Method 10

Multiplication of two digit numbers whose first digit are same and sum of last digits is 10 .

This method is based on the sutra " Antyayor Dasakepi " which means 'sum of last digit is 10 ' .

Explaining the method with the help of an example .

Example 1 : - Find the product of 47 * 43.

Answer : -

Just write the product of two end digits to the write and product of first digit and the digit next to it to the left .
Like This

4 * (4 + 1) / ( 7 * 3 )
4 * 5 / 21
20 / 21

Hence the answer to the question is

47 * 43 = 2021



Example 2 : -Find the product of 84 * 86 .

Answer : -

8 * ( 8 + 1 ) / ( 4 * 6 )
72 / 24

84 * 86 = 7224


Example 3 : - Find the product of 72 * 78 .

Answer : -
7 * ( 7+ 1 ) / ( 2 * 8 )
56 / 16

72 * 78 = 5616



It is further interesting to note that the same rule works when the sum of the last 2, last 3, last 4 - - - digits added respectively equal to 100, 1000, 10000 -- - - . The simple point to remember is to multiply each product by 10, 100, 1000, - - as the case may be . Your can observe that this is more convenient while working with the product of 3 digit numbers.

Example 4 : - Find the product of 292 * 208 .

Answer : -

Since 92 + 8 = 100 .
Hence the sutra is applicable .

2 * (2 + 1 ) * 10 / 92 * 8
60 / 736
(Retain the three digits as sum is 100)

292 * 208 = 60736