## My Fascination With The Abacus

### Subtraction

#### Introduction

If you are still reading this, you are probably the type of
person that thinks ahead. If that is the case, you may have decided
that subtraction simply follows the same principles as adding, but
in reverse. You would be right. The same principle of using
complimentary numbers works just as well in subtraction. For
example, 10 7 = 3 can be performed by subtracting 1 from the tens
rod and adding three to the units rod.

Below are some short examples, followed by another three digit
sum similar to the last chapter. As before, the first example is
very simple. White beads have not been moved in the last action,
blue have been added and red have been subtracted.

#### A First problem: 9 - 4 = 5

Subtracting 4 from 9 should be a pretty obvious problem. Diagram
12 shows the abacus set to 9:

Diagram 12. The 9 set on the frame ready for
subtraction

Using your index finger, move four 1 unit beads down away from
the beam. The result can be seen in diagram 13.

Diagram 13. The result on the frame after
subtraction

Pretty obvious huh? OK lets move on.

#### A More Complex Subtraction

Take the sum 353 164 = 189.

First, set 353 on the frame:

Diagram 14. Abacus set to 353

As before, we move from left to right. The leftmost figure in
164 is 1, so subtract the 1 from the 3. Easy enough. Subtracting
the 6 next poses a little more of a problem, until you remember
that the complement of 6 is 4. Simply subtract 1 from the hundreds
rod, and add 4 to the tens rod:

Diagram 15. Mid way through the calculation

Finally, we need to subtract the 4. This requires us to subtract
a 1 unit bead from the tens rod, and add 6 to the units rod:

Diagram 16. The final movements in the
problem

#### Moving on.

These principles, like those for addition in the previous
chapter, require practice. It is important not only to practice
subtraction, but also to try exercises that involve both addition
and subtraction together. This will result in the ability to
interchange quickly between the two techniques, rather than
favouring one over the other.

As before, use the Excel document in the downloads section to generate practice
exercises. Also, remember the 123,456,789 exercise? Just set
1,111,111,101 on the frame, and subtract 123,456,789 from the
number nine times and you should end up with 0!