Basics of Multiplication

Nikhilam Sutra

This technique is used to multiply numbers closer to the power of 10. We can divide the result into two compartments: the first compartment and the second compartment. The steps are as follows: 

• First, we subtract each number and the nearest power of 10. The results found for each number are known as excesses or deficits. 
• The excesses or deficits are multiplied together and are appended to the second compartment. 
• The deficit or excess multiplication result should equal the number of zeroes in the chosen base.
•  Suppose it is more than the number of zeroes forward the leftmost digit as carry to the first compartment. If it is less than the number of zeroes, append zeroes to the left side of the second compartment.
• Now for the first compartment do cross subtraction of numbers and the excesses or deficits.
• Finally, we get the result

Let us illustrate the above steps with the help of the example

Multiply 84 and 88
The nearest power of 10 to both numbers is 2. That is 100 is nearest to both numbers. 
Let us perform subtraction 
84-100 = -16 and 88-100 = -12
Then perform the multiplication of the above results
-16 × -12 = 192
Since number of digits is greater than the number of zeroes we will forward 1 
Therefore the value of our second compartment is 92
For the first compartment
Perform cross addition that is
84-12 = 72 or 88-16=72
The result of the first compartment is 72 + 1 =73
Here 1 is the carry that was found in the second compartment
The value is 84×88 =7392

Gyarasguna Sutra

The term Gyarasguna comprises three meanings Gyara means 11, guna means multiplication and sutra mean formula. Here we learn the trick on how to perform multiplication between 11 and any number. The steps are as follows:

• First, write the non-11 numbers twice.
• Add 0 to any one of the above numbers
• Perform addition

Let us illustrate the above steps with the help of the example

Multiply 99 and 11
Since 99 does not contain 11 we write 99 twice
99   99
Then add zero to intial number
990  99
Finally perform addition
990+99=1089
Therefore 99×11=1089

Ekanunena Purneva Sutra

This multiplication rule is applicable when the multiplier is either 9 or 99,999……. The steps are as follows

• Subtract 1 from the multiplicand 
• Perform subtraction between the result generated in step 1 and the array of 9s
• Combine the result

Let us illustrate the above steps with the help of the example

Multiply 999 and 81
81 - 1 = 80
999-80=919
999×81=80919 

Antyaordasake Pi

In this, we perform the multiplication of two numbers. We have to first check if the sum of the two last digits is equal to 10 and remaining previous digits or digits at places except at one place should be the same. The steps are as follows

• Add 1 to the first digit of the second number
• Replace the first digit of the second number with the result generated in Step 1
• Perform multiplication between the first digits of the two numbers
•  Perform multiplication between the second digits of the two numbers
• Combine the result 

Let us illustrate the above steps with the help of the example

Multiply 79 and 71
The sum of last digits is 10 and previous digits are same (Conditions fulfilled)
7+1=8
The second number now becomes 81
7×8=56
9×1=09
The result is 5609

Navamguna Sutra 

Navam means 9. Here we perform multiplication between 9 and any other number. This technique is useful when the multiplier is either 9 or 99 or 999 and so on. The steps are as follows:

• First, count the digits of the multiplier. Let it be denoted by n
• Convert the multiplier to the form 10ⁿ – 1
• Now perform the normal multiplication

Let us illustrate the above steps with the help of the example

Multiply 57×99
Number of digits in the multiplier is 2
Therefore 99 = (10)2 - 1
Now it becomes 57×(100-1)= 5700 -57 = 5643
The result is 5643

Vedic mathematics is one of the most popular systems of mathematics as it offers tricks that allow us to solve operations like multiplication, addition, subtraction, etc in less than a few seconds. There are many shortcut tricks of Vedic Mathematics that can help to solve complex problems and we do not have to remember the conventional tables. Vedic Maths was founded between AD 1911 and 1918 by Jagadguru Shri Bharathi Krishna Tirthaji. There are 16 formulas and 13 sub-formulas. The formulas are known as sutras. There are 5 basic rules of Vedic Maths: Nikhilam Sutra, Gyarasguna Sutra, Ekanunena Purneva Sutra, Antyaordasake Pi, and Navamguna Sutra. These rules deal with the multiplication operation.