If you were to multiply a number by 9, a common response would be to multiply by 10 and then go back one count. We can extend this same concept to many other multiplication situations.

What we effectively want to do is reduce the number of large digit multiplications and have more of smaller digits. This would come with the complexity of negatives, but is worth it.

Let us take an example of

**32 X 48**. Multiplying by 8 would result in larger answers, so we can convert 48 to 5(-2)
The calculations as described in the previous posts give us the answer as

**1536**.
One more example to illustrate this:

**89 X 72**
We can convert 89 to 1(-1)(-1) and 72 to 1(-3)2

As you can see, you could get the answer as

**6408**without too many large numbers to worry about.
This concludes the series of posts on basic arithmetic and how a comprehensive understanding of the placeholder systems can ease out mental calculations. So, do not feel afraid to use the number system in unconventional approaches.

Most of the mathematics an average person uses is arithmetic and I hope this set of posts would help.

Watch out for the next set of math topics to demystify…