Mathematics

MENTAL MULTIPLICATION

How to multiply a number by 11.

In a few moments we are going to learn a classic mathematical trick.

Suppose you have to multiply a number by 11. This can be done by inserting the sum of numbers between the numbers.

For Eg.

11X23= 2 _ 3 ---- Split the numbers

= 2(2+3)3 ---- Add the numbers

= 253 ---- Get the result

It can be traced as, when you multiply a number by 11 then split the numbers (2 and 3) and insert the sum (2+3=5) in between.

I suppose now you can do 11X24, 11X54, 11X36 and all the two digit numbers MENTALLY.

What about 11X89?

This can be done by

11X89=8_9 ----- Split the numbers

=8(8+9)9 ----- Add the numbers

=8(17)9 ----- 17 cannot be placed there so carry one to 8 and make it 8+1=9

=978 ----- Result

Now, What about three digit numbers?

11X123=1_2_3 ---- Split the numbers

=_ _ _ 3 ----Add 2+3=5 and write it down

=_ _53 ----Add 1+2=3 and write it down

=1253 ---- Write down 1.

So now you can easily do 11X134, 11X345, 11X125 and all the three digit numbers MENTALLY. You can remember the number backwards and write it in reverse order to do it mentally

Like 3, then 3+2=5, then 1+2=3 then 1 so number in your mind becomes 3521 and you write it backwards to get the desired result.

Always remember, while multiplying a number by 11, to keep end terms, i.e. the terminal numbers. So everything except the unit digit changes.

The same can be applied for 4,5,6.. digit numbers.

Go from right to left

11X13876=1_3_8_7_6 ------Split

=1(4)(11)(15)(13)6 ------ Add from right

=1(4)(11)(16)36 ----- Add 1 to 15 and write 3 (unit digit of this number)

=1(4)(12)636 -----Add 1 to 11 and write 6

=1(5)2636 -----Add 1 to 4 and write 2

=152636 ----- Answer

Notice that at max you have to carry 1. So you can do it in one go like

11X13876=_ _ _ _ _6 ------------Notice 7+6=13 so write 3 and forget about carry as it always going to be 1. (Or Remember 6)

=_ _ _ _ 36 ------------Notice 8+7=15 so write 5(unit digit)+1(carry)=6 and one carry. (Or Remember 63 and carry 1)

= _ _ _ 636 ------------ Add 8+3=11 and write 1(unit digt)+1(carry)=2 and one carry. (Or Remember 636 and carry 1)

= _ _ _ 2636 -----------Add 3+1=4 and write 4+1=5 with no carry. (Or Remember 6362 and carry 1)

= _ _ 52636------------ Now write 1+0(no carry) =1. (Or Remember 63625 and carry 0)

=152636 ---------------Answer. (Remember 636251 and write it backwards)

Its up to you whether to write first and then add or do it mentally as shown above. Believe me this is the best multiplication technique you can apply for multiplication by 11.

Why this trick works?

Suppose you multiply a number xy by 11

xy

X 11

xy

+ xy0

x (x+y)y

Which is what we have done :)

Now Do these MENTALLY (Select Between <> to see the answer):

11X33=<363>

11X78=<858>

11X234=<2574>

11X5543=<60973>

11X7244=<79684>

How can it help in CAT,GMAT,GRE,SAT etc.

Q: The current population of a village is 13876 million what would be its population next year, if growth rate is 11% and death rate is 0%.(Give answer in closest integer form)

Now conventionally you would go like

Let the population after one year be A.

So, A=13876X11% + 13876

A=13876X11/100 +13876

A=138.76X11 +13876 ----- And now you will do the tedious multiplication.

A= 1526.36 + 13876

A=15402.36

A=15402.

This one was easy, but do you think that you will have that much paper/time to waste for such a simple problem?

Through the above method you could have done wonders

11X13876=_ _ _ _ _6 ------------Notice 7+6=13 so write 3 and forget about carry as it always going to be 1. (Or Remember 6)

=_ _ _ _ 36 ------------Notice 8+7=15 so write 5(unit digit)+1(carry)=6 and one carry. (Or Remember 63 and carry 1)

= _ _ _ 636 ------------ Add 8+3=11 and write 1(unit digt)+1(carry)=2 and one carry. (Or Remember 636 and carry 1)

= _ _ _ 2636 -----------Add 3+1=4 and write 4+1=5 with no carry. (Or Remember 6362 and carry 1)

= _ _ 52636------------ Now write 1+0(no carry) =1. (Or Remember 63625 and carry 0)

=152636 ---------------Answer. (Remember 636251 and write it backwards)

Remember that if you practice you will get the result in seconds and that too in your mind.

Now 15636/100 = 1563.36 (Just shift the dot to number of zero equivalent places

1536+13876=15402. See how you have done it mentally (almost 90% of the problems didn't involve a pen stroke).

Now do these (If you cant do these then don't worry I will tell you later how to tackle such problems).

Q. A Shopkeeper is giving a discount of 11% on all household items. John's total bill is $1789 so what would be his bill after discount. A. <1592.21>

Q. After giving discount to John the shopkeeper decided to give him additional discount of 11% now what would be his bill after discount. A <1417.06>

Thats it folks, catch you next time, until then if you have any query regarding anything contact me at friggere.Sumit@gmail.com

We the Indians

Blog, I heard this word three years ago in Linux Asia, New Delhi. Someone from Google was very happy on the upcoming Web 2.0, at that time I was in my second year so I didn't understand much (neither i was interested). But I still remember that he mentioned that within a few days you people would be able to post your own content over the web and create your own websites, I thought, whats the big deal you can always post your content by buying a www domain as Yahoo and MSN does, but he was very excited by Web 2.0, as i was sitting in the front row (yes the front row) i thought i should pay some respect to this man after all he is from Google!.

Until recently i thought blogging is only for people who doesn't have anything to do in life and just want to post content on the web and unnecessarily increase the space on the web ( this might seem strange, but i am a very miser person and don't want any resource to be wasted, even if its not mine).

But as Microsoft releases its new versions of Microsoft Office, Microsoft Windows (with an enhanced stupidity in them, I still believe that Windows 98 was the best OS of Microsoft), my new version ( with a more positive thinking and a it more stupidity) thinks that everyone should get his/her chance to express himself/herself in front of world, because everyone is different, the things which interests me, might be boring for you, and the thing which interests you is always boring for me :).

On a serious note, time changes, people changes, what I am today, the way I think, might not be five years ago and five years from now life keeps on changing and thats the most impressive part about it nothing remains as it is, everything changes, many people says "Every good part of life is followed by a bad one and vice versa" but i say " Every good part of life is followed by a better one", of course I am not the great Ayn Rand, but still I think like that its just the mindset and even the worst part of life seems to be a better part of life if not the best.

Today I read a shocking news in of course newspaper that Bill Gates has left Microsoft. This was a shock for me and believe me for most of the Indians.Why Indians? First lemme tell you why i was shocked, Bill Gates has been my idol from a long time. I even chose computer engineering because i want to be like him, not for the stupid reason that I wanted to be as wealthy as him, but because he is an innovator, a thinker, a leader, a social worker. Very few people in this world can left Harvard university after scoring 1590/1600 in SAT. But great people thinks differently,isn't it?

Most of the Indians are shocked that he quited out of Microsoft at the age of 53, most of Indians believe that (Including me) the one who starts a company should always lead that company after all its his company not Steve's why should he give his power, his office to someone who was not even there when Microsoft was made, why should he stop making money and remain at the seat of Richest in the World for ever. This doesn't applies only to Bill Gates, it applies to everyone. Our politicians (i cant call them leaders because they don't and cant lead anyone) remains active in politics till they die, our cricketers play cricket till they are not dropped from the team (Hoping that this wont happen to Legendary Great Sir Sachin Tendulkar), Mahesh Bhupati and Leander Paes are still playing tennis at the age above 30 and they will play till they can, one question I always wanted to ask "is Sania Mirza really 21 years old?" No. I don't think so, is the reply for most of us, then why she says that she is 22? because she wants to extend her carieer more and more till she gets really old to play, Why so? Simply because she wants to earn more and more money. Even our actors/ actresses don't quit the film industry till they become very very very old. Miss Hansika Motwani is still 16 years old, Priyanka Chopra went abroad for her studies and returned home become miss world at the age of 18! The lastest buzz Deepika Padukone is mere 21 year old although she is modeling since 2001 that is from the age of 14.Our very own Amitabh Bachchan become a hero with a girl of half his age in Suryavansham and one third of his age in Nishabd. Nishabd was a biggest flops of the year and at the same time Cheeni Kam also rolled out and it was a decent movie even Tabu (Actress) got the best critics award for that. But what was the reaction of Bachchan on that? In this age the movies are not made by taking me as a central character, I am in side role and the mainstream belongs to someone else. What the hell, Mr. Bachchan why don't you tell everyone that I wanna make more and more money.

The problem is with mindset, we in India thinks that making money is all whats required in one's lifetime.If one is a billionaire by the age of 40 the he is a very successful person.Gimme a break.In west Porn stars makes more money then our so called Successful Persons. One of my teacher Mr. Md. Shorabbuddin said once (addressing the whole class) " look at you, you cant imagine what will happen to you peoples when you will turn 40 or so. In west the people work for a couple of years and then take a break for one year, but you cant do that". How right he was. In India if a person stays at home for one day the people starts to say "are you all right", If for one week "is everything is fine in office", if for one month then no one will ask you personally but they will make a small group and discuss his/her possible situation "he might be fired", "he should have made some mistake in office","he might have quited", don't ask for a year or so because we don't/cant take such long breaks, why ?? family pressure.

One doesn't become successful by earning more and more money. I know most of people wont agree with me. Even I want to earn money ( after all I am an Indian). Einstien wasn't a billionaire ( don't tell me that everyone is not like Albert Einstien), Ayn Rand wasn't a billionaire, even Bhagat Singh, M.K. Gandhi were not billionaires they were not even millionaires aren't they great, they were great, aren't they successful, they were successful.

It isn't like that I am against India and don't like India, I love India. Indian Civilization is one of the oldest civilization. I will discuss Indian Civilization in some later post. But our mindset has changed due to the western culture. When Britishers left us in 1947 we were in no where, we didn't have any money, any army, any weapons. All we had were 300 million Indians. We have to make everything from the very beginning, the west was already developed and Japan,China were catching them fast we were way behind them also, so we had to work hard, the things which west got in say about 50 years we had to get them in 10 years or less, our Grand Parents worked hard to earn money, then our Parents worked hard to earn more money and now we work hard to produce money. Because that is the only way we know how to become successful and be among one of the successful Country. Isn't it?