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, higherlevel 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 19111918.
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  SUB SUTRAS  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.  UrdhvaTiryagbyham  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.  Sankalanavyavakal anabhyam  Yavadunam Tavaduni kritya Varga Yojayet  By addition and by subtraction 
8.  Purana Purana Byham  Antyayor dashake  By the completion or noncompletion 
9.  ChalanaKalanabyham  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 twodigit 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 (nonx 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 = (1012)/(89) = 2
y = (1615)/(89) = 1
8. Puranapuranabhyam
– It means ‘By the completion or noncompletion’. 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
51= 4, 94 = 5
14 x 99 = 1386
141=13, 9913=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)(2x7)2
i.e. (x+3)³ = (x+3)(2x7)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 25 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.