# Vedic Math Techniques in Multiplication

There are several techniques of multiplication. We will discuss them one by one.

# Method 1: Base Method

In this method, one number is used as a base; for example, 10, 50, 100 etc. The number that is closer to both the numbers should be taken as the base.Example-1

105 Ã— 107

Solution

In this case, both the numbers are close to 100, so 100 is taken as the base. We will now find the deficit/surplus from the base.

Base = 100, Surplus = 5 and 7

Example-2

108 Ã— 104

Solution

Example-3

111 Ã— 112

Solution

Here, it is 11 Ã— 12 = 132. But it can have only two digits. Thus, 1 will be carried over to the left part and the right part will be only 32. Left part will be either 111 + 12 + 1 (1 for the carry over) or (112 + 11 + 1), i.e., 124. So, the result will be 12432.
For 102 Ã— 104, the answer will be 10608. Please note that the right part will be 08 and not simply 8.

Example-4

97 Ã— 95

Solution

Base=100, Deficit = 97 âˆ’ 100 = âˆ’3 and 95â€“100 =âˆ’5

Example-5

97 Ã— 102

Solution

97 Ã— 102

Base = 100, Deficit = 97 â€“ 100 = âˆ’3,

Surplus = 102 â€“ 100 = 2
The right part will now be (âˆ’3) Ã— 2, i.e., âˆ’06. To take care of the negative, we will borrow 1 from the left part, which is equivalent to borrowing 100 (because we are borrowing from the hundred digits of the left part). Thus, this part will be 100 â€“ 06 = 94.
So, the answer = 98 94

Base = 100, Deficit = 97 â€“ 100 = âˆ’3,

Surplus = 102 â€“ 100 = 2

Example-6

62 Ã— 63

Solution

We will assume here the base as 50 owing to the fact that the numbers are close to 50.
Base = 50, Surplus = 62 â€“ 50 = 12,

Surplus = 63 â€“ 50 = 13
The left hand side = 156 and the right hand side = 75. Since the base is assumed to be equal to 50, so the value of the right hand side = 75 Ã— 50 = 3750. Besides, only two digits can be there on the right hand side, so 1(100) is transfered to the left hand side leaving 56 only on the left hand side.
So, the value on the right hand side = 3750 + 100 = 3850
Value on the left hand side = 56
Net value = 3850 + 56 = 3906
Let us do the same multiplication by assuming 60 as the base.

Base = 60, Surplus = 62 â€“ 60 = 2, Surplus = 63 â€“ 60 = 3
Since the base is assumed to be equal to 60, the value of the right hand side = 65 Ã— 60 = 130 Ã— 30 = 3900
So, net value = 3906

Surplus = 63 â€“ 50 = 13

Base = 60, Surplus = 62 â€“ 60 = 2, Surplus = 63 â€“ 60 = 3

# Method 2: Place Value Method

In this method of multiplication, every digit is assigned a place value and the multiplication is done by equating the place values of multiplicands with the place value of the product.

Conventionally, the unit digit is assigned a place value 0, the tens place digit is assigned a place value 1, the hundreds place digit is assigned a place value 2, the thousands place digits is assigned a place value 3 and so on.

This multiplication is a two-step process.
For example, using the place values of the multiplicands, i.e., using 0, 1, 2 and 3 of the number 1254 and the same place values 0, 1, 2 and 3 of the another multiplicand 3321, we can get 0 place value in the product in just one way, i.e., adding 0 and 0.

This multiplication is a two-step process.

**Add the place values of the digits of the numbers given (1254 Ã— 3321) to obtain the place value of the digits of the product.***Step 1*Place value 1 in the product can be obtained in two ways.

Place value 2 can be obtained in three ways.

Place value 3 can be obtained in four ways.

Place value 4 can be obtained in three ways.

Place value 5 can be obtained in two ways.

Place value 6 can be obtained in one way.

And this is the maximum place value that can be obtained.

**Multiply the corresponding numbers one by one.***Step 2*In this manner, we can find the product = 4164534

This method is most useful in case of the multiplications of 2 digits Ã— 2 digits or 2 digits Ã— 3 digits or 3 digits Ã— 3 digits multiplication.

*ab*Ã—

*cd*

Similarly, we can have a proper mechanism of multiplication of 2 digits Ã— 3 digits or 3 digits Ã— 3 digits also using the place value method.

# Method 3: Units Digit Method

This method of multiplication uses the sum of the units digit, provided all the other digits on the left hand side of the unit digit are the same.Example-7

75 Ã— 75

Solution

The sum of the units digit = 10, so we add 1.0 in one of the digits on the left hand side.

Example-8

62 Ã— 63

Solution

The sum of the units digit = 5, so we add 0.5 in one of the digits on the left hand side.