Category Archives: Vedic Maths

Vertically and Crosswise – A simple and effective method of multiplication

In my workshops I have seen kids and children struggling with multiplication . Specially if it is two or three digit multiplication their faces will just turn sad in few seconds. And they will shout in unison , ” No Mam not again ”

So I teach them a simple method of multiplication which is not only easy to remember  but saves a lot of time . Once you understand this method , the time taken to do two digit and three digit multiplication reduces by half.

These methods are derived from Atharv Veda and they make calculations really simple.

This method is called Vertically and Crosswise

Two digit multiplication 

We are multiplying here 12 and 34

two digit

Step 1

Multiply the digits at unit place . Here they are 2 and 4 . Since it is 8 you keep the digit at units place . If in a case you get two digits you carry the ten’s digit to the next place value . This step is called vertically

Step 2

Multiply the digits at unit’s place to the  digit at tenth place and add both of them . Keep the unit’s digit and carry the remaining digits at the next place value. . This step is crosswise . When we multiply here in the above case i.e 1 with 4 and 2 with 3 , we got 4 and 6. When we add we got 10 . We kept 0 and carried 1 to the next place value

Step 3

Multiply the digits at the tenth place . Add the digits to the carry over digits. This step is again called vertically . We multiplied 1 with 3 here and added the carry over 1 from step 2.

Hence the answer is 408

Multiplication of three digit number by three digit number

Diagramatic representation of multiplication of 3 digit number by 3 digit

three digit multiplication

                 1   2   3

                 4   5   6


4   3    8    7      8

1   2   2    1      +


5    6    0    8     8

Let us work another problem by placing the carried over digits under the first row and proceed.
i) 3 X 6 = 18 : 8 is kept at the unit’s place and 1 is carried over to the next place value.

ii) (2 X 6) + (5 x 3) = 12 + 15 = 27 ; 7, the carried over digit 2 is placed to the next place value

iii) (1 X 6) + (3 X 4) + (2 X 5) = 6 + 12 + 10 = 28 ; 2, the carried over digit is placed below fourth digit.

iv) (5 X 1) + ( 2 X 4) = 5 + 8 = 13; 1, the carried over digit is placed below fifth digit.

v) ( 1 X 4 ) = 4

vi) Respective digits are added with the carry over digits.  So the answer is 56088

This method can be applied for any two digit or three digit multiplication and it reduces the time by half .

Keep watching this space for some more easy tricks which makes calculation really simple.

Vedic Maths Summer Work shop

We are pleased to announce the new batches for summer workshop – A fast paced workshop focusing on building concepts based on Vedic mathematics techniques to develop speed, accuracy and cognitive skills. The workshop is aligned to help alleviate the fear of numbers by using examples from life and help in identifying patterns in numbers using real life examples.

Workshop takeaways:

  • Increases problem solving speed.
  •  Alleviate the fear of mathematics from children through innovative techniques.
  •  Building skills like intelligent guessing and enhancing the child’s memory power.
  • Highly beneficial for all the competitive exams including NTSE, Math’s Olympiad, GMAT, GRE, CAT etc.

Work Shop Details:

Course Duration: 2 weeks (Only weekdays)
Time: 1.5 hours
Age group: 9 -17 years old.

New Batches starting from 5th May and 19th May @ SJR redwoods Apartment, Harlur Road, off Sarjapura Road, Bengaluru – 560102

For registrations call us @ +91-99860-72003 or email @

Vedic Mathemetics Sutras

Vedic Mathematics is based on sixteen sutras (Mathematical formulas derived rom Veda) which is presented a renowned Hindi Scholar Sri Bharati Krishna Tirthaji Maharaja. Here is the list of sixteen Sutras and thirteen sub sutras that drive the Vedic mathematics concepts. These sutras can be applied in various ways for faster calculations in arithmetic’s, algebra etc.


1) Ekādhikena Pūrvena   – “ By one more than the previous one”Ekādhikena Pūrvena “By” The sūtra means that the prescribed arithmetical operation is either multiplication or division. Both are implied since we may proceed leftward and multiply (and carry-over the excess value to the next leftward column) or we may go rightward and divide (while prefixing the remainder). When dividing by a nine’s family denominator, the digit to the left of the nine (previous) is increased by one to obtain the multiplier.

2) Nikhilam navatascaramam Dasatah –  “All from 9 and the last from 10”

3) Urdhva – tiryagbhyam – “ Vertically and crosswise (multiplications)”

The Ūrdhva Tiryaghyām Sūtra, gives the (Ūrdhva) general formula for multiplication for each place-value.  A vinculum (subtraction-bar) may be used on digits greater than five. The Ūrdhva-Tiryak process of multiplying for each place-value can also be applied to finding prices in aliquot parts as well as finding areas and volumes with dimensions of mixed units of measure. The converse of the Ūrdhva-Tiryak process can be used for division, both in arithmetic and with polynomials,

4) Paravartya Yojayet – “Transpose and adjust”

Parāvartya Yojayet, is applied for arithmetic division and division of polynomials by Vilokanam (mere observation) by column-wise notation. The use of the Ānurūpyena Sūtra to multiply or divide the quotient proportionately to bring it closer to a power of ten, eases the calculations.

5) Sunyam Samya Samuccaye –  “Samuccaya is the same, that Samuccaya is Zero.’ i.e., it should be equated to zero.

6) Anurupye – Sunyamanyat  – “If one is in ratio, the other one is zero”

7) Sankalana – Vyavakalanabhyam  ““By addition and by subtraction.”

Upasūtra Sankalana-Vyavakalanābhyām is used to solve a second special case of simultaneous linear equations where the x-coefficients and the y-coefficients are interchanged, immediately giving two equations with the values for (x+y) and (x-y).

8) Puranapuranabhyam “By the completion or non-completion”[

Purana is well known in the present system. We can see its application in solving the roots for general form of quadratic equation.

9) Calana – Kalanabhyam “Differences and Similarities”

The Gunaka-Samuccaya Sūtra, etc., deal with successive differentiations. Knowing the relation of the factors of a polynomial and successive differentials of that polynomial and with the use of the Ādyam Ādyena Sūtra (on the sum of the coefficients) one can factor polynomials, even ones with repeated factors.

10) Yaavadunam “By the Deficiency”

11) Vyashtisamanstih “Part and Whole”

12) Shesanyankena Charamena – “The Remainders by the Last Digit”

13) Sopaantyadvayamantyam – “The Ultimate and Twice the Penultimate”

14)Ekanyunena Purvena  – “By One Less than the One Before”

15)  Gunita Samuccayah  – “The product of the sum is equal to the sum of the product”

16)  Samuccaya Gunitah “The factors of the sum is equal to the sum of the factors”It is intended for the purpose of verifying the correctness of obtained answers in multiplications, divisions and factorizations.

Vedic Mathematics – an overview

 Vedic mathematics is an ancient Indian system of Matheatics, a unique and amazing system based on simple rules and principles. The methods and techniques are based on the pioneering work of the late Shree Bharati  Krishna Tirthaji, shankracharya of Puri , who established the system by study of ancient Vedic texts coupled with profound insight into natural process of mathematical reasoning. The whole system is based on sixteen sutras (formula or aphorisms) and thirteen sub-sutras or corollaries which form the fundamentals of Vedic Maths. The characteristic of Vedic Maths is that it presents the subject as a unified body of knowledge and reduce the burden and toil which young minds often experience during their initial years.


The current methods of calculation which are taught by schools are conventional and lack imagination. A simple example to illustrate this point is finding the product of 19 and 8. The conventional system will teach us to multiply first 9 and 8 to get 72 and then multiply 10 and 8 to get 80 and when you add both you get 152. On the other hand the Vedic method will say 8 times 20 is 160 and less 8 which is 152. We arrive at the same result but the time taken was relatively less. Many of the children who are brilliant will use the same way and Vedic Maths teach the same approach to calculations in a unified way.

Vedic Maths illustrates that all the numbers start with number one which is also an expression of unity. All the numbers are derived from 1. IF we do not have 1 we cannot have any other number .If students have fear of large numbers, it is a great solace to remember that there are only nine numbers to remember and there is nought or zero which stands for nothing.

The current method of teaching mathematics and coaxing the child to remember tables not only kills their creativity but also makes them  hate mathematics or more particularly arithmetic . Vedic mathematics not only enhances the creativity of the child but also makes mathematics fun and easy to remember. In many of the workshops which I have conducted I find that calculation is a great hindrance and Vedic mathematics makes calculation very simple and almost a child’s play.

Vedic Mathematics has been adopted by many schools in UK and Europe and has been integrated into the main curriculum. But in India, its country of origin, it is still in very nascent stage. Though there are many organizations which are conducting Vedic maths/ Speed maths workshop it will benefit only when it is integrated in the course curriculum for various classes in all the schools. I hope the day comes soon.

Watch out this blog posts to get an insight of some of the principles of Vedic maths on which the sutras are based. Mathematics is really very easy and fun to learn. And I truly believe that maths is like poetry as it enhances the cognitive skills and creativity of children if it is taught in a interesting way. Till then HAPPY LEARNING…