Vedic Maths Tricks l Simple Tricks for Multiplication

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. 

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

Some other Multiplication Tricks

Apart from these basic sutras, there are some tricks present in Vedic Maths that helps to perform this operation at ease. Some of them are as follows:

Performing Square of a Number whose Unit Digit is 5

This technique is applicable if the unit digit is 5. The steps are as follows

• First, perform units digits multiplication
• Then perform the multiplication between the digit in the tens place that can be denoted as the previous digit and the previous digit + 1
• Combine the results

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

Perform the square of 65
5 × 5=25
6 × (6+1)=42
The result is 4225

Performing Multiplication by 5

This technique is applicable if the multiplier is 5. The steps are as follows

• Express 5 as 10/2
• Perform  multiplication between the multiplicand and 10
• Divide the result by 2

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

Perform multiplication between 209 and 5
5 = 10⁄2
209 × (10⁄2)= 2090⁄2= 1045

Performing Multiplication by 25

This technique is applicable if the multiplier is 25. The steps are as follows

• Express 25 as 100/4
• Perform  multiplication between the multiplicand and 100
• Divide the result by 4

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

Perform multiplication between 209 and 25
25 = 100⁄4
209 × (100⁄4)= 20900⁄4= 5225

Practice Questions

Here are some examples which will help you to find the approach to solve the question using different methods.

Que 1. Multiply 569 and 25

Solution:

= 569×25

= 569×(100⁄4)

= 14225

Que 2. Multiply 465 and 5 

Solution:

= 465×5 

= 465×(10⁄2)

= (4650⁄2)

= 2325

Que 3. Find the square of 95

Solution:

First, perform units digits multiplication

5×5= 25

Then perform the multiplication between the previous digit and the previous digit + 1

9×(9+1)=90

After combining the number result is 9025

Que 4. Use Gyarasguna Sutra to perform multiplication of 109 and 11.

Solution:

First, write the non-11 numbers twice that is write 109 two times

109  109

Add 0 to the initial number

1090  109

Perform addition

1090+109=1199

The result is 1199

Que 5. Using Navamguna Sutra  to perform 466 × 999

Solution:

The digit of multiplier is 3

999 can be denoted as (10³ – 1) Now 466 × 999 can be written as 

= 466 × (1000 – 1)

= 466000 – 466

= 465534

Que 6. Perform multiplication of 63 and 67 using Antyaordasake Pi

Solution:

The sum of the last digits is 10 and the previous digits are the same (Conditions fulfilled)

6+1=7

The second number now becomes 77

= 6×7=42

= 7×3=21

The result is 4221