September 08, 2014

De-mystifying Mathematics (Part 6) – flexibility of the placeholder system in subtraction

De-mystifying Mathematics (Part 6) – flexibility of the placeholder system in subtraction
Now that we understand the placeholder system and its uses, let us ask an out of the box question – can I put a negative digit in a place?
Let us see what it would mean. For ease of representation, we can put the ‘–‘ sign on top on the number. Let us take an example of a number as  
 
What this number implies is that it has 1 hundreds, 2 tens and 2 ones-short. To convert this into a regular number, we can transfer 1 tens out of 2 and give it to the ones to cover for this shortage. If you go through the above mentioned steps, you will find that this number can be represented as 118!

You can try these examples – the answers are posted at the end of the post.
 


So, if you have got the above answers, you would notice that you can convert your subtractions into this representation and translate that into a final answer at the end. Let us take a subtraction example to see how this works:
The interesting thing to note is that instead of using a carryover method and converting 5 (tens) to 15 (tens) and subtracting 7 from it, you need to subtract 7 from 5 = (-2) or ‘2 short’ and then adjust from 10 that you get from hundreds making it (10-2 = 8). Effectively all your subtractions are between numbers up to 10!

This will need some practice. Once you figure it out, you will find that it speeds up your mental calculations. And needless to say, this does not impose you to start from the right or left. You can do each column independently and remove the negatives in any order!

Let us try one more before you go.

Answers to the earlier questions:







Enjoy till the next one – where we will merge negatives and multiplications :-) 

Read the next part here
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