Abacus (soroban) division

Hello,

I’ve been training on the soroban for about 3 months now. So far I’ve been practicing just addition and subtraction, of 4 digit numbers with 5 different 4 digit numbers per problem. The movements are starting to become very natural and are starting to require less and less thought. So I figured now might be a good time to start looking into multiplication and division on the abacus. Multiplication looks very straight forward but division looks rather tricky. I have no doubt that I can preform division on the abacus, but my worry is that it won’t transfer over to the mental abacus. Which would be problematic as my long term goal is to become a strong mental calculator through the use of the mental abacus. I want to be able to do things like 4893/374 and 39488/28 and 384929/2445 in my head rather quickly. So, is the abacus an efficient method for computing division or am I better off sticking to the “standard” way to divide.

1 Like

I am pretty sure your performance on the physical abacus will transfer to the mental abacus. What will happen after a lot of practice is that - because of muscle memory - you will even feel your fingers moving when doing mental bead shifting.

You need to develop strong visual skills skills in manipulating the mental soroban of course. That is a matter of training.

Let’s do the examples you give me here and through PM.

39488/28

28 is almost 30. So let’s take 30 and for each 30 we subtract from the dividend we add 2.
A quick look at the dividend shows that the answer begins with a 1, then 3 other digits.
In short the answer is one thousand something.

Put the dividend, 39488, on the soroban.
Focus on the 39. Subtract 30, add 2.
Put 1 on the soroban, left of the dividend.
Mentally visualize the rod with the 1, an empty rod and the dividend.
The soroban now shows “1 11488”.

Focus on 114. Subtract 330 (24), add 32, makes 30. So we could have done 4 times instead of 3. Subtract 30, add 2 remainder is 2.

The soroban now shows “14 288”.
Focus on 28. 1 time.

The soroban now shows “141 8” and since 8 < 28, you might think we are done.
The last subtraction was 280, because we went from 288 to 8.
So we need to add a zero or empty rod.

The soroban now shows “1,410 8”
Answer 1,410 remainder 8.

384929/2445

Use 2,500 and for each 2,500 subtracted add 55. First digit is 1, then another 2 digits.
So the answer is one hundred something.

Focus on 3,849. Subtract 2,500 => 1,349. Add 55 => 1,404.

The soroban now shows "1 140429”.
Focus on 14,042.
Subtract 10,000, which is 4 * 2,500.
And add 4 * 55= 220.
14,042 => 4,262.
Subtract another 2,500 and add 55.
4,262 => 1817

The soroban now shows "15 18179”.
6 * 2,500 15,000. Subtract 18,179 => 3,179.
Add 6*55 = 330 => 3,509.
Subtract another 2,500. Add 55 => 1064.

The soroban now shows "157 1064.”.
Answer: 157 r 1,064.

You also asked me questions per PM and we decided to answer them on the forum:

I think so…The whole point is automation of movements.
This means you need a lot of practice.
You will not always have your soroban with you, but I assume you do carry your phone.On android I use this for practice:
https://play.google.com/store/apps/details?id=br.net.btco.soroban

In PM you gave me some examples of divisions. Let’s go through them:

89/36.
Put 89 on the mental soroban.
I round 36 to 40, since that will work much faster as we will see.
Using 40 means that for every 40 I subtract I have to add 4.
89 is more than twice 40, so subtract 80 and add 8. So we get:
89 - 80 = 9. 9 + 8 = 17.Add zero for next digit => 170.
4 times 40 makes 160. Subtract => 10 left. Add 16 makes 26.
Add zero: 260.
6 times 40 makes 240. Subtract from 260 => 20 left. 6 times 4 makes 24 add to 20 makes 44. 44 is bigger than 36, so we could have done one more.
So, the digit is not 6, but 7.

What happens here is important.
Working on the soroban or abacus means automation.
You could devise tricks in order to immediately find that 36 goes into 260 7 times (instead of 6).
However, I decided to use 40 in order to quickly find 260/40.
So this means I need to use 6 times. Quickly subtract 240 from 260 and lastly add 24 to get 44.
It might seam that the last part (subtracting 36 from 44) is superfluous, if we are only able to find out quicker that we can use 7 instead of 6.
My point is; don’t do that. Stick with the process.
In this case stick with 40 and use 6 and if the remainder is bigger than the devisor, then add 1 and subtract 36.

Let’s do that now:0
Subtract 36 from 44. 8 left. Add zero: 80.
2 times. 80-80 = 0. 0+8 = 8.Add zero: 80.
See the repetition?

So answer is: 2.47222222…

Next example:4583 / 283

Put 4583 on the mental soroban.
Focus on 458 for the first digit. One time.
Subtract 283 from 458 => 175. Keep in mind that there is a 3 on the next rod.
So the soroban now holds: 1753.

283 is almost 300. So work with 300 and add 17 for each 300 we subtract.
6 times 300 makes 1800, 1753 - 1800 = -47.
However, we need to add 6 X 17 = 102.
-47 + 102 = 55.
Add a zero. Mentally btw, this is done by just adding an empty rod to the right.
550.

Since 283 * 2 = 566, the remainder of 550 leads to a rounded 2 as the next digit.

Answer: 1.62.

Also take a look at this:

1 Like