Friday 30 December 2011

Multiplying Two 3-digit numbers which have zero in the middle

Actually this is a two digit multiplication only.

Consider, 304 * 608

Forget about zero now. Now as you would multiply two numbers which are 2-digits. multiply them.

I will represent them in a picture now, so that it is easy.







I think I have made it clear. Since the three parts were only two-digits I have simply attached them. I say, this is simplest thing that one can learn as a shortcut. Squaring a three digit number that has a zero in the middle, multiplying two 3-digit numbers which have zero in the middle. You literally have to remember the parts of the answer and just say them. Ya, I know that you can feel that it is simple.

So now try this operation: 705 * 809 = ?.

First, you try the method. Then verify the answer with my steps. I know that you can do it. Try try.





So the parts would be: 56 103 45. If you have the answer already 5610345 is not the anser. I say agin, these are only the parts. You have got the answer correctly as 570345, give yourself a pat on your back and appreciate yourself. You have mastered this trick. If you have not got the, No probs, you will be master in few more seconds.

You can see that you have three digit number in the middle. So add the hundredth digit "1" to the previous number 56. Then as usual, just attach everything. That's it. You are "Master too.

AND ONE MORE "GOOD NEWS":

You just have to add one to the previous number whenever a 3-digit number arises in the middle. Why I am saying this is, even when you multiply 909*909[the largest possible number to use this method(three digit numbers alone)] you get 81 162 81, is it not? Yaa... Its nice to hear. Really a good news.

Similarly were you to multiply a numbers like this: 7005 * 8009. Even more good news, you have no possibility of adding. You have to simply attach or tack up or whatever. You have to add only the thousandth digit which would never occur. Hmm... great great! Really I am not appreciating myself. I simply love maths just it. That's what making me to write like this.

So we will end this topic with a question: What is 9009^2 ?
I will tell the answer. However you too know. You would have already calculated in your mind.


The answer is 81162081.


One more thing, that zero has come before 81, just to fill the vacancy of the hundredth digit.

Any doubts still ask me.

With warm regards,

Harish Chakrawarthy :-)





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