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Vedic Mathematics is a collection of Formulae/Techniques called Sutras which help us solve arithmetic problems. The techniques are said to have been taken from multiple Sanskrit texts. The Sutras in Vedic Mathematics were put together by Indian Mathematician Shri Bharati Krishna Tirthaji around the early 20th century.

Multiplication Tricks! Get quicker at calculations

In this section, we will see a few multiplication tricks listed in the Sutras.
Multiplication of a 2-digit number from 11 to 20

Step 1: Add the larger number to the unit digit of the smaller number

Step 2: Multiply the answer obtained from step 1 by 10

Step 3: Multiply the unit digits of both the numbers

Step 4: Add the answers from Step 2 and Step 3

Let us see an example.

Multiplication of numbers closer to the power of 10
(Nikhilam)

This can be further divided into two categories.

Numbers lesser/greater and closer to the power of 10 (both numbers on the same side to the power of 10)
Numbers closer and lying on both sides to the power of 10

Numbers lesser/greater and closer to the power of 10 (on the same side)

Step 1: Find the difference between the numbers from the closest power of 10 and multiply them.

Step 2: Add one of the two given numbers to the difference of the other number from the closest power of 10 (Subtract the closest power of 10 from the number)

Step 3: Final answer is obtained by joining the answer from step 2 and step 1

Example

Multiply 93 × 96

Numbers closer and lying on both sides to the power of 10

Step 1: Find the difference between the numbers from the closest power of 10 and multiply them.

Step 2: Add one of the two given numbers to the difference of the other number from the closest power of 10

Step 3: Final answer is obtained by joining the answer from step 2 and step 1 using the Vinculum method
Vinculum numbers are the basis for Vedic Mathematics.

What is Vinculum?

Vinculum Method

We know that any number can be written in its expanded form based on the digits’ place values.

For example,

2456 can be written as 2000 + 400 + 50 + 6. This is one method of expansion.

Can we write 2456 in a different manner?

Yes. For instance, 2456 can also be written as 2500 – 44

In this case, it is represented as 25¯¯¯¯¯¯44

in the Vinculum method. They are called Bar numbers. A bar is seen on top of the negative part of the numbers.

This number 25¯¯¯¯¯¯44

is expanded as: 2000 + 500 - 40 – 4 = 2456

Let us try to solve the multiplication of 2 numbers lying on either side to the power of 10.

Multiply 97 × 104

Multiplication of numbers when one of the numbers is entirely made of 9
(Ekayunena Purvena)

The method is employed when one of the numbers consists of all 9s.
There are subcategories in this method.

When the number of digits in both the multiplier (number with 9s) and the multiplicand is the same

Step 1: The first part of the answer is one less than the multiplicand

Step 2: The second part of the answer is the complement of the multiplicand

Let us see an example.

Multiply 22 × 99

Square of numbers ending with 5
(Ekadhikena Purvena)

Step 1: First part of the answer is the product of the digits in the number (excluding 5) and its next number.

Step 2: The second part of the number is always 25

Example

Square of 75

Multiplication of numbers close to each other (but not close to a power of 10)
(Anurupyena)

When two numbers that are close to each other are multiplied, the following technique can be employed.

Step 1: Consider the base as the nearest power of 10. For example, if the number is close to 80, we should take the base as 80 (8 ×10). Here the factor is 8. If the number is close to 50, we should take the base as 50 (5 ×10 or 100 ÷ 2). Here the factor can be 5 or 2.

Step 2: Apply the same rules as those of Nikhilam

Step 3: Multiply or divide by the factor obtained in step 1

An example is shown here.

Multiply 84 × 85

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