Multiplying with the Japanese abacus

So far, we have learned the principles of addition and subtraction. Now let's look at multiplication.

Let's say we want to multiply 83 by 47

We first multiply the 8 by the 4 and enter the result onto the abacus (positioning the answer to allow for the two following zeros).

M1

Note the sequence of entry (using only the thumb because these are the 1 - 4 beads), first the 3, then the 2. And notice that because the question has a total of 4 digits, we know we must start in the 4th column. The result of this first (and all subsequent) multiplication is always treated as 2 digits, so small mubers, like 7 are entered a 07. That way they end up in the right place.

Next we multiply the 8 by the 7.

M2

Again, we enter the 5 first, then the 6, this time using the first finger for the 5 and pinching the 6 with both thumb and first finger. Notice that we have shifted one place to the right, because we have one less trailing zero.

So now we have dealt with the 8. The third step is to multiply the 3 by the 4, moving first the 1, then the 2.

M3

And finally the 3 by the 7. This is tricky. To get the 2(0), we have to take away 8(0) and add 1(00), in that order. Taking away the 8(0) uses a reverse pinch as all of the beads are moved simultaneously away from the bar using the thumb to push down and the first finger to push up. Then after adding the 1(00) we add the 1.

M4

So there we have it. Read the beads 3 9 0 1. In a future article I will show you how we divide using the Japanese abacus.

 

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