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Why is there no 8 in the first half of the product of 1111111111x1111111111

 Jul 6, 2016
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1 x 1  =  1

11 x 11  =  121

111 x 111  =  12321

1 111 x 1 111  =  1234321

...

11 111 111 x 11 111 111  =123456787654321

111 111 111 x 111 111 111  =  12345678987654321

 

Now, when you multiply  1 111 111 111 111 x 1 111 111 111 111

you get ten 1s in a column that requires a sum of  10  which results in a  0  and a carry of 1

This '1' (placed into the column to the left) results in the next column having its original nine 1's  plus the extra carry of   1 

to alsoe have a sum of  10  resulting in a  0  and a carry of 1.

This carry is placed into the next column (to the left) along with its  eight  1's, giving a sum of 9. 

Thus there is no  '8'  on the left-hand side.

 

To see why, try it!

It's not difficult; just write neatly ...

 Jul 6, 2016

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