Once again it is proved that old is gold! I am not talking about old melodies or classic movies, it is VEDIC MATHS that is gaining importance day by day worldwide. The ancient principles of Mathematics given to us by our own Vedic sages are nowadays termed as Vedic Maths. Though these are the principles used in Vedas for different calculations, it was not till early 90’s that these principles came into light as a set of 16 principles. High Speed Vedic Mathematics was founded by Swami Sri Bharati Krishna Tirthaji Maharaja who was the Sankaracharya (Monk of the Highest Order) of Govardhan Matha in Puri. They are called “Vedic” as because the sutras are said to be contained in the Atharva Veda – a branch of Mathematics and Engineering in the Ancient Indian Scriptures.

Not only the competition is increasing the importance of Vedic Maths but also the ease of solving complex calculations is the main aspect. The objective type competitive exams are taught to solve using these basic principles of Vedic Maths with much of ease and in less time. Vedic Mathematics is far more systematic, simplified and unified than the conventional system. It is a mental tool for calculation that encourages the development and use of intuition and innovation, while giving the student a lot of flexibility, fun and satisfaction. For your child, it means giving them a competitive edge, a way to optimize their performance and give them an edge in Mathematics and logic that will help them to shine in the classroom and beyond. Therefore it’s direct and easy to implement in schools – a reason behind its enormous popularity among academicians and students.

It complements the Mathematics curriculum conventionally taught in schools by acting as a powerful checking tool and goes to save precious time in examinations. The origin of Vedic Maths is dated back to the time of Vedas. These principles are not mentioned separately but are used in many ways in the ancient writings. These were rediscovered from the Vedas between 1911 and 1918 by Sri Bharati Krishna Tirthaji (1884-1960). According to his research all of Mathematics is based on 16 Sutras or word-formulae. The best feature of Vedic Maths is that the system is simplified to its best and all the concepts are inter-related with a striking simplicity and unified in a stunning way. The whole system is beautifully done in a different but perfect 16 sutras or principles. The general multiplication method, for example, is easily reversed to allow one-line divisions and the simple squaring method can be reversed to give one-line square roots. And these are easily understood. This unifying quality is very satisfying and it makes Mathematics easy and enjoyable and encourages innovation.

Vedic Maths is the best way of approach because ‘difficult’ problems or huge sums can often be solved immediately by the Vedic method. These striking and beautiful methods are just a part of a complete system of Mathematics which is far more systematic than the modern ‘system’. Vedic Mathematics manifests the coherent and unified structure of Mathematics and the methods are complementary, direct and easy.

There has been much controversy among Indian scholars about Tirthaji’s claims that Mathematics is Vedic and that it encompasses all aspects of Mathematics. First, Tirthaji’s description of the Mathematics as Vedic is most commonly criticised on the basis that, thus far, none of the sûtras can be found in any extant Vedic literature (Williams, 2000). When challenged by Prof K.S. Shukla to point out the sutras in question in the Parishishta of the Atharvaveda, Shukla reported that the swamiji said that the 16 sutras were not in the standard editions of the Parishishta, and that they occurred in his own Parishishta and not any other. Considering the lack of references to the sûtras, coupled with the fact that the language style does not seem Vedic, some propose that the sûtras were simply composed by Tirthaji himself. In this direction the Sankaracharya of Govardhan Matha Puri Jagadguru Swami Sri Bharati Krishna Teerthaji Maharaja has explored the encoded Vedic mysteries and retrieved a set of Mathematical sutras from the Vedic literatures. Swami Sri Bharati Krishna Teerthaji was a scholar extraordinaire, a profound master of modern subjects including Mathematics. Later after attaining sanyasa he went into solitude at Saradha Peeth in Sringeri and relentlessly pursued the study of Vedic scriptures with the consequence that he reconstructed a set of 16 sutras and 13 subsutras from the Vedic text covering every branch and part of Mathematics.

We owe deeply to the Sankaracharya for his revelation to popularise Vedic Mathematics. Sources of the Sutras Bharati Krishna Teerthaji got his revelations from a particular portion of the Atharvaveda called the Ganita Sutras. The Ganita Sutras are also called Sulba Sutras, ”the easy mathematical formulae”, that’s the meaning of the expression. Now these texts were in Sanskrit and the grammar, the literature and the figures of speech in Sanskrit give great facility of expressing one’s dispositions in a number of different subjects but with the same set of words. Hence it becomes difficult for a person to understand the different layers of meanings encoded in one text.

Bharati Krishnaji underwent meditation for long years in the forest of Sringeri. He took the help of lexicographies, lexicons of earlier times, because as a language develops and comes in context with other languages words change their meaning. Words get additional meaning, words get deteriorated in meaning. Hence Bharti Krishnaji studied old lexicons, including Visva, Amara, Arnava, abdakalpardruma etc. With these, he got the key in that way in one instance and one thing after another helped him in the elucidation of the other sutras (formulae). It was to His Holiness’s extreme amazement that the sutras dealt with Mathematics in all its branches. He realised only 16 sutras cover all branches of Mathematics – Arithmetic, Algebra, Geometry, Trigonometry, Physics, Plain and Spherical Geometry, Conics, Calculus, both differential and integral, applied Mathematics of various kinds, dynamics, hydrostatics, static, kinematics and all. The less complexity of Vedic Mathematics means that calculations can be carried out mentally (though the methods can also be written down).

There are many advantages in using a flexible, mental system. Pupils can invent their own methods, they are not limited to the one ‘correct’ method. This leads to more creative, interest and intelligent pupils. Interest in the Vedic system is growing in education where Mathematics teachers are looking for something better and finding the Vedic system is the answer. Research is being carried out in many areas including the effects of learning Vedic Maths on children; developing new, powerful but easy applications of the Vedic Sutras in Geometry, Calculus, Computing etc. But the real beauty and effectiveness of Vedic Mathematics cannot be fully appreciated without actually practising the system. One can then see that it is perhaps the most refined and efficient Mathematical system possible. The Vedic Mathematics Sutras This list of sutras is taken from the book Vedic Mathematics, which includes a full list of the 16 Sutras in Sanskrit, but in some cases a translation of Sanskrit is not given in the text and comes from elsewhere.

This formula ‘On the Flag’ is not in the list given in Vedic Mathematics, but is referred to in the text.

The Main Sutras
• By one more than the one before.
• All from 9 and the last from 10.
• Vertically and Cross-wise
• Transpose and Apply
• If the Samuccaya is the Same it is Zero
• If One is in Ratio the Other is Zero
• By Addition and by Subtraction
• By the Completion or Non-Completion
• Differential Calculus
• By the Deficiency
• Specific and General
• The Remainders by the Last Digit
• The Ultimate and Twice the Penultimate
• By One Less than the One Before
• The Product of the Sum
• All the Multipliers

The Sub-Sutras
• Proportionately
• The Remainder Remains Constant
• The First by the First and the Last by the Last
• For 7 the Multiplication is 143
• By Osculation
• Lessen by the Deficiency
• Whatever the Deficiency lessen by that amount andset up the Square of the Deficiency
• Last Totalling 10
• Only the Last Terms
• The Sum of the Products
• By Alternative Elimination and Retention
• By Mere Observation
• The Product of the Sum is the Sum of the Products
• On the Flag These are the main and sub principles of Vedic Maths.

Now let us try a few of these principles and see how it works. The following tutorials are based on examples and exercises given in the book ‘Fun with figures’ by Kenneth Williams, which is a fun introduction to some of the applications of the sutras for children.
## Use the formula ALL FROM 9 AND THE LAST FROM 10 to perform instant subtractions.
• For example 1000 - 357 = 643
We simply take each figure in 357 from 9 and the last figure from 10.So the answer is 1000 - 357 = 643
And that’s all there is to it!

This always works for subtractions from numbers consisting of a 1 followed by noughts:
100; 1000; 10,000 etc.
• Similarly 10,000 - 1049 = 8951
• For 1000 - 83, in which we have more zeros than figures in the numbers being subtracted, we simply suppose 83 is 083.
So 1000 - 83 becomes 1000 - 083 = 917
## Using VERTICALLY AND CROSSWISE you do not need multiplication tables beyond 5 X 5.
• Suppose you need 8 x 7
8 is 2 below 10 and 7 is 3 below 10.
Think of it like this: The answer is 56.

The diagram below shows how you get it. You subtract crosswise 8-3 or 7 - 2 to get 5, the first figure of the answer. And you multiply vertically: 2 x 3 to get 6, the last figure of the answer. That’s all you do:See how far the numbers are below 10, subtract one number’s deficiency from the other number,and multiply the deficiencies together.
· 7 x 6 = 42
Here there is a carry: the 1 in the 12 goes over to make 3 into 4.
## Multiplying numbers just over 100.
• 103 x 104 = 10712
The answer is in two parts: 107 and 12,
107 is just 103 + 4 (or 104 + 3),and 12 is just 3 x 4.
• Similarly 107 x 106 = 11342 107 + 6 = 113 and 7 x 6 = 42
## A quick way to square numbers that end in 5 using the formula BY ONE MORE THAN THE ONE BEFORE.
• 752 = 5625
752 means 75 x 75.
The answer is in two parts: 56 and 25.
The last part is always 25.
The first part is the first number, 7, multiplied by the number “one more”, which is 8:so 7 x 8 = 56
• Similarly 852 = 7225 because 8 x 9 = 72.
## Method for multiplying numbers where the first figures are the same and the last figures add up to 10.
· 32 x 38 = 1216
Both numbers here start with 3 and the last figures (2 and 8) add up to 10.
So we just multiply 3 by 4 (the next number up) to get 12 for the first part of the answer.
And we multiply the last figures: 2 x 8 = 16 to get the last part of the answer.
Diagrammatically:
• And 81 x 89 = 7209
We put 09 since we need two figures as in all the other examples.
## An elegant way of multiplying numbers using a simple pattern.
· 21 x 23 = 483
This is normally called long multiplication but actually the answer can be written straight down
using the VERTICALLY AND CROSSWISE formula.
We first put, or imagine, 23 below 21:
There are 3 steps:
a) Multiply vertically on the left: 2 x 2 = 4.This gives the first figure of the answer.
b) Multiply crosswise and add: 2 x 3 + 1 x 2 = 8 This gives the middle figure.
c) Multiply vertically on the right: 1 x 3 = 3 This gives the last figure of the answer. And that’s all there is to it.
• Similarly 61 x 31 = 1891 • 6 x 3 = 18; 6 x 1 + 1 x 3 = 9; 1 x 1 = 1
Multiply any 2-figure numbers together by mere mental arithmetic!
If you want 21 stamps at 26 pence each you can easily find the total price in your head.
There were no carries in the method given above. However, there only involve one small extra step.
• 21 x 26 = 546
The method is the same as above except that we get a 2-figure number, 14, in the middle step, so the 1 is carried over to the left
(4 becomes 5). So 21 stamps cost £5.46.
## Multiplying a number by 11.
To multiply any 2-figure number by 11 we just put the total of the two figures between the 2 figures.
• 26 x 11 = 286
Notice that the outer figures in 286 are the 26 being multiplied.
And the middle figure is just 2 and 6 added up.
• So 72 x 11 = 792
## Method for diving by 9.
• 23 / 9 = 2 remainder 5
The first figure of 23 is 2, and this is the answer. The remainder is just 2 and 3 added up!
• 43 / 9 = 4 remainder 7
The first figure 4 is the answer and 4 + 3 = 7 is the remainder.
These are a few concepts of Vedic Maths. This is the fun way of learning Maths and one could enjoy the real concepts only by practise. So
practise more and get the expertise.