Speed Multiplication by 111 : Vedic Maths

Multiplication of a number consisting of only ones with another number becomes very easy using Vedic Maths techniques. You must see the earlier post on shortcut for multiplying a number by 11

MULTIPLYING A NUMBER BY 111
To multiply a two-digit number by 111, add the two digits and if the sum is a single digit, write this digit TWO TIMES in between the original digits of the number. Some examples:

36×111= 3996
54×111= 5994

The same idea works if the sum of the two digits is not a single digit, but you should write down the last digit of the sum twice, but remember to carry if needed. So

57×111= 6327
because 5+7=12, but then you have to carry the one twice.

For 3 digit numbers
Carry if any of these sums is more than one digit.
Thus 123×111 = 1 | 3 (=1+2) | 6 (=1+2+3) | 5 (=2+3) | 3

Similarly,
241×111 = 26751

For an example where carrying is needed

Say, 352×111=3 | 8 (=3+5) | 10 (=3+5+2)| 7 (=5+2)| 2
= 3 | 8 | 10 | 7 | 2 = 3 | 9 | 0 | 7 | 2
= 39072

(Because of the carries, it may be easier to do the sums and write the answer down from right to left.)

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Vedic Multiplication by 11

Speed Vedic Multiplication Trick

Vedic Multiplication by 11

Step 1.

Assume that there are two invisible 0 (zeroes), one in front and one behind the number to be multiplied with 11

say if the number is 234, assume it to be  0 2 3 4 0

Step 2.

Start from the right, add the two adjacent digits and keep on moving left

02340

Add the last zero to the digit in the ones column (4), and write the answer below the ones column. Then add 4 with digit on the left i.e. 3. Next add 3 with 2. Next 2 with 0.

0+4 = 4

4+3 = 7

3+2 = 5

2+0 = 2

So answer is 2574

Similarly,

36 x 11 = 0+3   |   3+6   | 6+0  = 396

74 x 11 =0+ 7 |  7+4 |  4+0 =  7  | 11 |  4 = 814   (1 of 11 is carried over and added to next digit, so 7+1 = 8 )
6349 x 11 = (0+6)  |  (6+3)   |   (3+4)   |   (4+9)  |   9+0 =  69839

This method works for all the number, no matter how long or short, times 11. Just try it yourself and get amazed at the simplicity of the concept.

In the next post will learn Vedic Multilplication by 111, 1111, 11111, and so on.

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Multiply 2 numbers, sum of whose unit places is 10

Vedic Multiplication: This method of multiplication which is from Vedic Maths will make it very easy to multiply two numbers when sum of the last digits is 10 and previous parts are the same

You will get the answer in two parts.

First part, to get left hand side of the answer: multiply the left most digit(s) by its successor

Second part, to get right hand side of the answer: multiply the right most digits of both the numbers.

Example

First part: 4 x (4+1)

Second part: (4 x 6)

Combined effect:  (4 x 5)  | (4 x 6) = 2024

*| is just a separator. Left hand side denotes tens place, right hand side denotes units place

More Examples

37 x 33 = (3 x (3+1)) |  (7 x 3) = (3 x 4) | (7 x 3) = 1221

11 x 19 = (1 x (1+1)) |  (1 x 9) = (1 x 2)  | (1 x 9) = 209

As you can see this method is corollary of  “Squaring number ending in 5”

It can also be extended to three digit numbers like :

E.g. 1: 292 x 208.

Here 92 + 08 = 100, L.H.S portion is same i.e. 2

292 x 208 = (2 x 3) x 10 | 92 x 8  (Note: if 3 digit numbers are multiplied, L.H.S has to be multiplied by 10)

60 | 736 (for 100 raise the L.H.S. product by 0) = 60736.

E.g. 2: 848 X 852

Here 48 + 52 = 100,

L.H.S portion is 8 and its next number is 9.

848 x 852 = 8 x 9 x 10 | 48 x 52 (Note: For 48 x 52, use methods shown above)

720 | 2496

= 722496.

[L.H.S product is to be multiplied by 10 and 2 to be carried over because the base is 100].

Eg. 3: 693 x 607

693 x 607 = 6 x 7 x 10 | 93 x 7 = 420 / 651 = 420651.

Note: This Vedic Maths method can also be used to multiply any two different numbers, but it requires several more steps and is sometimes no faster than any other method. Thus try to use it where it is most effective

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