Vedic Mathematics Sutra for Addition

Introduction

Arithmetic is a branch of mathematics that consists of the study of numbers, especially the properties of the elementary operations between them.

The addition is the first basic elementary operation. As such there are comparatively few techniques to enhance its potency, those techniques that exist are primarily ways in which to organize the calculation to form it less complicated to calculate mentally.

Subtraction is similar however, in this case, there also are some techniques to assist with borrow method that in contrast to addition will see multiple digits.

You will no doubt already use most of the addition and subtraction techniques described here intuitively without thinking about them, many of the techniques may seem to be so basic that they don't deserve explanation, but it is worth re-iterating them even if just to make you aware that you are probably already using techniques that can be expanded upon to improve your arithmetical ability.

What is an Addition? 

Adding two or more numbers to find their sum or total is called as Addition. 

Symbol: '+' (read as plus).

In addition, the numbers we add are called Addends and the result is called a Sum.

Now we are going to learn how to perform addition using Vedic sutras. The three sutras used for addition are:  

EKADHIKENA PURVENA SUTRA 

We use this method to make the Addition easy. As the name suggests, we consider one number more than the previous one.

Sutra: Ekhadhikena Purvena

Meaning: By One more than the previous one.

CASE1: 2, 3, 4 DIGITS WITH CARRYOVER

Let us understand with the help of examples.

 Note: The symbol star (*) indicates that we must add one.

 Example 1: Add 47 and 68

Step1: Add the numbers in the unit’s place i.e. 7+8 = 15.

 Since carry over, we place the last digit in the unit's

Concepts of Vedic Mathematics

 Vedic Mathematics

 Interesting Concept of Vedic Mathematics

It is very important to learn and understand the three basic concepts to make any calculation easy. These three concepts are the pillars of Vedic Mathematics.

They are,

             

1.        Base
2.        Parama Mitra (Compliment)
3.        Sum Root / Digital Root

BASE

A base is the number which starts with 1 and remaining all other digits are 0’s i.e. Powers of 10 such as 10, 100, 1000, 10000, etc are called as Base numbers.

To understand the base method, first observe whether the numbers are near to the base numbers.

Let us understand with the help of examples.

Example1: Find the base for 12

Since 12 is nearer to base 10 i.e.12 can be written as 10+2

Hence 10 is the working base for 12.

Example2: Find the base for 95

Since 95 is closer to base 100 i.e. 95 can be written as 100 – 5

Hence 100 is the working base for 95.

Example3: Find the base for 989

Since 989 is nearer to base 1000 i.e.989 can be written as 1000 – 11

Hence 1000 is the working base for 989.

Example4: Find the base for 9991

Since 9991 is nearer to base 10000 i.e. 9991 can be written as 10000 – 9

Hence 10000 is the working base for 9991.

PARAMA MITRA

Parama Mitra is a Sanskrit word derived from two words ‘Param’ and ‘Mitra’. Parama means ‘best’ and Mitra means ‘friend’ which literally means Complementary. 

Two numbers are said to be Parama Mitra (complimentary) if the sum of the given two numbers is equal to nearest base numbers.

Parama Mitra for numbers 1,2,3, …., 7, 8, 9,10 (to the working base 10) are 9,8,7, …., 3, 2, 1, 0 respectively

Let us see the examples.

Example1: Find the Parama Mitra for number 6.

The nearest base for 6 is 10. By adding 4 to 6 we will get 10   i.e. 6 + 4 = 10

Hence 6 and 4 are complements to each other.

Example2: Find the Parama Mitra for the number 72.

The nearest base for 72 is 100. By adding 28 to 72 we will get 100

i.e.72 +28 = 100

Hence 72 and 28 are complements to each other.

Example3: Find the Parama Mitra for the number 654.

The nearest base for 654 is 1000. By adding 346 to 654 we will get 1000

i.e. 654 +346 = 1000

Hence 654 and 346 are complements to each other.

MULTIPLICATION TABLE USING PARAMA MITRA

Let us discuss how to remember tables using Parama Mitra Method. This method is very useful for those who find difficulty in remembering tables above 5. For using this method, one must be good in tables 2, 3, 4 and 5.

Let us understand with the help of examples.

Example1:  Find 7 *8

        Step1: Write the Parama mitra of numbers which we want to multiply. In this case, 3 and 2 are the Parama Mitra

of 7 and 8 respectively.

It can be represented as shown in the table

                                                                               

7	×	8
3		2

                        

Step2: Divide the answer into two parts i.e. LHS and                               RHS. 

     

                                                                                                   

  LHS=

                                                                                                                                                                       Step3: Write the difference of numbers cross-wise and           

 write the result in the LHS.

 It can be written as 7-2 = 5 and 8-3 = 5 
               both give the same answer 5. 

LHS=

 Step4: To get the R.H.S we must multiply the Parama mitra

of numbers.

i.e. 3 * 2 = 6 which is the RHS of the answer.

answer=

Step5:  Hence 7 *8 = 56

SUM ROOT / DIGITAL ROOT

Digital Root or Sum root is the Single-digit value that results from the continuous summation of digits of the given number.

To calculate the Digital root, we should add all the digits of the given number until the single-digit is reached.

Let us understand with the help of examples.

Example1: Find the Digital Root of 459.

Hence, the Digital root of 459 is 9.

Hence, the Digital root of 9542672 is 8.

                                                                                             

These are the basic concept of Vedic Mathematics that makes any calculation very easy and these concepts are the pillars of Vedic Mathematics.

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Importance of Vedic Mathematics

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INTRODUCTION TO VEDIC MATHEMATICS

The ancient system of Vedic Mathematics was rediscovered from the Indian scriptures known as the Vedas. The term Vedic Mathematics is derived from two words of the book called “Veda Ganitha” written by Swami Bharati Krishna Tirtha and was first published in the year 1965. “Veda” and “Ganitha”, which means Knowledge and Mathematics. It contains an inventory of mental calculation techniques claimed to be supported the Vedas.

“Vedic Mathematics” can be a mathematical elaboration of Sixteen easy Mathematical Formulae from the Vedas. It is a collection of Techniques or Sutras to solve mathematical arithmetic in an easy and faster way. It consists of 16 Sutras (Formulae) and 13 sub-sutras (Sub Formulae) which can be used to solve problems related to arithmetic, algebra, geometry, calculus.

                 

            In the field of Arithmetic, ancient Indians created 3 distinct contributions:

•          The Notation System
•               The Decimal System·           
•        The use of Zero

The Sutras are applied to almost every branch of Mathematics.

IMPORTANCE OF VEDIC MATHEMATICS

         The Vedic arithmetic system is predicated on sixteen sacred writing sutras or aphorisms, that area unit word-formulae describing natural ways in which of resolution a complete vary of mathematical issues.

         Some samples of sutras area unit "By another than the one before", "All from nine and therefore the last from 10", and "Vertically & Crosswise".

         These sixteen formulae area unit originally written in Indo-Aryan, which may be simply memorized, permits one to resolve long mathematical issues quickly.

         These formulae describe the method the mind naturally works and thus a big facilitate help in guiding the code to the suitable methodology of resolution.

         Vedic mathematics is entirely done in mind.

         Vedic arithmetic conjointly starts at a basic level of numbers and step by step planning to straightforward additions, subtractions, multiplications, and division.

     With Vedic mathematics, one can also solve complex geometrical theorems and algebraic problems.

         Vedic arithmetic may be started at later ages likewise, with none issue.

There are many special features of Vedic mathematics. Some of them are:

·          It reduces the burden of remembering a large amount of stuff.

•  It enriches and enhances the knowledge and understanding of math.
•      It helps to reduce finger counting and scratch work.
•      It plays a crucial role in increasing concentration furthermore as rising confidence.
•     It cultivates strong logical thinking & problem-solving skills.
•   Vedic mathematics methods are boon for all competitive exams.
•       It ends up in improvement in sharpness, creativity, and intelligence.
•        It involves logic and understanding the fundamental concepts, which improves concept clarity.
•     It will introduce creativeness in intelligent and sensible students whereas serving to the slow-learners grasp the fundamental ideas of mathematics.
•    It helps to develop the spiritual side of our personality.
•       It improves the mental ability

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INTRODUCTION TO VEDIC MATHEMATICS

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INTRODUCTION TO ANCIENT INDIA

Indian civilization includes a robust tradition of Science and Technology. Many theories and techniques discovered by the traditional Indians have created and strengthened the fundamentals of modern Science and Technology.

Ancient Asian country was a land of sages, saints, and seers similarly as a land of student and scientists. Science and technology in ancient and medieval Asian Country coated all the foremost branches of human data and activities together with arithmetic, astronomy, physics, chemistry, medical science and surgery, fine arts, mechanical and production technology, applied science and design, building and navigation, sports and games.

ANCIENT INDIA'S CONTRIBUTION TO SCIENCE AND TECHNOLOGY

• Mathematics

In the ancient Republic of India, roots to arithmetic are often derived to Veda traced to Vedic literature, that is around 4000 years old. Vedic literature is replete with ideas of zero, the techniques of algebra and algorithm, square root and cube root. The origins of Calculus lie in India before 300 years. Leibnitz and Newton, Will Durant, an American historian said that “India was the mother of our philosophy and much of our mathematics”.

It is now proved that India is the birthplace of several mathematical concepts like including zero similarly decimal system, algebra and algorithm, square roots and cube roots.

• Astronomy

       The earliest references to astronomy are found in the Rig Veda, which is dated 2000 BC. In some instances, astronomical principles were borrowed to explain matters, pertaining to astrology like the casting of a horoscope.

Apart from this, linkage of physical science with pseudoscience in ancient India, the science of physical science continued to develop severally and culminated into original findings like:

• The calculation of occurrences of eclipses
• Determination of Earth's circumference
• Theorizing about the theory of gravitation
• Determining that the sun was a star and determination of the number of planets under the solar system.

• Physics:   

       The root concept of the atom in ancient India is derived from the classification of the five basic elements present in nature by ancient Indian philosophers. The five elements were the Earth (Prithvi), Fire (Agni), Air (Vayu), Water (Jala) and Ether or Space (Akasha). These elements were also associated with human sensory perceptions like Earth with a smell, Air with feeling, Fire with vision, Water with taste and Ether/Space with sound. 

• Chemistry:

In civilization, Metallurgy has remained an activity center to all civilizations from the Bronze Age and the Iron Age. It is believed that the essential plan of “Smelting” reached ancient India from the geographic area and therefore geographic region.

Ancient India's development in chemistry was not confined at an abstract level, but also finds expression in Distillation of perfumes and fragment ointments, Manufacturing of dyes and chemicals, Polishing of mirrors, Preparation of pigments and colors.

• Medicine and Surgery: 

Ayurveda as a science of drugs owes its origins in ancient Bharat. It constitutes ideas about ailments and diseases, their symptoms, diagnosis, cures and relies heavily on herbal medicines which include extracts of several plants having medicinal values.
In ancient India, several advancements were also made in the field of medical surgery. Specifically, these advancements include areas like plastic surgery, extraction of cataracts and even dental surgery. Ancient medical compendium describes seven branches of surgery such as Excision, Scarification, Puncturing, Exploration, Extraction, Evacuation and Suturing.

• Civil Engineering and Architecture:

 India's urban civilization is traceable to Mohenjo-Daro and Harappa. The ancient Indian design and technology found manifestation within the construction of temples, palaces, and forts across the Indian ground and also the neighboring regions.

There square measure many marvels of ancient India's beaux-arts together with World heritage sites like Ajanta, Ellora, Khajuraho, Mahabodhi Temple, Sanchi, Brihadishvara Temple, and Mahabalipuram.

• Production Technology:

Mechanical and production technology of ancient India ensured the processing of natural products and their conversion into merchandise of trade and export. The number of travelers and historians have indicated a variety of items which were produced, consumed and exported around that society’s "Known world" by the ancient Indians.

• Shipbuilding and navigation:

The science of building and navigation was documented to ancient Indians. Sanskrit and Pali texts are replete with maritime references were having commercial relations with several countries across the Bay of Bengal like Cambodia, Java, Sumatra, Borneo and even up to China. The early Hindu astrologers used the magnet in fixing the North and East, in laying foundations and other religious ceremonies. 

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