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>

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

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