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December 01, 2013

The how of the two digit squaring method (2)

With the distributive property 'demonstrated' I continued splitting areas to get comfortable with the idea.

If we look at the square of a two digit number say 13. As shown below its 13x13. The 13 at the top and the left side are meant to act as rulers and are not to be added to the count.

The distributive property can be seen as a vertical split in this area
This can be written as
13x13 = 13x(10+3)
          = 13x10 + 13x3

We can now split the figure horizontally as well by splitting 13 as 10+3 again.
This is equivalent to 
13x10 + 13x3 = (10+3)x10 + (10+3)x3
                    = 10x10 + 3x10 + 10x3 + 3x3

All that remained is connecting the method to the madness :).

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