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

place and put a star (*) below the 6 in Ten’s place.

Step2: Add the numbers in Ten’s place.

            Here star indicates carryover 1 i.e. we must add one to 6. i.e. 4+(6 + 1) = 11

Result: 47 + 68 = 115

VILOKANAM SUTRA:

Sutra: Vilokanam Sutra

Meaning: Mere Observation

CASE1: 2, 3, 4 DIGITS WITH CARRYOVER

Let us understand with the help of examples.

Example1: Add 89 and 27

Step1: First represent the numbers in columns as shown and start adding from the left side of the number. Add the digits in Ten’s place i.e. 8 + 2 = 10 and write it in Ten’s place.

Step2: Add the digits in Unit’s place i.e. 9 + 7 = 16, since it has two digits we make use of the Ekadhikena purvena method and start adding from right i.e. we write 6 in one’s place and put a star in the tens place.

Here we have 10 in tens place, so we need to add 1 to 10 i.e. 10 + 1 = 11

Result:  89 + 27 = 116

NIKHILAM SUTRA:

It can be used when the numbers are given are close to the base number (i.e. Powers of 10 like 10, 100, 1000….).

Sutra: Nikhilam Sutra

Meaning: All from 9 and the last from 10.

Let us understand with the help of examples

Note:

• When the given number is below the base number, we represent by minus (-) sign.
• When the given number is above the base number, we represent by the plus (+) sign.

Example1: Add 89 and 95

Step1: Find the nearest base number to the Addends and subtract the base number from Addends to get the difference.

Here 100 is the nearest base number to both the numbers.

i.e. 89-100 = -11 and 95-100 = -5. So, -11 and -5 are the difference.

89(100) → -11

                                       95(100) → -5

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Step2: Add the base numbers and add the differences obtained in Step1.

i.e. Sum of base numbers is 100 + 100 = 200

 Sum of differences is (-11) + (-5) = -16

89(100) → -11

95(100) → -5

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 200   → -16

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Step3: Add the Sum of base numbers and the sum of differences to get the final answer.

i.e.  200+(-16) = 200-16 = 184

Result: 89 + 95 = 184

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