How to add 2 numbers

To add numbers on the soroban, you proceed in a very similar way that you do addition on paper. You go on, digit by digit, column by column, with any carry that you might need. One notable difference is that you proceed from left to right.

To sum it up, you basically have to put on the soroban the number you want to add. In the most simple case, you add the beads for each digit on each rod. In others, you have to do a little gymnastic that becomes an automatism other time.

Adding one digit at a time

13 + 21 — Let's see this on an example: say we have 13 on the soroban; and wanted to add 21.

So first, let's add 2 on the dozen rod. Let's activate 2 beads. Then on the unit rod, let's add 1 by activating one bead. We finally, get 34.

So we see that to add a digit on a row, we simply activate the needed beads that we want to add.

The same principle holds true for:

0+1; 0+2; 0+3; 0+4;
1+1; 1+2; 1+3;
2+1; 2+2;
3+1;
5+1; 5+2; 5+3; 5+4;
6+1; 6+2; 6+3;
7+1; 7+2;
8+1;

Go to the training page to exercise this

This was for earth beads only. But this works the same for heaven beads too. So to add 6 to 1, one acitvate one heaven bead and one earth bead.

The same principle holds true for:

1+5; 1+6; 1+7; 1+8;
2+5; 2+6; 2+7;
3+5; 3+6;
4+5;

Go to the training page to exercise this

Complement to 5

If we want to add more than is available on the rod, then we have to use the complement to 5.

3 + 2 — For example, say we have 3 on a rod. And we want to add 2. We can't do that in the easy way, because we can't activate 2 beads.

So instead of adding 2, we will use the complement to 5 of 2 which is 2 = 5 - 3. So we will add 5 and remove 3. That is activate the heaven bead, and deactivate the 3 heaven beads.

The same principle holds true for:

1+4;
2+3; 2+4;
3+2; 3+3; 3+4;
4+1; 4+2; 4+3; 4+4;

Go to the training page to exercise this

Complement to 10

6 + 4 — So let's say now that we have 6 on the rod. And we want to add 4. We can't activate 4 beads. We can't use the complement to 5 either. So we use the complement to 10.

We have:4 = 10 - 6. So we add 10 and remove 6. We will add 1 on the adjacent column, and remove 6 on the current rod.

The same principle holds true for:

7+3; 7+4;
8+2; 8+3; 8+4;
9+1; 9+2; 9+3; 9+4;
1+9;
2+8; 2+9;
3+7; 3+8; 3+9;
4+6; 4+7; 4+8; 4+9;
6+4;6+9;
7+8; 7+9;
8+7; 8+8; 8+9;
9+6; 9+7; 9+8; 9+9;

Go to the training page to exercise this

Both at the same time

5 + 7 — And if you want to add 7 to 5?

Let's do it. 7 = 10 - 3. So we have to add 10 and remove 3. But ... we can't remove 3 because we have a heaven bead for 5.

So let's use the complement to 5. -3 = -5 + 2. Instead, we will remove 5 and add 2.

So to sum it up:

The same principle holds true for:

5+5; 6+5; 7+5; 8+5; 9+5;
5+6; 5+7; 5+8; 5+9;
6+6; 6+7; 6+8;
7+6; 7+7;
8+6;

Go to the training page to exercise this

Automatism

Now you have to forget all about this, by practicing and practicing until it becomes an automatism, so that you don't have to think about it every time.

Don't forget that you can see real examples, played for you on the tutorial page: look at the "Simple addition", "Addition", and "Complicated addition" examples.