The name Vedic Maths is derived from a Sanskrit word ‘Veda’ which means ‘Knowledge’. It is a group of sutras/techniques to solve math problems in a much faster and easier way.

These mathematics techniques introduce wonderful and unique applications of Arithmetical computation, theory of numbers, mathematical and algebraic operations, higher-level mathematics, calculus, and coordinate geometry, etc.

It is very important that children learn Vedic maths tricks and concepts at an early stage to build a strong foundation.

Once the mind of a student develops an understanding of vedic mathematics, they begin to think systematically and creatively. Finally they may become human calculator, which is the main aim of Vedic Maths.

In Vedic maths, long problems can be solved immediately in one line e.g. 68844578 × 99999999. The beauty is that whole calculations can be carried out mentally within seconds.

It is also useful for higher classes because it has a shorter way for solving quadratic and other polynomial functions and equations that one would encounter in higher classes.

The importance of these vedic maths tricks is most realized in the higher exams where time is less and questions are more like Banking exam, CAT, JEE, etc.

So, knowledge of vedic maths helps every age group of people, including homemakers.

In this article, we discussed some of the most Vedic math tips and tricks for all ages under different categories, with relevant examples and explanations.

Vedic Mathematics was discovered by Indian mathematician Jagadguru **Sri Bharathi Krishna Tirthaji** during the period between 1911-1918.

In the year 1957, he wrote an introductory volume of 16 sutras which is called as Vedic Mathematics. These sutras or techniques are useful to solve various mathematical problems in a simpler way.

Vedic maths is one of the most refined and efficient mathematical calculation systems possible today. It has certain specific rules and principles to perform various calculations in mathematics.

Using regular mathematical steps is complex and time consuming. But using Vedic Mathematics General and Specific Techniques numerical calculations can be done very easily and quickly.

**Benefits of Vedic Maths**

**16 Sutras, Subsutras And Their Meanings**

S.NO | SUTRAS | SUBSUTRAS | MEANING |

1. | Ekadhikena Purvena | Anurupyena | By one more than the previous one |

2. | Nikhilam Navatash- caramam | Dashatah Sisyate Sesasamjnah | All from 9 and the last from 10 |

3. | Urdhva-Tiryagbyham | Adyamad- yenantya mantyena | Vertically and crosswise |

4. | Paravartya Yojayet Kavalai | Saptakam Gunyat | Transpose and adjust |

5. | Shunyam Saamyas amuccaye | Vestanam | When the sum is the same that sum is zero |

6. | Anurupye Shunya manyat | Shunya Anyat | If one is in ratio, the other is zero |

7. | Sankalana-vyavakal anabhyam | Yavadunam Tavaduni kritya Varga Yojayet | By addition and by subtraction |

8. | Purana Purana Byham | Antyayor dashake | By the completion or non-completion |

9. | Chalana-Kalanabyham | Antyayoreva | Differences and Similarities |

10. | Yavadunam | Samuccay agunitah | Whatever the extent of its deficiency |

11. | Vyashti Samashti Lopanasth apanabhyam | Lopanasth apanabhyam | Part and Whole |

12. | Shesany ankena Charamena | Vilokanam | The remainders by the last digit |

13. | Sopaanty- advaya- mantyam- Gunitasa- muccayah | Samucc ayagunitah | The ultimate and twice the penultimate |

14. | Ekanyunena Purvena | Dhvajanka | By one less than the previous one |

15. | Gunita Samuchaya | Dwandwa Yoga | The product of the sum is equal to the sum of the product |

16. | Gunaka samuchyah Adyam | Antyam Madhyam | The factors of the sum is equal to the sum of the factors |

**Vedic Maths Addition **

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In vedic maths addition is one of the most basic operations. It has certain ways of adding numbers, which is different from traditional methods.

It is easier to add numbers which are closer to 10s multiple. For example,

7, 8, 9 are closer to 10 or 21, 22, 23 are closer to 20 and so on.

Suppose, we have to add 38 and 97.

Step 1: Add 40 and 100 which are closer to numbers (38 – 40, 97 – 100). It gives 40 + 100 = 130

Step 2: Add the differences, 2 + 3 = 5

(40 – 38 = 2, 100 – 97 = 3)

Step 3: Subtract results obtained from step 2 and step 1, that is 130 – 2 = 125

》Answer is 125

?**To Learn More About Addition Click Here **?

**Vedic Maths Multiplication **

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In Vedic Maths, there are various methods of multiplication which can make your calculation easy and quick. Regular practice of these multiplication methods enable you to choose the one that best suits a particular problem.

Suppose you have to multiply 543 with 999. You might be thinking it’s easy. Yes it is, but it will take so much time and in between you may make many mistakes when you try to solve it by using traditional method.

So how to solve it?

543 × 999

**Traditional method**:

9 9 9

×5 4 3

______ ( first line)

_____× ( second line)

___× × ( third line)

________

542457 ( final answer) Takes a lot of time

**Vedic maths method**:

**Example 1:** 543 × 999

First write down one number lesser than 543, that is 542, then apply the complement method. Deduct 543 from 9, 9, 10 (All from 9 and the last from 10′ method)

First step: write one number lesser than 543 that is 542

Second step: deduct 543 from 9 9 10

9 | 9 | 10 (solve in your mind)

-5 4 3

4 5 7

Final step: Write 542 first and then 457

So the answer is 542457.

(Remember in vedic maths always start from left side and write the actual value)

Isn’t it so exciting?

Same way you can solve any number with 99, 999, 9999, 99999 etc

?**To Learn More About Multiplication Click Here**?

**Vedic Maths Subtraction**

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**Nikhilam Navatashcaramam Dashatah**

The sutra basically means start from the leftmost digit and begin subtracting ‘9’ from each of the digits; but subtract ‘10’ from the last digit.

– All from 9 and the last from 10 i.e. subtract the last digit from 10 and the rest of digits from 9.

To subtract 4568 from 10000. Each figure in 4568 is subtracted from 9 and the last figure is subtracted from 10, yielding 5432.

9 9 9 10 (solve it in your mind)

-4 5 6 8

_________

5 4 3 2 ( Applying ‘All from 9 and the last from 10’ method)

??**To Learn More About Subtraction Click Here**?✈️

**Vedic Maths Divisio**

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The division is a method of distributing or splitting a large group of things into equal smaller parts. It is a major arithmetic operation apart from addition, subtraction and multiplication, in which large numbers are divided in such a way that it forms a new number.

In order to perform division, we use two symbols. They are ÷ and /.

For example, 8 ÷ 2 = 4, and 8/2 = 4

The formula of division is:

Dividend = (Divisor × Quotient) + Remainder

?**To Learn More About Vedic Maths Division Click Here**??

**Vedic Maths Square & Square Root**

**( x )² √44**

**Square**

**Square of 11, 111, 1111….**

Squaring 11 or all multiples if 11 is very easy as compared to others. Understand carefully there are two ones to make 11. So write upto two numbers and return back.

( 11 )² = 1 2 1

( 111 )² = 1 2 3 2 1 ( here 3 one’s are present so write upto 3 numbers, means 123 and then come back after 3 that is 2 and 1)

( 1111 )² = 1234321

**Square of 22, 33, 44 ……99, 222, 333…..999 etc.**

Here you can apply same formula as 11 after taking out actual number.

(22)² = 2² × (11)² = 4 × 121 = 4 8 4

(33)² = 3² × (11)² = 9 × 121 = 1089

(77)² = 7² (11)² = 49 × 121 = 5929

(99)² = 9² (11)² = 81 × 121 = 9801

(222)² = 2² × (111)² = 4 × 12321 = 49284

(444)² = 4² × 12321 = 16 × 12321 = 197136

?♂️ **To Know More About Square And Square Root Click Here** ?♀️

**Vedic Maths Cube & Cube Root **

**( 55 )³ ∛55**

**Cube of Number**

For finding a Cube of any number we need to use two Vedic maths sutras

Anurupyena Sutra (Specific Technique)

Yavadunam Sutra (Specific Technique)

Cube by applying Anurupyena Sutra

Algebraic expression

(x + y)³ = x³ + 3x²y + 3y²x + y³

**Example 1: (23)³**

(23)³ — Apply a³ + 3a²b + 3b²a + b³ formula

= 2³ + (3 × 2² × 3) + (3 × 3² × 2) + 3³

= 8 + 36 + 54 + 27

= 8 | 3 6 | 5 4 | 2 7 (use Balancing rule)

= 12 1 6 7

》 Answer is 12167

?**To Know More About Cube & Cube Root Click Here **??

**Vedic Digital Sum**

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Digital sum means adding digits of any group of numbers. It is also known as C9 method and Magic with 9 method.

Simply we need to add every digit of any big numbers, irrespective of point, percentage etc in between the numbers like 234.56 or 56%.

Digital sum technique is very useful for the students giving competitive exams as they are already provided four choices to every answer.

The digital sum technique is also very useful to check answers involving multiplication, division, addition, squares, square roots, cube roots etc.

The procedure of digital sum is very simple, only we have to convert any given number into a single digit by repetitive adding of all the digits of that number. e.g. digital sum of 23456 is 2+3+4+5+6 = 20

**Click Here To Learn More About Digital Sum **

**Description Of 16 Sutras**

1. **Ekadhikena Purvena**

– Ekadhikena Purvena is One More than the Previous. This sutra is useful in finding squares of numbers (like 25×25, 95×95, 105×105, 992×992 etc) or for any integer ending with 5, the square always ends with 25 and begins with the multiple of the previous integer and one more than the integer. For example:

- 34 x 36 = (3 x (3+1)) (4 x 6) = (3 x 4) (4 x 6) = 1224
- 64 x 66 = (6 x (6+1)) (4 x 6) = (6 x 7) (4 x 6) = 4224
- (25)² is 2 x (2+1) and 5²= (2×3) (5×5)= 625
- (85)² is 8 x 9 .. 25 = 7225

2. **Nikhilam Navatashcaramam Dashatah**

The sutra basically means start from the leftmost digit and begin subtracting ‘9’ from each of the digits; but subtract ‘10’ from the last digit.

– All from 9 and the last from 10 i.e. subtract the last digit from 10 and the rest of digits from 9.

To subtract 4568 from 10000. Each figure in 4568 is subtracted from 9 and the last figure is subtracted from 10, yielding 5432.

9 9 9 10 (solve it in your mind)

-4 5 6 8

_________

5 4 3 2 ( Applying ‘All from 9 and the last from 10’ method)

3. **Urdhva – Triyagbhyam**

– It means Vertically and crosswise

For multiplication of any two two-digit numbers,

Step 1: Multiply the last digits and first digits of both number and put two bars in between results by keeping some gaps

23 × 54= (2 × 5) (3 × 4)= 10 | ? | 12

Step 2: Multiply numbers diagonally and add them. Put the result in between previous results. (2 × 4) (3 × 5)= 8 + 15= 23

10 | 23 | 12 (Now use Balancing Rule)

__________

1 2 4 2

Answer: 1 2 4 2

4. **Paravartya Yojayet**

–It means Transpose and adjust

This method is used for dividing large numbers by numbers greater than 10. For example 1225 divided by 12, 1697 divided by 14, 2598 by 123 etc.

5. **Sunyam Samya Samuccaya**

**Case 1** – When a term occurs as a common factor in all the terms is equated to 0.

14x+5x = 7x + 3x … As x is a common factor on both sides. So, x = 0.

Example : 9(x+3) = 4(x+3)

According to the definition, Since x+3 is a common factor, x + 3 = 0 therefore, x = -3

Calculation with a traditional algebraic method,

9x + 27 = 4x + 12

5x = -15

x = -3

**Case 2** – When the product of the independent terms is the same on both sides then equated to 0.

Examples:

(x+5)(x+4) = (x+2)(x+10)

As a product of independent terms (non-x terms): 5 x 4 = 2 x 10 , is the same on both sides.

Therefore, x=0.

6. **Anurupyena – Sunyamanyat**

This multiplication method is used whenever both numbers are not closer to power of 10(10, 100, 1000, etc)

21 — + 1 ( by taking 20 as base)

22 — + 2

___________

22+1= 23 | 2 (2×1)

×2

_____________

46 | _ 2 (Use Balancing rule)

⬇️

________

46 2

7. **Sankalana – Vyavakalanabhyam**

–It means ‘By addition and By subtraction’

In two general equation such as, ax + by = p and cx + dy = q, where x and y are unknown values,

x = (bq – pd) / (bc – ad)

y = (cp – aq) / (bc – ad)

For example:

3x + 2y = 4 and 4x + 3y = 5

x = (10-12)/(8-9) = 2

y = (16-15)/(8-9) = -1

8. Puranapuranabhyam

– It means ‘By the completion or non-completion’. We can use this technique

to solve the quadratic equations. This method is useful for completion of polynomials to find its factors.

9. Chalana – Kalanabhyam

– It means ‘Differences and Similarities’ or

‘Differential Calculus’. It is used to find the roots of a quadratic and to factorise expressions of 3rd, 4th, and 5th degree.

10. **Ekanyunena Purvena**

– It means ‘By one less than the previous one’. For multiples of 9 as a multiplier, the first digit is 1 less than the first digit and the second digit is subtracting the lessened digit.

Examples:

5 x 9 = 45

5-1= 4, 9-4 = 5

14 x 99 = 1386

14-1=13, 99-13=86

11. **Yavadunam**

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

12. **Vyashtisamanstih**

It means ‘Part and Whole’

This is used to solve the equation of polynomials

For example:

i. x³ + 7x² + 14x + 8 = 0

i.e. x³ + 7x² = – 14x – 8

We know that (x+3)³ = x³+9x²+27x+27 = 2x² + 13x + 19 (Substituting above step).

i.e. (x+3)³= 2x² + 13x + 19

Now we need to factorize RHS in terms of (x+3). So apply Paravartya sutra.

Dividing 2x² + 13x + 19 by (x+3) gives

2x² + 13x + 19 = (x+3)(2x-7)-2

i.e. (x+3)³ = (x+3)(2x-7)-2

put y = x+3

So, y³ = y(2y+1) -2

Which gives y = 1,-1,2

Hence, x= -2, 4, 1, -1

13. **Shesanyankena Charamena**

– It means ‘The Remainders by the Last Digit’. This sutra is used to express a fraction as a decimal to all its decimal places

Example: 1/7

As seen earlier successive remainders are 1, 3, 2, 6, 4 and 5.

We will write them as 3, 2, 6, 4, 5 and 1.

Multiply them with the last digit of divisor (7): 21, 14, 42, 28, 35 and 7

Now take their last digits and that’s the final answer: 0.142857.

14. **Sopaantyadvayamantyam**

It means ‘the ultimate and twice the penultimate’ of given multiplication

For the equation in the format 1/AB + 1/AC = 1/AD + 1/BC, the result is 2C(penultimate) + D(ultimate) = 0.

Example:

1/(x+2)(x+3) + 1/(x+2)(x+4) = 1/(x+2)(x+5) + 1/(x+3)(x+4)

Appying the formula, 2(x+4) + (x+5) = 0

or, x = -13/3

15. **Gunita Samuchaya**

– It means ‘The product of the sum is equal to the sum of the product’

This Sutra is used for the quadratic equation, in order to verify the result, the product of the sum of the coefficients of ‘x’ in the factors is equal to the sum of the coefficients of ‘x’ in the product.

Examples:

(x + 3) (x + 2) = x² + 5x + 6

or, (1+3) (1+2) = 1 + 5 + 6

or, 12 = 12 ; thus verified.

(x – 4) (2x + 5) = 2x² – 3x – 20

or, (1 – 4) (2 + 5) = 2 – 3 – 20

or -21 = – 21 ; thus verified.

16. **Gunakasamuchyah**

–It means ‘The factors of the sum is equal to the sum of the factors’

Used for a quadratic equation, the factor of the sum of the coefficients of ‘x’ in the product is equal to the sum of the coefficients of ‘x’ in the factors.

**Basic Fundamentals of Vedic Maths**

For becoming a pro in vedic maths you need to know some basic things first. So that when you solve various maths calculations from basic to advanced you should not face any problems.

Base and complement are fundamental concepts of Vedic Maths.

In mathematics we work in a base 10 number system, but in Vedic Math you will use **Base** as a basis for calculation. The numbers taken can be either less or more than the base considered.

The difference between the number and the base is termed as **complement**. Complement can be either positive or negative

**Base And Compliment**

Like for a given number 6 the base is 10. And the difference between 6 and 10 is 4, so 4 is a complement of 6.

Numbers | Base | Complement |
---|---|---|

13 | 10 | 3 |

7 | 10 | – 3 |

85 | 100 | – 15 |

106 | 100 | 6 |

998 | 1000 | 2 |

The complement can be obtained from “All from 9 and the last from 10” sutra (Nikhilam Navatashcaramam / Dashatah Sisyate Sesasamjnah). Which is generally used for big numbers.

For example: the base of number 875 is 1000 and the difference is 125. Now to find 125 takes time which goes against vedic maths rule, which says you should solve problems in 2-5 sec.

Method to find complement by using ‘All from 9 and the last from 10’.

Subtract 875 from 9,9 and 10. Subtract first 8 from 9, second 7 from 9 and last 5 from 10. This method you need to use in your mind.

**9 9 10**

-8 7 5

_________

1 2 5

One more example:

Base of number 4568 is 10000

Now to find differences you need time if you use traditional methods. But if you apply Vedic maths technique, then you can solve it within 2 seconds.

10000 – 4568 = 5432

**Traditional method**:

10000

-4568

_______

5432 (Takes more time)

**Vedic Maths method**

9 9 9 10 (solve it in your mind)

-4 5 6 8

_________

5 4 3 2 ( Applying ‘All from 9 and the last from 10’ method) takes 2 sec.

By applying base and complement methods we can solve any big addition, subtraction and multiplication.

**Caution- ***DON’T USE CALCULATOR***, otherwise you will not become master of Vedic maths**

Initially you may take some time.

But….

More you practice, the more you will become a pro.

You can even play with other fellows or friends. Tell them to ask anything and you solve it quickly. They will be amazed.

**Balancing Rule Technique**

Balancing Rule in Vedic maths is a very effective technique. Here we have to start from the right side. Let’s understand with some simple examples, then we will apply this same technique to solve multiplication, addition etc.

25 | 46

⬇️

Right side

Every time we need to drop one’s place and carry the remaining to the next number. Here in 46 one’s place is 6, so drop it first. Remaining number is 4 that should be carried to the next number 25, 25+4=29. Drop 29. So the answer is 296.

**Example 1**:

2 5 | 4 6

⬇️

_________

25+4 | 6

296 – Answer

**Example 2:** 53 | 6

In this case simply drop 6, but there is no remaining number to carry to the next number, so drop the whole 53. So the answer will be 536.

53 | _ 6

⬇️ ⬇️

53 6 so, 536 is the Answer

**Example 3: **3 | 47

Drop 7 carry 4 to next number, it will become 3+4=7, no need to take tens place

3 | 4 7

⬇️

________

3+4= 7 7 so the answer is 77

**Example 4:** 23 | 38 | 14

It’s very simple, drop 4 carry 1 to next number 38, it will become 38+1=39, again drop 9, carry remaining 3 to next number 23, it will become 23+3=26. So the answer will be 2694

2 3 | 3 8 | 1 4

| | | |⬇

________________

23+3= **26** 8+1= **9 4**

Therefore 2694 is the answer.

**Example 5: **2345 × 6

This is also very simple: first multiply 6×5=30 drop as it is put a bar, 6×4=24 drop 24 put a bar, 6×3=18, drop 18 put a bar and 6×2=12, drop 12. Then apply Balancing Rule

2 3 4 5

× 6

_____________

1 2 | 1 8 | 2 4 | 3 0

| | | | | | ⬇️

______________ ⬇️

12 8 4 ⬇️

+2(1+1) +2 +3 ⬇️

_______________ ⬇️

↖️

14 1️⃣ 0 7 0

(1 carry to next number)

Therefore the answer is 14070

You may feel it’s very hard but when you practice a few times with different numbers it will become easy for you.

Now let’s do some assignments

Find base of:

92 – ___

24 – ___

885 – ___

Find Complement of:

8 – ___

16 – ___

89 – ____

Solve using balancing rule:

26 | 54 – _____

45 | 64 | 76 – _____

67 | 32 | 12 | 56 – ____

2467 × 4 – ____

5673 × 3 – ____

Like this you can make your own questions and solve them with ease.

**Frequently Asked Questions **

Question 1: What is Vedic Maths?

Answer: Vedic Maths is a collection of sutras or techniques which helps you to solve mathematical problems in a fast and easy way.

Question 2: How many techniques are there in Vedic Maths?

Answer: There are total 29 sutras/techniques are there, in which 16 are main sutras and 13 are sub sutras.

Question 3: Is Vedic Maths helpful for kids?

Answer: It is very important that children learn Vedic maths tricks and concepts at an early stage to build a strong foundation.

Question 4: Is vedic maths helpful for college students?

Answer: Knowledge of Vedic maths is important for all age group. These Techniques/Sutras is not only beneficial for school or college students but can also be useful for higher exams like CAT, CET, SAT, Banking Exams, etc.

Question 5: Do Vedic Maths is useful?

Answer: Vedic maths is one of the most refined and efficient mathematical calculation systems possible today. It has certain specific rules and principles to perform various calculations in mathematics.

**Final Words **

From the above article and FAQ you must have understood the value of Vedic Maths. It involves fast mental calculation techniques that, if you practise well, you can reduce your calculation time. We recommend you to try this Vedic Maths once and judge for yourself the effectiveness of these techniques or tricks.