basics of vedic mathematics - multiplication (1 of 2)

Basics of Vedic Mathematics

BASICS OF VEDIC MATHEMATICSBased on ‘Vedic Mathematics’ by Jagadguru Swami Sri Bharati Krishna Tirthaji Maharaja

Module Developed by Prakasam Akondy

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MULTIPLICATIONPart 1 of 2

30 Minutes

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Basic Example

Principles of Vedic Mathematics help in simplifying multiplication, especially when it involves large numbers. Let us first look at how we can calculate the product of two, two-digit numbers.

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Consider the product of the two numbers, 91 and 92.


The first step is to identify the closest base for each of the given numbers.

For the purpose of this module, the base is a power of 10 such as 10, 100, 1000 etc.

The closest base is that particular base in which the power is equal to the number of digits in the given number.

Basic Example

For example, the closest base to 91^ is 100. Similarly, the closest base to 92^ is also 100.

^ (For the purpose of this module, we assume both numbers have the same base.)

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Basic Example

Now, we will use a format derived using Vedic Mathematics principles, to simplify the calculation of 91 * 92.

Just follow my guidelines on the following slides to understand the use of this format.


91 -9

92 -8

Basic Example

Closest base to 91 and 92 = 100

Numbers to be multiplied

91 – 100 (closest base)

92 – 100 (closest base)

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91 -9

92 -8

91 + 92 - 100 -9 * -8

83 72

Basic Example

Now, perform the calculations indicated below.

Numbers to be multiplied

91 - 100

92 - 100

Closest Base

ContinueClick anywhere


Basic Example

The product of 91 and 92 is given by the four-digit number resulting from joining the two results!

91 -9

92 -8

91 + 92 - 100 -9 * -8

83 72

91 92 =837

2*

91

83

92

72

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Simple isn’t it?


Any guesses?

Now that you have seen an example, can you guess if this method will work for calculating the product, 107 * 113.

A. Yes, this method will work because we can use the base 100.

B. No, this method will not work because both numbers are greater than the base 100.

Click an option.


Any guesses?

The product, 107 * 113 can indeed be calculated using the same method. Here is how:

107 +7

113 +13

107 + 113 - 100 7 * 13

120 91Calculation result 2Calculation result

1

107

113 = 12091*

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Example with Carry Forward

I hope you have now got an idea about how Vedic Mathematics can simplify calculations. Let me now show a slightly more complex calculation.

Consider the product, 88 * 91.



Since 100 is the nearest base, using the format we get:

88 -12

91 -9

88 + 91 - 100 -12 * -9

79 108 Calculation result 2Calculation result 1

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In the final step, if we were to use the rationale as before, we would (mistakenly) conclude that 88 * 91 = 79108


If the number of digits in the result on the right exceeds the number of zeroes in the selected base, then the left-most digit gets carried over.

88 -12

91 -9

88 + 91 - 100 -12 * -9

7980


081

Therefore, the product 88 * 91 = 8008

Click anywhere. Continue

Two zeroes

Three digits


Quiz

Which of the following values represents the product, 89 * 97 ? Calculate the product using the principles of Vedic Mathematics.

A. 8633

B. 8533

C. 8643

D. 9233

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Quiz

The product, 89 * 97 = 8633. It can be calculated as follows:

89 -11

97 -3

89 + 97 - 100 -11 * -3

86 33Calculation result 2Calculation result

1

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Principle

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Now that you have seen a few examples, let us understand the generic principle behind this calculation technique.


Principle

For the purpose of this module, the base is a power of 10 such as 10, 100, 1000 etc. Let x be the base. Let two numbers be written as:

A= x + a and B = x + b. To find A * B, we write:

A * B = (x + a) * (x + b) = x (x + a + b) + ab

Þ x[x + (A-x) + (B-x)] + ab

Þ x[A + B – x] + ab

The format used is thus explained.

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A a

B b

A + B - x a * b


Summary

107 +7

113 +13

107 + 113 - 100 7 * 13

120 91

107

113 = 12091*

1. Sum the numbers to be multiplied

2. Subtract the closest base from the sum

4. Calculate the difference between each number and the closest

base.

3. This forms result 1

5. Multiply the two numbers.

6. This forms result 2

7. Combine results 1 and 2.


Summary

88 -12

91 -9

88 + 91 - 100 -12 * -9

79 108

80 08If the number of digits in this result is greater than the power of the base, the left-most digit gets carried over.

88 91 = 8008*


What Next…

• What happens if the differences from the base are of opposite signs?

• What if the closest base is different for both numbers?

• Will this work for larger numbers?

…and so on.

More on such variations in the next module. See you soon!

I am sure after you have mastered this particular technique, you will have several questions.


Thank You

Prakasam Akondy Linkedin

http://www.linkedin.com/in/avprakasam

basics of vedic mathematics - multiplication (1 of 2)

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