Re: soroban (Japanese abacus)

Andreas Freise <ad...@mpq.mpg.de> wrote:

Andreas Freise <ad...@mpq.mpg.de> wrote:

>On 16 Nov 2002 llizard wrote:
>> I am just relearning how to add and subtract on one of these fantastic
>> devices:
[snip of soroban]
>
>`Relearning' ? Oh.
>
>So, how _does_ it work then? I can imagine how to add but I 
>never knew how one does the other operations.

I only know how to add and subtract but apparently, one can multiply and
divide as well.
                                       
Of course, lgbeard's beads on the abaci that he submitted are more correct
for the Japanese style. They really are shaped more like: <>

The Chinese abacus has the round beads.  

     _____________________________________
      |o o o o o o o o o o o o o o o o o|
      |o o o o o o o o o o o o o o o o o|
      ||_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_||
      || | | | | | | | | | | | | | | | ||
      |o o o o o o o o o o o o o o o o o|
      |o o o o o o o o o o o o o o o o o|
      |o o o o o o o o o o o o o o o o o|
      |o o o o o o o o o o o o o o o o o|
ejm  _|o_o_o_o_o_o_o_o_o_o_o_o_o_o_o_o_o|_

Here is how the soroban works:
 ___________________________________________
|<_> <_> <_> <_> <_> <_> <_> <_> <_> <_> <_>|<-- each bead equals 5
|_|___|___|___|___|___|___|___|___|___|___|_| 
| |   |   |   |   |   |   |   |   |   |   | | 
|<e> <_> <_> <_> <_> <_> <_> <_> <_> <_> <_>|<-- each bead equals 1
|<j> <_> <_> <_> <_> <_> <_> <_> <_> <_> <_>|<-- each bead equals 1
|<m> <_> <_> <_> <_> <_> <_> <_> <_> <_> <_>|<-- each bead equals 1
|<_>_<_>_<_>_<_>_<_>_<_>_<_>_<_>_<_>_<_>_<_>|<-- each bead equals 1
                                  ^   ^   ^
                                  |   |   |
                     (etc. etc.) 100s 10s 1s

The adding is done from left to right instead of the way I learned, which
was from right to left.

Example with the numbers 153 and 39

traditional western method:

1. starting in the ones column:  3+9=12, carry the 1
           |
           _  _
        | |_  _)
        |  _) _)
           _  _
   _|_     _)(_)
    |      _) /
      ___________
              _ 
               )
              /_ 

2. moving to the tens column: 1+5+3=9
           |
           _  _
        | |_  _)
        |  _) _)
           _  _
   _|_     _)(_)
    |      _) /
      ___________
           _  _ 
          (_)  )
           /  /_ 
 
3. moving to the hundreds column: 1+0=1
           |
           _  _
        | |_  _)
        |  _) _)
           _  _
   _|_     _)(_)
    |      _) /
      ___________
           _  _ 
        | (_)  )
        |  /  /_ 

Adding 153 to 39 with the soroban:

1. Put 153 onto the soroban, then starting with the hundreds column: 1+0=1
(89 is less than 100 so zero is the number in the 100's column for it)
   _____________________________________
    |o o o o o o o o o o o o o o o | o|
    ||_|_|_|_|_|_|_|_|_|_|_|_|_|_|_o_||
    || | | | | | | | | | | | | | o | o|
    |e o o o o o o o o o o o o o | o o|
    |j o o o o o o o o o o o o o o o o|
    |m o o o o o o o o o o o o o o o ||
   _|o_o_o_o_o_o_o_o_o_o_o_o_o_o_o_o_o|_

2. Moving to the tens column: 5+3=8
   _____________________________________
    |o o o o o o o o o o o o o o o | o|
    ||_|_|_|_|_|_|_|_|_|_|_|_|_|_|_o_||
    || | | | | | | | | | | | | | o o o|
    |e o o o o o o o o o o o o o | o o|
    |j o o o o o o o o o o o o o o o o|
    |m o o o o o o o o o o o o o o | ||
   _|o_o_o_o_o_o_o_o_o_o_o_o_o_o_o_o_o|_

3. Moving to the ones column: 3+9

   oh oh, not enough beads to move in the ones column! okay, so
   add 1 to the tens column (adding 10) and subtract one from the
   ones column.

    3a:
   _____________________________________
    |o o o o o o o o o o o o o o o | o|
    ||_|_|_|_|_|_|_|_|_|_|_|_|_|_|_o_||
    || | | | | | | | | | | | | | o o o|
    |e o o o o o o o o o o o o o | o o|
    |j o o o o o o o o o o o o o o o o|
    |m o o o o o o o o o o o o o o o ||
   _|o_o_o_o_o_o_o_o_o_o_o_o_o_o_o_|_o|_


   3b:
   _____________________________________
    |o o o o o o o o o o o o o o o | o|
    ||_|_|_|_|_|_|_|_|_|_|_|_|_|_|_o_||
    || | | | | | | | | | | | | | o o o|
    |e o o o o o o o o o o o o o | o o|
    |j o o o o o o o o o o o o o o o ||
    |m o o o o o o o o o o o o o o o o|
   _|o_o_o_o_o_o_o_o_o_o_o_o_o_o_o_|_o|_

Answer: 192


Subtraction is done from left to right as well.

After learning the basics of adding on the soroban, I find that doing
mental arithmetic is suddenly much easier for me to do: mentally adding 38
to 23, I get fifty eleven and quickly convert it to sixty one. 

Before, I would add 8 and 3, hold 11 in what's left of my mind, then
remind myself what the original numbers were, start over because I'd
already forgotten the eleven, remember the 11, carry the one mentally over
to the... Drat!!! what were the original numbers again? oh yeah, 38 and
23... so 3+2+carried1=6, so the answer is sixty what was it again??? oh
yeah, 3+8=11... so that's sixty eleven.  NO! fifty eleven... No no no
no!!! It's.... 

-- 
See? left to right is MUCH easier.... >%^7^^^7^^

llizard aka ejm llizard@idirec+.ca
ASCII-art & ASCII-animation
www.crosswinds.net/~llizard/ascii-art/

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