Tag Archives: Vedic Mathematics

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

Vedic Mathematics – an overview

 Vedic mathematics is an ancient Indian system of Matheatics, a unique and amazing system based on simple rules and principles. The methods and techniques are based on the pioneering work of the late Shree Bharati  Krishna Tirthaji, shankracharya of Puri , who established the system by study of ancient Vedic texts coupled with profound insight into natural process of mathematical reasoning. The whole system is based on sixteen sutras (formula or aphorisms) and thirteen sub-sutras or corollaries which form the fundamentals of Vedic Maths. The characteristic of Vedic Maths is that it presents the subject as a unified body of knowledge and reduce the burden and toil which young minds often experience during their initial years.

 

The current methods of calculation which are taught by schools are conventional and lack imagination. A simple example to illustrate this point is finding the product of 19 and 8. The conventional system will teach us to multiply first 9 and 8 to get 72 and then multiply 10 and 8 to get 80 and when you add both you get 152. On the other hand the Vedic method will say 8 times 20 is 160 and less 8 which is 152. We arrive at the same result but the time taken was relatively less. Many of the children who are brilliant will use the same way and Vedic Maths teach the same approach to calculations in a unified way.

Vedic Maths illustrates that all the numbers start with number one which is also an expression of unity. All the numbers are derived from 1. IF we do not have 1 we cannot have any other number .If students have fear of large numbers, it is a great solace to remember that there are only nine numbers to remember and there is nought or zero which stands for nothing.

The current method of teaching mathematics and coaxing the child to remember tables not only kills their creativity but also makes them  hate mathematics or more particularly arithmetic . Vedic mathematics not only enhances the creativity of the child but also makes mathematics fun and easy to remember. In many of the workshops which I have conducted I find that calculation is a great hindrance and Vedic mathematics makes calculation very simple and almost a child’s play.

Vedic Mathematics has been adopted by many schools in UK and Europe and has been integrated into the main curriculum. But in India, its country of origin, it is still in very nascent stage. Though there are many organizations which are conducting Vedic maths/ Speed maths workshop it will benefit only when it is integrated in the course curriculum for various classes in all the schools. I hope the day comes soon.

Watch out this blog posts to get an insight of some of the principles of Vedic maths on which the sutras are based. Mathematics is really very easy and fun to learn. And I truly believe that maths is like poetry as it enhances the cognitive skills and creativity of children if it is taught in a interesting way. Till then HAPPY LEARNING…