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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?
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Multiplying numbers with11Multiplying numbers with11
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Lets take for example 32 x 11
Multiplying numbers with11Multiplying numbers with11
www.vedicmathsindia.orgLets take for example 32 x 11
Multiplying numbers with11Multiplying numbers with11
Step 1: Split 3 and 2 into left & right parts
3 2
3 __ 2
www.vedicmathsindia.orgLets take for example 32 x 11
Multiplying numbers with11Multiplying numbers with11
Step 1: Split 3 and 2 into left & right parts
3 2
3 5 2
Step 2: Simply Add 3 + 2 and place 5 in between
www.vedicmathsindia.orgLets take for example 32 x 11
Multiplying numbers with11Multiplying numbers with11
Step 1: Split 3 and 2 into left & right parts
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.
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Now lets take for example 1234 x 11
Multiplying numbers with11
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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.
Multiplying numbers with11
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Step1: We put two strokes beside 1234 and place two zero’s
Multiplying numbers with11
0 1 2 3 4 0
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Step2: Now we start Adding to the Neighbor. First we Add 4 to 0.
Multiplying numbers with11
0 1 2 3 4 0
Gives us:- 4
(4+0 =4)
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Step3: Add 3 to 4 gives us 7.
Multiplying numbers with11
0 1 2 3 4 0
Gives us:- 7 4
(4+0 =4)
(3+4=7)
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Step4: Add 2 to 3 gives us 5.
Multiplying numbers with11
0 1 2 3 4 0
Gives us:- 5 7 4
(4+0 =4)
(3+4=7)
(2+3=5)
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Step5: Add 1 to 2 gives us 3.
Multiplying numbers with11
0 1 2 3 4 0
Gives us:- 3 5 7 4
(4+0 =4)
(3+4=7)
(2+3=5)
(1+2=3)
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Step6: Finally Add 0 to 1 gives us 1.
Multiplying numbers with11
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.
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Now lets take for example 777 x 11This sum will involve a carryover.
Multiplying numbers with11
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Step1: We put two strokes beside 777 and place two zero’s
Multiplying numbers with11
0 7 7 7 0
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Step2: Now we start Adding to the Neighbor. First we Add 7 to 0.
Multiplying numbers with11
0 7 7 7 0
Gives us:- 7
(7+0=7)
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Step3: Add 7 to 7 gives us 14. We write 4 and take 1 as carry to the next step.
Multiplying numbers with11
Gives us:- 1 4 7
0 7 7 7 0 (7+0=7)
(7+7=14)
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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.
Multiplying numbers with11
Gives us:- 1 5 4 7
0 7 7 7 0 (7+0=7)
(7+7=14)
(7+7=14+1=15)
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Step5: Finally we add 0 to 7 and then add 1 of the carry over to give us 8.
Multiplying numbers with11
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.
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Multiplying numbers with 12Multiplying numbers with 12
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Now lets take for example 1234 x 12
Multiplying numbers with12
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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.
Multiplying numbers with12
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Step1: We put two strokes beside 1234 and place two zero’s as before.
Multiplying numbers with12
0 1 2 3 4 0
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Step2: Now we start Doubling and Adding to the Neighbor. First we double 4, gives us 8.We then add 8 to zero.
Multiplying numbers with12
0 1 2 3 4 0
Gives us:- 8
(4x2=8+0 = 8)
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Step3: We now double 3 to get 6. Add the neighbor 4 to get 10. We write 0 and carry 1.
Multiplying numbers with12
0 1 2 3 4 0
Gives us:- 1 0 8
(3x2 =6+4=10)
(4x2=8+0 = 8)
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Step4: We now double 2 to get 4.Add 1 of carry gives us 5. Add neighbor 3 gives us 8.
Multiplying numbers with12
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
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Step5: Double 1 to get 2. Add neighbor 2, gives 4.
Multiplying numbers with12
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
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Step6: Finally Double 0 to gives us 0. Add neighbor 1 , gives us 1.
Multiplying numbers with12
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)
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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.
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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
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Answers
• 497 629 • 78 384 • 2 028 • 805 044 • 49 952
• 1 029 639 • 1 697 479 • 351 180 • 8 418 456 • 587 769
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