How to multiply 2 numbers

One of the technique to multiply a number ma (the multiplicand) with another number me (the multiplier) is to use an analog to the long multiplication algorithm you already know and do on paper. It is the recommended method to use on the soroban.

One key difference is that you do partial sum along the way instead of waiting until the end to do a multiple operand addition.

You will need to know your multiplication table [Wikipedia].

As the multiplication of decimals is commutative, one prefers to choose the multiplier as the smaller of the 2 operands.

The principle is, for each digit of the multiplicand, multiply it with each digit of the multiplier (going from left to right), beginning by the rightmost digit of ma and finishing by the leftmost one.

One digit multiplier example

Let's take an example with a one digit multiplier, 57 x 6

We put 57 (the multiplicand) at the center of the soroban(left image) and place 6 (the multiplier) on the left by letting 2 empty rows between ma and me.

We multiply 7 by 6 and put 42 at the right of ma(right image).

We can now deactivate 7 on the soroban(left image), as we are finished with it.

Then, we multiply 5 by 6 and add 30 on the soroban(right image), one column to the left from the previous product. We can now again deactivate 5, and read our final product 342.

Multiple digit multiplier

It's basically the same as above but we need to repeat the process for each digit of the multiplier.

For example, let's multiply 43 with 21, 43 x 21.

So we mutiply 3 by 2 and put 6 on the soroban(left image).

We multiply 3 by 1 and add 3 on the soroban. We can deactivate 3 (right image).

We continue with the next digit of the multiplicand 4. We multiply 4 with 2 and add 8 on the soroban (left image).

And finally, we multiply 4 by 1, and add 4 on the soroban, and deactivate 4. We got the product 903 (right image).

Decimal numbers

For number with decimals, we can put the numbers on the soroban so that the marker is placed on the decimal separator.

Or you can consider the operands as integer, and report the missing decimal at the end of the operation.

For example, to multiply 45.242 with 6.78, multiply 454242 with 678 and divide the result by 100000 aka 5 decimals.