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:

Soroban showing 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.

Soroban showing 5

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:

Soroban showing 353

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:

Soroban showing subtraction in progress

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:

Soroban showing solution

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!