How to subtract 2 numbers

To perform a subtraction on the soroban, you proceed very much like you do on paper: you operate on each column, and subtract digit by digit, borrowing a carry if need be.

Say we want to subtract s (the subtrahend) to m (the minuhend). First you put the number m on the soroban. We go, digit by digit, from left to right, by subtracting the digit of s to the digit of m. If the digit of s is greater than the one of m, we make a borrow on the previous column.

All the principles that we have seen so far for the addition, will be mirrored for the subtraction. Each case will be reversed so that instead of adding we will be able to subtract.

What's left on the soroban after you have removed the digit of s, is the difference m-s.

All is good

If the digit of s is lesser than the one of m, then we simply remove the beads on the rod for the digit of m.

For example, if the digit is 4, and we need to subtract 2, then ... we remove 2 beads.

The same principle holds true for:

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

Go to the training page to exercise this

But this is also true for digit greater than 5. For example, to subtract 6 to 9, you remove one heaven bead and one earth bead.

We can use the same principle for:

5-5;
6-6; 6-5;
7-7; 7-6; 7-5;
8-8; 8-7; 8-6; 8-5;
9-9; 9-8; 9-7; 9-6; 9-5;

Go to the training page to exercise this

Complement to 5

The digit of s might be lesser than the digit of m, but there might not be enough beads to remove on the rod.

For example, to subtract 4 to 6, we need to use the complement to 5 for 4. 4 = 5 - 1 So we will subtract 5 and add 1. Or remove the heaven bead, and activate one earth bead.

The same principle holds true for:

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

Go to the training page to exercise this

We need to make a borrow

If the digit of s is lesser than the digit of m, we make a borrow in the previous column. Or we subtract the digit of s not the digit of m but the digit of m+10.

For example, to subtract, 4 to 3, we borrow 1 on the previous, or subtract 4 to 13.

Like seen for the addition, we use complement to 10. 4 = 10 - 6 We want to subtract 4, so we will subtract 10 and add 6. This means subtract one the previous column, and add 6 on the current column.

The same principle holds true for:

1-2; 1-3; 1-4; 1-5; 1-6; 1-7; 1-8; 1-9;
2-2; 2-3; 2-4; 2-5; 2-6; 2-7; 2-8; 2-9;
3-4; 3-5; 3-6; 3-7; 3-8; 3-9;
4-5; 4-6; 4-7; 4-8; 4-9;
5-6; 5-7; 5-8; 5-9;
6-7; 6-8; 6-9;
7-8; 7-9;
8-9;

Go to the training page to exercise this

In those cases, we can distinguish the case where we can add directly the needed beads. But there is also the case when we need to use the complement to 5 to add the needed beads. Please refer to this section in "How to add numbers".

Final word

Like previously for the addition, you need to master those techniques to the point you don't think about it each time, so that it becomes an automatism. Then, you will be able to perform subtraction at the speed of light.

It is best to go to the tutorials page to see a real example, like Simple subtraction or Subtraction or Complicated subtraction.