Using the Abacus, part 2: Multiplication

Once you can add on an abacus, the next thing to learn is multiplication. Like addition, it follows pretty closely on the old pencil-and-paper method. But it’s worth taking the time to look closely and see it step by step, because it’s an important subroutine (to use a programming term) that will be useful in more complicated stuff.

Just for clarity, I’ll write out the basic pencil and paper algorithm:
1. Write down a “0” for the initial value of the result.
1. For each digit si in the *second number* number, from right to left
1. For each digit dj in the first number, from right to left:
1. Multiply si × dj
2. Take the result of that multiplication, and add it to the result, starting at the *j+i-1*th column from the right.
When you finish, you’ll have the product. Since this sounds a bit different from how you probably learned it in school, let’s just step through it quickly, so that you can see that it really is the same thing. Let’s multiply 219 × 163.
* Initial result=0.
* i=1,j=1: Multiply 3 × 9. That gives us 27. Add it starting in the (i+j-1)th column; i+j-1=1+1-1=1. So:


* i=1,j=2: 3×1=3. Add it to the 1+2-1=2nd column:


* i=1,j=3: 3×2=6; add it to the 3rd column:


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