Two digit multiplication

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Lets look at two digit multiplication in generic way

Ex : 23 x 45

Here two numbers are there
first number :  23
first digit  : 3 second digit : 2

second number : 45
first digit  : 5 second digit :4

Result :

first digit = first digit x first digit = 3 x 5 = 15
second digit = first digit x second digit  + second digit x first digit
                    = 3 x 4 + 2 x 5 = 12 + 10 = 22
third digit = second digit x second digit = 2 x 4 = 8

wherever two digits are there in result, carry one digit to next place.

first digit in result = 15 = 5 and 1 carry forward to next place
second digit in result = 22 + 1 ( carry forward )
                                 = 23 = 3 and 2 carry forward to next place
third digit in result = 8 + 2 ( carry forward )
                              = 10 = 0 and 1 carry forward to next place

So the result is 1035


result = second digit x second digit / first digit x second digit + second digit x first digit / first digit x first digit


In simple terms

ab x  cd = ac / ad + bc / db

b and d are first digits of numbers ab and cd
a and c are second digits of numbers ab and cd