## My Fascination With The Abacus

Baldrick, the ape creatures of the Indus have mastered this.

#### Reset the Abacus

Adding is the bread and butter of using an abacus. We will start with some basics. If you clear the abacus as described in the previous sections you should have an abacus that looks like the one in diagram 3. Diagram 3. A Soroban, showing 0

In the diagrams that follow, the following colour code is used to represent the different states a bead may be in:

• White Beads that have not moved during the last operation
• Blue Beads that have been added during the last operation
• Red Beads that have been subtracted during the last operation.

As before, we will define the units as represented on the rod four from the end. If we add 1 to this abacus, we move a 1 unit bead from the bottom towards the beam with our thumb: Diagram 4. A Soroban, showing 1 added to 0

The blue bead shows the movement that has just taken place.

If we now add a further 2 to this number, (1 + 2 = 3) we add two more 1 unit beads from the bottom towards the beam with our thumb: Diagram 5. A Soroban, showing 2 added to 1, making 3

#### Add 3 - Carrying Fives

Things get a little more complicated when you need to carry, however the abacus has a surprise up its sleeve in the form of complimentary numbers.

There is no need to think to yourself, three plus three equals six, you simply need to think adding three is the same as adding five minus two. Ill explain. When performing 3 + 3 = 6 on the abacus, you simply move a 5 unit bead down with your index finger, and then move two 1 unit beads down with your index finger. The result appears on the abacus automatically. No maths, no thinking.

Magic. Diagram 6. A Soroban, showing 3 added to 3, making 6

In diagram 6, the red beads have been subtracted and the blue beads have been added, while all the white beads remain in place.

This principle greatly contributes to the speed of the abacus. There are only a handful of simple complementary number rules to remember, e.g. [1 + 4], [2 + 3], and thats it. For adding numbers less than five, apply whichever rule is relevant from the following:

Either move up a 1 unit bead with your thumb,
-or-
Move down a five unit bead with your index finger, then move down four 1 unit beads with your index finger.

Either move up two 1 unit beads with your thumb,
-or-
move down a five unit bead with your index finger, then move down three 1 unit beads with your index finger.

Either move up three 1 unit beads with your thumb,
-or-
move down a five unit bead with your index finger, then move down two 1 unit beads with your index finger.

Either move up four 1 unit beads with your thumb,
-or-
move down a five unit bead with your index finger, then move down one 1 unit bead with your index finger.

#### Carrying Tens

You should be able to see that this principle extends to numbers that are greater than five. For example, to add nine to the above abacus, simply subtract a 1 unit bead, and add a 1 unit bead on the next column to the left, to indicate 10. Diagram 7. A Soroban, 6 + 9 = 15

As before, there are a few rules to remember in relation to compliments of ten:

Either move a 5 unit bead with your index finger,
-or-
raise a 5 unit bead with your index finger and raise a 1 unit bead with your thumb in the next column.

Either move a 1 unit bead up and a 5 unit bead down at the same time,
-or-
Move a 1 unit bead up, move a 5 unit bead up and then add one to the next column, i.e. carry the five.
-or-
Move four 1 unit beads down, and ten add one to the next column, i.e. carry the ten.

Either move two 1 unit beads up and a 5 unit bead down at the same time,
-or-
Move two 1 unit beads up, move a 5 unit bead up and carry to the next column.
-or-
Move three 1 unit beads down, and ten add one to the next column.

Either move three 1 unit beads up and a 5 unit bead down at the same time,
-or-
Move three 1 unit beads up, and carry the five,
-or-
Move two 1 unit beads down, and carry the ten.

Either move four 1 unit beads up and a 5 unit bead down at the same time,
-or-
Move four 1 unit beads up, and carry the five,
-or-
Move four 1 unit beads down, and carry the ten.

Believe it or not, that's all there is to adding with an abacus.

#### Adding multiple digit numbers

When using an abacus, always move from left to right. For example, consider the following sum:
123 + 678 = 801

First, set the 123 on the abacus as shown in diagram 8: Diagram 8. 123 Added to the frame

The next step is to add the left most columns; in this case a 6 from 678 is to be added to the 1 from 123. Add the 6 to the hundreds rod by moving down a 5 unit bead, and moving up a 1 unit bead at the same time. Diagram 9. Showing the addition of 6 to the hundreds rod

Then add the tens together, adding the 7 to the 2 by moving down a 5 unit bead, and moving up two 1 unit beads at the same time. Diagram 10. Showing the addition of 7 to the tens rod

Lastly, add the units together. Add the 8 to the three by moving down two 1 unit beads, and carry the ten. As you can see, adding the ten will mean moving down the four 1 unit beads, moving up the five unit bead, and finally carrying one to the hundreds. The result can be seen in diagram 11. Diagram 11. Showing the solution, 801

#### Summing up

Ok, I'm sorry. I like puns.
Take time to make sure you have understood this section, as it forms the basic knowledge that will help you with the more complex operations later. Although the principles are relatively simple, there is quite a lot to remember. This is especially so when you are trying to add as quickly as you can.

Above all, practice. Practice as often as you can. Remember, it is better to practice for short periods regularly, than for a long time less often.

In the downloads section of the site is an Excel document that generates random numbers. There are sums on different sheets, one for addition, one for subtraction and so on.

Another good practice technique is to add 123,456,789 nine times. If you do this sum correctly, the result should be 1,111,111,101. Add it another nine times and the result should be 2,222,222,202, and so on.

Good Luck!