Traditional division (帰除法)
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| Image from Shinoda's Jitsuyou Sanjutsu (実用算術) (1895) explaining division |
This is the main objective of this website. Since almost everything I can do of interesting with the abacus depends in one way or another on the division and that division is much more comfortable for me when using the Traditional Method (帰除法, Kijohou in Japanese, Guīchúfǎ in Chinese), I tend to consider this division method as the true core of
Bead Arithmetics (珠算, Shuzan, Zhūsuàn). It took me a while in the past to gather, understand, and get the full picture of traditional division, so my purpose with these pages is that, when they mature, they provide enough information to make it easier for others to study this wonderful technique.
Modern and traditional division; close relatives
You may think that the traditional and modern divisions are very different, but in fact, if you are already an expert with modern division, you are also an expert with traditional division. What happens is that nobody has told you yet ...
This article tries to be about WHY to use traditional division.
Guide to traditional division (帰除法)
How to start with the traditional division method and not die trying. You can use it in 1: 4, 2: 5, 1: 5, etc. as you can choose to use the modern division arrangement or the traditional one.
This article tries to be about HOW to use traditional division.
Dealing with overflow
In the case of a 2/5 or 3/5 abacus we can use the additional upper beads (including the suspended one) to represent values from 10 to 20 that appear when using some traditional techniques, specially division, but, What can be done on an 1/5 or 1/4 abacus?
Example of suspended lower bead use
How to learn the division table (In project)
To memorize or not to memorize, that is the question. Some patterns that appear in the division table can help you to memorize it.
Specialized division tables
Tables for multi-digit divisors. Useful if you have lots of divisions to do with a common divisor. It will be used in Tide abacus and Julian day articles.
HTML, PDF
Traditional division examples
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