Tag Archives: Vedic Math Sutra

Vertically and Crosswise – A simple and effective method of multiplication

In my workshops I have seen kids and children struggling with multiplication . Specially if it is two or three digit multiplication their faces will just turn sad in few seconds. And they will shout in unison , ” No Mam not again ”

So I teach them a simple method of multiplication which is not only easy to remember  but saves a lot of time . Once you understand this method , the time taken to do two digit and three digit multiplication reduces by half.

These methods are derived from Atharv Veda and they make calculations really simple.

This method is called Vertically and Crosswise

Two digit multiplication 

We are multiplying here 12 and 34

two digit

Step 1

Multiply the digits at unit place . Here they are 2 and 4 . Since it is 8 you keep the digit at units place . If in a case you get two digits you carry the ten’s digit to the next place value . This step is called vertically

Step 2

Multiply the digits at unit’s place to the  digit at tenth place and add both of them . Keep the unit’s digit and carry the remaining digits at the next place value. . This step is crosswise . When we multiply here in the above case i.e 1 with 4 and 2 with 3 , we got 4 and 6. When we add we got 10 . We kept 0 and carried 1 to the next place value

Step 3

Multiply the digits at the tenth place . Add the digits to the carry over digits. This step is again called vertically . We multiplied 1 with 3 here and added the carry over 1 from step 2.

Hence the answer is 408

Multiplication of three digit number by three digit number

Diagramatic representation of multiplication of 3 digit number by 3 digit

three digit multiplication

                 1   2   3

                 4   5   6

_________________

4   3    8    7      8

1   2   2    1      +

___________________

5    6    0    8     8

Let us work another problem by placing the carried over digits under the first row and proceed.
Steps:
i) 3 X 6 = 18 : 8 is kept at the unit’s place and 1 is carried over to the next place value.

ii) (2 X 6) + (5 x 3) = 12 + 15 = 27 ; 7, the carried over digit 2 is placed to the next place value

iii) (1 X 6) + (3 X 4) + (2 X 5) = 6 + 12 + 10 = 28 ; 2, the carried over digit is placed below fourth digit.

iv) (5 X 1) + ( 2 X 4) = 5 + 8 = 13; 1, the carried over digit is placed below fifth digit.

v) ( 1 X 4 ) = 4

vi) Respective digits are added with the carry over digits.  So the answer is 56088

This method can be applied for any two digit or three digit multiplication and it reduces the time by half .

Keep watching this space for some more easy tricks which makes calculation really simple.

Sutra 10 – Yaavadunam

The Sutra means “By the Deficiency”. Here find the deficiency of the number to its nearest base. The difference between the number and the base is termed as deviation or reference base or complement which may be positive or negative.

Example:

Number

Base

Deficiency

8

10

10 – 8 = 2

14

10

10   – 14 = -4

88

100

100 – 88 = 12

109

100

100   – 109 = -9

999

1000

1000 – 999 =    1

99995

100000

100000   – 99995 = 5

Exercise:

1)      Find the deficiency of the following numbers to its nearest base

a)      98

b)      7

c)      13

d)      98

e)      105

f)       989

g)      99999

h)      1000001

Square of a number:

Square of a number can be determined by implementing the corollary of this Sutra “Yavadunam Tavadunikrtya Varganca Yojayet

This means” Whatever  is deficiency,  subtract  it from the number and write the square of that deficiency” This Sutra can be applied to find the square of any number closer to the base of  powers of 10. Below are the easy steps.

1)      Find the deficiency with the nearest base.

2)      Square the deficiency and place at the right side.

3)      Subtract the Deficiency from the number

4)      Result = [Number – Deficiency + carry over][Square of Deficiency]

Example 1 – Find the Square of 9

1)      Base = 10, Deficiency = 1

2)      Square of the Deficiency = 1

3)      Subtract the Deficiency from Number -> 9 – 1 = 8, Carry over = 0

4)      Square of 9 is [Number – Deficiency + Carry over][Square of Deficiency] = 81

 Example 2 – Find the Square of 14

1)      Base = 10, Deficiency =  – 4

2)      Square of the Deficiency = 16

3)      Subtract the Deficiency from Number -> 14 – (-4) =  18, Carry over =1

4)      Square of 9 is [Number – Deficiency + carry over][Square of Deficiency] = 196

Example 3 – Find the Square of 98

1)      Base = 100, Deficiency =  2

2)      Square of the Deficiency = 04

3)      Subtract the Deficiency from Number -> 98 –  2 =  96, Carry over =0

4)      Square of 9 is [Number – Deficiency + carry over][Square of Deficiency] = 9604

Example 4 – Find the Square of 104

1)      Base = 100, Deficiency =  – 4

2)      Square of the Deficiency = 16

3)      Subtract the Deficiency from Number -> 104 –  (-4) =  108, Carry over = 0

4)      Square of 9 is [Number – Deficiency + carry over][Square of Deficiency] = 10816

Example 5 – Find the Square of 9997

1)      Base = 10000, Deficiency =  3

2)      Square of the Deficiency = 0009

3)      Subtract the Deficiency from Number -> 9997 –  3 =  9994, Carry over =0

4)      Square of 9 is [Number – Deficiency + carry over][Square of Deficiency] = 99940009

Exercise

Find the Square of following Numbers

1)      96

2)      6

3)      990

4)      111

5)      102

6)      10003

7)      999995

8)      10000008

9)      12

10)  89

Answers:

Sutra 2 – Nikhilam navatascaramam Dasatah

The Sutra means “All from 9 and the last from 10”.  In mathematical terms, this means find complement of a number.  Subtract the number from the nearest power of 10 such as 10, 100, 1000 etc. The power of 10 from which the difference is calculated is called the Base.

The difference between the number and the base is termed as deviation or reference base or complement which may be positive or negative.

Example:

 Number Base Base – Number Complement / Nikhilam
7 10 7 – 10 -3
14 10 14   – 10 4
88 100 88 – 100 -122
109 100 109   – 100 9
5200 10000 5200 – 10000 -4800

Exercise:

1)      Find the compliment and the nearest base of the following numbers

a)      45

b)      8

c)      13

d)      8910

e)      98

f)       105

g)      989

h)      99999

i)        1000001

Sutra 1 – Ekadhikena Purvena

The Sutra means “By one more than the previous one”.  In simple words, add 1 to the previous number to obtain the next number.

Example

  • To get 6, Add 1 to the previous number 5 (5 + 1 = 6)
  • To get 26, add 1 to the previous number 25 ( 25 + 1 = 26)

All right, this is straight forward need no brainer. So what’s great about this Sutra? Below are some great usage of this Sutra which makes it amazing.

1)      Square of Number ending with 5 such as 15, 25, 35, 45, 95, 105 etc.

Solution is just two simple steps to be done in mind.

  1. Multiple the number except the last digit (5) with the next number.
  2. Write 25 after the result of 1st step.

Example:

  • Square of   5 =  [0 x (0 + 1)] 25 = [ 0 x 2] 25 = 25
  • Square of 15 =  [1 x (1 + 1)] 25 = [ 1 x 2] 25 = 225
  • Square of 25 =  [1 x (2 + 1)] 25 = [ 2 x 3] 25 = 625
  • Square of 35 =  [3 x (3 + 1)] 25 = [ 3 x 4] 25 = 1225
  • Square of 45 =  [4 x (4 + 1)] 25 = [ 4 x 5] 25 =  2025
  • Square of 55 =  [5 x (5 + 1)] 25 = [ 5 x 6] 25 =  3025
  • Square of 85 =  [8 x (8 + 1)] 25 = [ 8 x 9] 25 =  7225
  • Square of 95 =  [9 x (9 + 1)] 25 = [ 9 x 10] 25 =  9025
  • Square of  125 =  [12 x (12 + 1)] 25 = [ 12 x 13] 25 =  15625
  • Square of  505 =  [50 x (50 + 1)] 25 = [ 50 x 51] 25 =  255025