 459 for a result of 39.
- We still have another number left in the divisor: 2. We want to multiply the 7 by that number.
- Multiply: 7 x 2 to get 14. Subtract this number from 39.
- You will notice 25 is still on the ones and tens column. This is your remainder.
- Now, clear the divisor. Your answer should look like the photo below.
- 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.
Was this a new technique for carrying out division on the abacus for you?
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.