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### Using an Abacus

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

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
the best way to answer your question may be to send you to

http://www.ee.ryerson.ca:8080/~elf/abacus/

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

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.

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

. . .

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

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

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
representing the result.
_________________________________

I hope you have an abacus to practice with!

- Doctor Sarah,  The Math Forum

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