Vedic Maths: Multiplying numbers by 11-19 in less than five seconds

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How to multiplyHow to multiplynumbers with 11-19numbers with 11-19

in less than 5 seconds? in less than 5 seconds?



Multiplying numbers with11Multiplying numbers with11


Lets take for example 32 x 11


www.vedicmathsindia.orgLets take for example 32 x 11


Step 1: Split 3 and 2 into left & right parts

3 2

3 __ 2




3 2

3 5 2

Step 2: Simply Add 3 + 2 and place 5 in between




3 2

3 5 2

Step 2: Simply Add 3 + 2 and place 5 in between

Step 3: Our Final Answer 352

Try with other numbers now.Try with other numbers now.


Now lets take for example 1234 x 11

Multiplying numbers with11


The method is called Adding to the Neighbor.Adding to the Neighbor.

In 1234, the neighbors of 2 are 1 & 3 and the neighbors of 3 are 2 & 4 respectively.



Step1: We put two strokes beside 1234 and place two zero’s


0 1 2 3 4 0


Step2: Now we start Adding to the Neighbor. First we Add 4 to 0.


0 1 2 3 4 0

Gives us:- 4

(4+0 =4)


Step3: Add 3 to 4 gives us 7.


0 1 2 3 4 0

Gives us:- 7 4

(4+0 =4)

(3+4=7)




0 1 2 3 4 0

Gives us:- 5 7 4

(4+0 =4)

(3+4=7)

(2+3=5)




0 1 2 3 4 0

Gives us:- 3 5 7 4

(4+0 =4)

(3+4=7)

(2+3=5)

(1+2=3)


Step6: Finally Add 0 to 1 gives us 1.


0 1 2 3 4 0

Gives us our Answer:- 1 3 5 7 4

(4+0 =4)

(3+4=7)

(2+3=5)

(1+2=3)

(0+1=1)

Simple Isn't it? Now try 12345 x 11 on your own.


Now lets take for example 777 x 11This sum will involve a carryover.



Step1: We put two strokes beside 777 and place two zero’s


0 7 7 7 0


Step2: Now we start Adding to the Neighbor. First we Add 7 to 0.


0 7 7 7 0

Gives us:- 7

(7+0=7)


Step3: Add 7 to 7 gives us 14. We write 4 and take 1 as carry to the next step.


Gives us:- 1 4 7

0 7 7 7 0 (7+0=7)

(7+7=14)


Step4: Add 7 to 7 gives us 14. We add 1 from carryover gives us 15.We write 5 and again take 1 as carryover to the

next step.


Gives us:- 1 5 4 7

0 7 7 7 0 (7+0=7)

(7+7=14)

(7+7=14+1=15)


Step5: Finally we add 0 to 7 and then add 1 of the carry over to give us 8.


Gives us our final answer:- 8 5 4 7

0 7 7 7 0 (7+0=7)

(7+7=14)

(7+7=14+1=15)

(0+7=7+1=8)

Simple Isn't it? Now try any number multiplied with 11.


Multiplying numbers with 12Multiplying numbers with 12


Now lets take for example 1234 x 12



The method is called Doubling and thenDoubling and then Adding to the NeighborAdding to the Neighbor

We note that we double since the number 12 has a 2. Had the multiplier been 13 we would have

tripled and then added to the neighbor.



Step1: We put two strokes beside 1234 and place two zero’s as before.


0 1 2 3 4 0


Step2: Now we start Doubling and Adding to the Neighbor. First we double 4, gives us 8.We then add 8 to zero.


0 1 2 3 4 0

Gives us:- 8

(4x2=8+0 = 8)


Step3: We now double 3 to get 6. Add the neighbor 4 to get 10. We write 0 and carry 1.


0 1 2 3 4 0

Gives us:- 1 0 8

(3x2 =6+4=10)

(4x2=8+0 = 8)


Step4: We now double 2 to get 4.Add 1 of carry gives us 5. Add neighbor 3 gives us 8.


0 1 2 3 4 0(3x2 =6+4=10)

(4x2=8+0 = 8)

(2x2 =4+1=5+3=8)

Gives us:- 8 0 8


Step5: Double 1 to get 2. Add neighbor 2, gives 4.


0 1 2 3 4 0(3x2 =6+4=10)

(4x2=8+0 = 8)

(2x2 =4+1=5+3=8)

(1x2 =2+2=4)

Gives us:- 4 8 0 8


Step6: Finally Double 0 to gives us 0. Add neighbor 1 , gives us 1.


0 1 2 3 4 0

Gives us our Final Answer:- 14808

Simple Isn't it? Now try 12345 x 12 on your own.

(3x2 =6+4=10)

(4x2=8+0 = 8)

(2x2 =4+1=5+3=8)

(1x2 =2+2=4)(0x2 =0+1=1)


Thumb rule for 13-19Thumb rule for 13-19

• For 13 its three times add to the neighbor

•For 14 its 4 times add to the neighbor•For 15 its 5 times add to the neighbor

and so on.•For 18, its 8 times add to the neighbor•And finally for 19 its 9 times add to the

neighbor.

Amazing Rules Isn't it?

Try some sums now.


SumsSums

• 45239 x 11• 6532 x 12• 156 x 13• 67087 x 12• 3568 x 14

• 60567 x 17• 89341 x 19• 23412 x 15• 467692 x 18• 45213 x 13


Answers

• 497 629 • 78 384 • 2 028 • 805 044 • 49 952

• 1 029 639 • 1 697 479 • 351 180 • 8 418 456 • 587 769

Education

Vedic Maths: Multiplying numbers by 11-19 in less than five seconds