MULTIPLY Easily and Fast - Solve (997 X 998) in seconds!

Hi friends. Have you wished to solve greater numbers like a person remembers 2, 5, 7, etc. tables by heart. Like you know what 9 X 7 is ? , with the same pace friends can you tell what 997 X 998 is = ? 

Now, to solve it one method is to write a number below the other and then multiply each digit and so on (the 'conventional multiplication method' ). Another method which is fast and super efficient is the Vedic method, which will solve this problem in seconds ! (Note: And also without a calculator :) ). So let's see it.

As every giant aim requires a simple and humble starting so first lets see how 9 * 7 is solved using this technique to make you understand the concept for larger problems much better once the basics are clear!

The vedic technique has '4' steps for solving multiplication problems like 9 X 7, 99 X 98, etc. These are :-

•  Select a 'BASE'.

•  Calculate the 'DEVIATION'.

•  Calculate the 'SUM'.

•  Calculate the 'PRODUCT'.

It's simple friends and upon performing it practically you will see how much exciting as well as easy it is to learn. So friends, grab up your pens, pencil and notebook and let's begin!

 EXAMPLE 1   :   9 X 7 = ? 

 STEP 1  - SELECT A BASE

'Base' means a number that will form the basis of our calculation further. In math base is usually referred to the number of different digits that a number system utilizes. For example, most common base used is 10 as the most common number system is decimal number system. It has 0 - 9, i.e. total '10', different digits to form numbers. So its base is 10. 

But 'base' in vedic math is a bit different than the usual base. Take a look at the following table to understand it :-

Usually multiples of 10 are taken as base (it makes calculations easier) but any number which is simple and closer to both the numbers of the problem is eligible for becoming the base in vedic math multiplication. 

So  base for the numbers 9 and 7 will be 10  as it is a multiple of 10 as well as closer to both 9 and 7.

 STEP 2  - CALCULATE THE DEVIATION

'Deviation' in vedic math is the 'value' by which the number in our problem is either greater than or less than the base. This step consists of calculating the value of deviation for each number. The general formula for calculating deviation is :  

Number - Base = DEVIATION

Deviation can be either positive or negative. For understanding more about deviation, look at the following table :-

Hence, the value of  deviation for  9 is '-1' and for 7 it is '-3'. 

Write the calculated value of deviation for both the numbers in the following manner :-

	NUMBER	DEVIATION
	9	-1
X	7	-3
	______________ ? ______________

So, now let's move to next step.

 STEP 3  - CALCULATE THE SUM

** This step requires you to memorize the working by heart as if understood with full concentration you can definitely perform calculations for larger numbers with ease.**

In step 3, add the number with the deviation value crosswise (i.e. diagonally).
Write the sum of both in the following manner (as a part of the final answer) :-

Here is something special : Adding any two numbers crosswise (diagonally) will give the same result. Either add 9 and -3 or add 7 and -1, the result will be same! (Take care of the signs its -3, i.e., 'negative 3' , and -1.)

9 + (-3) = 9 - 3 = 6

or

7 + (-1) = 7 - 1 = 6

So this sum becomes the first part of the final result. Now let's move quickly to the final step of our problem.

 STEP 4  - CALCULATE THE PRODUCT

The second part of our result will be determined in this step. Let's see this how? :-

Just multiply the deviations with each other. Simple isn't it? As the name suggests, this step is all about calculating the product of the deviations like this :-

	DEVIATION
	-1
X	-3
Product	____________ 3 ____________
	Always take care of the signs. The product here will be +ve as: (-1) X (-3) = +3

Now use value of the product in our result in the following way :-

	NUMBER
	9
X	7
Answer	_______________ 63 _______________
	Just write 3 (value calculated as ‘product’) alongside of 6 to produce the final result.

** Always remember ** 

The number of digits in the product = The number of zeroes in the base       

As the product calculated is 3 so the number of digits is 1 = 1 as the base is 10 i.e. one zero

-> Suppose the product value comes out to be 3. 

-> Now, if the base is 100 then the product value to be used in result will be '03' otherwise it will be just '3', if base is 10. 

-> This will make the final result always correct. For example : 96 X 98 = 9408 and not  just 948. 

-> It is more useful when the numbers become large. For a more clear understanding about it, just see the next example where this concept is applied.)

                                               

So what we knew from the beginning, our answer is also the same i.e. 9 X 7 = 63. Hence, this method is worth of using. Now let's quickly apply the same method on a larger number to see it's another specialty i.e. speed or time - saving apart from easiness in calculating result.

 EXAMPLE 2  :  97 X 98 = ? 

Now that you know the steps (Base, Deviation, Sum, Product) lets quickly apply each to find the answer for this example.

 STEP 1  - Finding the 'base' 

Here as both the numbers are close to 100 and also 100 is a multiple of 10 so our base for this example is 100.

 STEP 2  - Finding the 'deviation'

The deviation is calculated as :

Number - Base = Deviation

Therefore, 

deviation for number 97 = 97 - 100 = -3 , and

deviation for number 98 = 98 - 100 = -2

So writing the deviations and numbers in the following manner :- 

	NUMBER	DEVIATION
	98	-2
X	97	-3
	______________ ­­­? ­­______________

 STEP 3  - Calculating the 'sum'

The sum can be calculated as :-

Add the value of deviation with the number in a diagonal manner (cross-wise) i.e.,

So this value of the sum becomes the first part of the result. Next, let's calculate the second part of the result.

 STEP 4  - Calculating the 'product'

The product of can be calculated as :-

Multiply the deviation values calculated with each other to determine the product.

	DEVIATION
	-3
X	-2
Product	____________ 6 ____________
	Always take care of the signs. The product here will be +ve as: (-3) X (-2) = +6

After calculating the product just check the following,whether :-

Number of digits in the product = Number of zeroes in the base

As the base here is 100, therefore, number of zeroes = 2. But number of digits in the product (which is '6') is 1 only so to make the equality correct just do this :

Instead of using the value of product as 6, use the value in the final result as 06 to make number of zeroes in the base (i.e. 2) and the number of digits in the product (which is now '06') equal.

So now the answer calculated will be :-

	NUMBER
	97
X	98
Answer	_______________ 9506 _______________
	Just write 06 (value calculated as ‘product’) alongside of 95 to produce the final result.

** Always check and correct the equality whenever the number of digits in the number is not equal to number of zeroes in the base. **

So this is how answer is calculated in some time. Hence, friends practice this technique more, even with larger numbers like 995 X 994, 991 X 993, 9991 X 9998, etc. , and you will see the difference!

As the time taken is less than the first example so believe it friends, with practice it will be a matter of few seconds that the answer is calculated!

Do follow for more interesting posts about vedic mathematics. If you require any topic to be covered just comment.

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