Easy steps to multiply numbers using vedic mathematics

Hi Friends, as you all know how complex it is to multiply multiple digits number in targeted time frame. But if you practice the tricks and formulas it becomes a play to solve maths problems. The Maths puzzle book by Sakuntala Devi is the awesome work of these techniques and formulas. It will surely sharpen you mind.

Shakuntala Devi was an Indian writer and mental calculator, popularly known as the “human computer”. Her talent earned her a place in the 1982 edition of The Guinness Book of World Records. 

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Specific and general methods to multiply numbers in vedic mathematics by Tirthaji Maharaj 

Specific Multiplication Methods

Specific Multiplication Methods can be applied when numbers satisfy certain conditions like both numbers closer to 100 or numbers closer to each other or addition of last digits of both numbers is 10, etc. While

General Multiplication Methods

General Multiplication Methods can be applied to any types of numbers.

Multiplication in Vedic Mathematics are classified in the form of Sutras as below

  1. Nikhilam Sutra (Specific Technique)
  2. Anurupyena Sutra (Specific Technique)
  3. Urdhva Tiryak Sutra and Vinculum Process (General Technique)
  4. Ekayunena Purvena (Specific Technique)
  5. Antyaordaske’pi (Specific Technique)

Nikhilam Sutra:

This Sutra is a Specific method of Multiplication in Vedic Mathematics which shows shortcuts to multiply numbers which are closer to power of 10 (10, 100, 1000, etc. )

Using Nikhilam Sutra it is simpler to multiply numbers like 98 & 96, 997 & 988, 103 & 113, 997 & 1007 i.e. the numbers which are closer to power of 10.

This will generate 3 cases:

Numbers closer and less than power of 10. Example: 97 * 96, 994 * 992, etc
Numbers closer and greater than power of 10. Example: 102* 108, 1004 * 1012, etc
Numbers closer and lying on both sides of power of 10. Example: 102* 95, 1004 * 991, etc

Example :

Anurupyena Sutra:

Anurupyena Sutra is a sub-type of Nikhilam Sutra and another trick when numbers are not closer to power of 10 but are closer to themselves. It works on concept of Working Base and then apply Nikhilam Sutra.

Example

Multiplication of Numbers like 63 & 67.

Process Flow:

Working Base(W.B.) concept: As the numbers (63 & 67) are closer to 60, we take working base as 60 (6*10) instead of 100, here factor is 6.

Appling the concept of Nikhilam as discussed previously i.e. 63 is 3 greater than 60 and 67 is 7 greater than 60

Multiply 3 and 7 to get 21 in 2nd compartment. As base is *10, thus we need to have only 1 digit in 2nd compartment and hence need to carry forward 2 to 1st compartment.

As in Nikhilam Sutra, Cross Addition of 63 & 7 or 67 & 3 gives 70.

In Anurupyena Sutra, before adding carry forward directly to 1st compartment we need to multiply by the factor (6) and then add the carry forward.

This Carry Forward (2) is added to 420

Final Answer: 4221

Same multiplication 63 and 67 can be solved by considering Working Base of 70 (10 * 7)

Urdhva Tiryak Sutra:

Urdhva Tiryak Sutra is also a General method of multiplication which provides shortcut to multiply any types of numbers.

It can be applied very easily to multiply 3 digit numbers, multiply 4 digits numbers and even more than 4 digit numbers.

Example Multiplication of 3 digit numbers:

Formula Used:

(ax2+bx+c)(dx2+ex+f) = adx4 + (ae+bd)x3 + (af+be+cd)x2 + (bf+ce)x + cf

Process Flow: (Left –> Right)

  1. Vertical Multiplication of 1st digits of 2 numbers.
  2. Crosswise Multiplication Addition of 1st 2 digits 2 numbers. (i.e. Crosswise Multiplication of 1st 2 digits and adding them.)
  3. Crosswise Multiplication Addition of all 3 digits of both the numbers.
  4. Crosswise Multiplication Addition of last 2 digits 2 numbers.
  5. Vertical Multiplication of last digits 2 numbers.
  6. For all steps, except 1st step, each compartment needs to have ONLY 1 digits. If not then carry forward initial digits to previous compartment

Vinculum Sutra:

Vinculum Sutra is a special method used with Urdhva Tiryak whenever we have bigger digits like 6,7,8 and 9.

This process works on carrying out operations like multiplication with bigger digits is time consuming and little tougher as compared to smaller digits. Hence such digits 6,7,8 and 9 are converted to smaller digits like 4,3,2 and 1 using Vinculum Process.

Ekayunena Purvena Sutra:

Ekayunena Purvena Sutra is applicable whenever multiplier has only 9’s as digits.

Antyaordasake’pi Sutra:

Antyaordasake’pi sutra can be applied when last digits of both numbers totals as 10.

Steps:

  1. Check if addition of last digits of the numbers is 10.
    If yes, multiply them and write in 2nd compartment.
  2. Apply Ekadhikena Purvena for the remaining digits
    i.e. Add 1 to the remaining digits.

    Example:
    In case of 34 x 36,
    Apply Ekadhikena Purvena on 3 so we have 4.
    Now multiply 3 and 4 and write in the 1st compartment.

I have done some practice on the tricks and found it time saving in calculation of multiplication. I have added the puzzle book by Shakuntala Devi which will be useful to you people.