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Using an Abacus

Date: 1/12/96 at 15:22:27
From: Anonymous
Subject: Abacus

Our fifth grade class of gifted and talented math students is 
trying to figure out how to use an abacus.  Please send any 
information you have.

Thank you.
Andy, Alex, David, and Bret  

Date: 1/12/96 at 17:23:48
From: Doctor Sarah
Subject: Re: Abacus

Hi there!

I'm going to hope that since you're sending your question via the 
Internet, you have access to a Web browser like Netscape, since 
the best way to answer your question may be to send you to   

This is a great site with an interactive abacus, an Introduction, 
and detailed instructions for adding and subtracting.  Here are a 
few excerpts:

2.0 Addition

Addition on the abacus involves registering the numbers on the 
beads in the  straight-forward left-to-right sequence they are 
written down in. As long as the digits are placed correctly, and 
the carry's noted properly, the answer to the operation 
immediately presents itself right on the abacus. There are 4 
approaches to performing additions (or subtractions), each applied 
to particular situations. Each of thesetechniques is explained (!) 
in tabular form in the sections that follow. 

2.1 Simple Addition

When performing the addition 6+2, one would move 1 bead from the 
upper deckdown (value = 5) and one bead from the lower deck up 
(value = 1); this represents 6.  Moving 2 beads from the lower 
deck (in the same column) up (value = 1 * 2 beads = 2) would 
complete the operation. The answer is then obtained by reading 
resultant bead positions. 

. . . 

3.0 Subtraction

Subtraction is performed by first registering the minuend and then 
subtracting, starting from the left, by removing beads form either 
or both the lower or upper decks. The final bead-positions 
represent the answer. 

3.1 Simple Taking-off

This is achieved by simply taking off one or more beads from the 
lower deck, or sometimes both. Example: When subtracting 7 
(represented by -5-2 = -7) from 9, remove 1 bead from the upper-
deck (-5) and 2 beads from the lower deck (-2). The remaining 2 
beads represent the result. 

3.2 Combined Adding-up And Taking Off

When the number of beads in the lower deck is less than the 
subtracter (the number being subtracted), one or more beads are 
added in the lower deck and 1 bead is removed from the upper-deck. 

Example: When subtracting 4 (+1-5 = -4) from 7 (represented by 1 
bead in the upper-deck and 2 beads in the lower deck (less than 4, 
the subtracter), one bead is added to the lower deck (+1) and 1 
bead is removed from the upper-deck (-5) leaving 3 beads, 
representing the result. 

I hope you have an abacus to practice with!

- Doctor Sarah,  The Math Forum

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