Vedic Multiplication of two numbers close to Hundred

Vedic Method of Multiplication: Base System of multiplication

Application: Multiplication of two numbers close to Hundred

Case 1: Both numbers greater than 100.

Rule: You will get the answer in two parts

First part, to get left hand side of the answer: Add the difference between 100 and either of the numbers to the other number

Second part, to get right hand side of the answer: multiply the difference from 100 of both the numbers

Example

103 x 104 = 10712

The answer is in two parts: 107 and 12,

107 is just 103 + 4 (or 104 + 3), and 12 is just 3 x 4.

Similarly 107 x 106 = 11342

107 + 6 = 113 and 7 x 6 = 42

123 x 103 = 12669

(123 + 3) | (23 x 3) = 126 | 69 =12669 .

 

If the multiplication of the offsets is more than 100 then this method won’t work. For example 123 x 105. Here offsets are 23 and 5.

Multiplication of 23 and 5 is 115 which are more than 100. So this method won’t work.

But it can still work with a little modification. Consider the following examples:

 

Example 1

122 x 123 = 15006

Step 1: 22 x 23 = 506 (as done earlier)

Step 2: 122 + 23 (as done earlier)

Step 3: Add the 5 (digit at 100s place) of 506 to step 2

Answer: (122 + 23 + 5) | (22 x 23) = 150 | 06 = 10506

 

Example 2

123 x 105 (Different representation but same method)

123 + 5 = 128

23 x 5 = 115

128 | 115

= 12915

 

In the next post I'll tell you about vedic multiplication, i.e.,  how to multiply two numbers lesser than the base (in this case 100).

Here's the promised post for you - http://www.quickermaths.com/base-method-of-multiplication/

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