Traditional Abacus and Bead Arithmetic/Division/Traditional division examples

One-digit divisors (short division)
The number 123456789 has also been used to demonstrate multiplication and division in many ancient books on the abacus. Some, like the Panzhu Suanfa, start with the traditional multiplication (see chapter: Multiplication) of this number by a digit and use the division to return the abacus to its original state; others, like the Jinkoki , do it the other way around, starting with division and ending the exercise with multiplication. The latter is what we do here.

The number 123456789 is divisible by 3, 9 and 13717421, so divisions by 2, 3, 4, 5, 6, 8 and 9 have results with finite decimal expansion (2 and 5 are divisor of the decimal basis or radix 10 ). Only division by 7 leads to a result with an infinite number of decimal places, so here we will cut it off and give a remainder.

Unfortunately, this exercise does not use all the division rules, but it is a good start and allows you to practice without a worksheet.

Division of 412 by 896
Note: See chapter: Abbreviated operations



External resources
You can practice traditional division online with Soroban Trainer (see chapter: Introduction) using this file kijoho-1digit.sbk that you should download to your computer and then submit it to Soroban Trainer (It is a text file that you can inspect with any text editor and that you can safely download to your computer).