June 25, 2014

De-mystifying Mathematics (Part 5) – using the flexibility of the placeholder system in multiplication


We usually follow one method for all multiplication problems we need to solve. I still remember struggling with understanding the zeros/ “+” sign that I had to put at the end of each new line. It was done as a matter of process without appreciating what we were doing.
If I have to redo this now, I would think of it differently. Ones multiplied by Ones would give me the Ones in the answer. Tens by Tens would give me the Hundreds in the answer and the Tens by Ones will give me the Tens.
The answer in this case is technically 2 Hundreds 17 Tens and 8 ones that translates into 378 in our accepted notation.
This can easily be expanded to larger numbers are illustrated below:
The beauty of this approach is that each single digit multiplication is treated as an independent calculation and the answer put in the right column.  All the smaller answers are then added in the last step to get the final number. You do not need to start from right or left – you just have to make sure all combinations are multiplied!

In fact, if you have built a multiplication module using electronic chips in computer programming, this is exactly what you would have done.

So, enjoy this while I come back with subtraction and handling negative numbers in the next post.