Both numbers near but above 100

Suppose we want to multiply two numbers X and Y which are near and above 100. 

Then,

XxY  =  X+D2|D1xD2    or    Y+D1|D1xD2

Where,   D1 = X – 100 and D2 = Y – 100

 

Example:

 Calculate 103 x104.

Solution:

Here X = 103 and Y = 104 And  D1 = 103 – 100 = 3 and D2 = 104 – 100 = 4
X + D2|D1xD2
= 103 + 4|3x4
= 107|12
= 10712

 Note: D1xD2 should always be a 2 digit number. if it is single digit then add ’0′ before that digit

 

Example:

Calculate 102 x 103

Solution:

Here D1 = 102 – 100 = 2 and D2 = 103 – 100 = 3
X + D2|D1xD2
=102 + 3|2x3

(here 2x3 is single digit so we added 0 before it)

=105|06

=10506

Note: D1xD2 should always be a 2 digit number. if it is more than 2 digit then carry forward extra digits to the left part of the solution.  

 

Example:

Find 110 x 111
Solution:

D1 = 110 – 100 = 10 and D2 = 111 – 100 = 11
X + D2 + (carry forward)|D1xD2
=110+ 11 + (carry forward)|10x11

=110 + 11 + 1|10

(here 10x11 is more than 2 digit so we carry forward extra digits to the left part)
=122|10
=12210