pocket abacus

Step 8 How to multiply

here's where the abacus comes into it's own.

multiplication vocabulary:
multiplicand : the number to be multiplied 
multiplier : the number to be multiplied by
(In multiplication these terms are generally interchangeable)
product: result of the multiplication

Let's take 2 larger numbers:
                                                    5286 x 654
The trick here is to count the digits in the equation, in this example there is 7 digits. This means we'll need 7 columns of beads to compute our answer. Reading right to left that puts us at the red column, this is where we'll start.

Now we take our top row and multiply it by our first multiplicand (5286 x 6). Our first calculation is 5 x 6 which we know is 30, this makes our 7th column (red) at +3 and the 6th column (yellow) left at +0. Continue over and take 2 x 6 which is 12, this makes our 6th row +1 bead and our 5th row +2 beads. Continue this process until the multiplier is exhausted.

Dropping the first digit of the multiplier there are now only 6 digits, this means we will start on 6th column over for the next multiplicand. Repeat the multiplication, adding beads in each column and carrying over the remainders.
When you exhaust the multiplicand the calculation is done.

We can verify this on a calculator and we see that it is correct.