Vedic Mathematics – Complex multiplications

Overview

The page explains how to multiply two numbers using one of the techniques from Vedic Maths. This technique is called as “Nikhilum Sutra” which means “all from nine and last from ten”.

Terminology used in explaining this method

1. Nearest working base – Working base is going to be nearest of 10, 100, 1000 and so on based on the numbers being multiplied.  For example – if 98 is multiplied with 92 (98*92) then nearest working base for both these numbers is 100.

2. Complement of a number – Difference between the number being multiplied and it’s nearest working base. If number being multiplied is less than nearest working base, then complement is a negative number otherwise it’s positive. For example – if we are calculating 96*102, then complement of 96 is -04 whereas complement of 102 is +02.

Formula 1 – Both the numbers being multiplied as less than the nearest working base

Example 1 – Multiply 7 and 4

Steps –

a) Write down the complement of each number in front of them. In our example, nearest working base is 10 so complement of 7 and 4 are -3 and -6 respectively.

7            -3

4            -6

b) Take the product of complements nad put them below the line. In our case, it comes out to be (-3) * (-6) = 18

7            -3

4            -6

18

c) Take cross sum of numbers which would always be same in this formula. In our example, it’s 7 + (-6) = 1 or 4 + (-3) = 1. Write this number on left hand side below the line

7            -3

4            -6

1     /     18

d) This is the most important step of this whole formula. If two numbers being multiplied are single digit numbers, right hand side number in the result below the line would also be a single digit (highlighted above). Same would be the case when two double digit numbers are multiplied, right hand side number below the line would also be two digit.

Going by this rule, highlighted number 18 above should result into single digit hence 1 is carry forwarded and added to the left side.

7            -3

4            -6

2     /       8

e) Hence 7 *4 = 28.

Example 2 – Multiply 93 and 96

Steps –

a) Write down the complement of each number in front of them. In our example, nearest working base is 100 so complement of 93 and 96 are -07 and -04 respectively.

93        -07

96        -04

b) Take the product of the complements and put them below the line. In our case, it comes out to be (-07) * (-04) = 28.

93        -07

96        -04

28

c) Take cross sum of numbers which would always be same in this formula. In our example, it’s 93 + (-04) = 89 or 96 + (-07) = 89. Write this number on left hand side below the line.

93        -07

96        -04

89    /    28

d) Since right side number (28) is already a two digit number, there is no carry forward required in this scenario. Hence 93 * 96 = 8928

Example 3 – Multiply 992 and 995

Steps –

a) Write down the complement of each number in front of them. In our example, nearest working base is 1000 so complement of 992 and 995 are -008 and -005 respectively.

992        -008

995        -005

b) Take the product of the complements and put them below the line. In our case, it comes out to be (-07) * (-04) = 28.

992        -008

995        -005

040

c) Take cross sum of numbers which would always be same in this formula. In our example, it’s 992 + (-005) = 987 or 995 + (-008) = 987. Write this number on left hand side below the line.

992        -008

995        -005

987    /    040

d) Since right side number (040) is already a three digit number, there is no carry forward required in this scenario. Hence 992 * 995 = 987040

Hope this formula is easy enough to practise and use in actual life. You can post your comments below in case of any questions or comments. You can also solve different other examples like – 92*91, 992*998, 93*99 etc and post the answers to these multiplications in comments below.

Have fun solving some more examples using the above formula! More formulas are coming soon.