hakusama on Nostr: Trachtenberg starts from the right like regular multiplication, but doubles and ...
Trachtenberg starts from the right like regular multiplication, but doubles and halves instead of memorising the times tables. Carried numbers are maximum 2 so there is very little room for simple errors.
The rule for 12 is "double each number in turn then add its neighbour". The neighbour is the number to the right.
So 12 x 123456 would be:
Double 6 plus 0 = 12. Keep the 2 and take the 1 to the next number.
Double 5 plus 6, plus the 1 from 12 = 17. Keep the 7 and carry the 1.
Double 4 plus 5, plus carried 1 = 14. Keep 4, carry 1.
Double 3 plus 4, plus the carried 1 = 11. Again carry 1.
Double 2 plus 3, plus the carried 1 = 8.
Double 1 plus 2 = 4.
Finally there's always an invisible "0" at the start of each number. So it's double 0 plus 1 = 1.
Answer: 12 x 123,456 = 1,481,472.
It looks complicated the way I've explained it, but I promise it's not!
The rule for 12 is "double each number in turn then add its neighbour". The neighbour is the number to the right.
So 12 x 123456 would be:
Double 6 plus 0 = 12. Keep the 2 and take the 1 to the next number.
Double 5 plus 6, plus the 1 from 12 = 17. Keep the 7 and carry the 1.
Double 4 plus 5, plus carried 1 = 14. Keep 4, carry 1.
Double 3 plus 4, plus the carried 1 = 11. Again carry 1.
Double 2 plus 3, plus the carried 1 = 8.
Double 1 plus 2 = 4.
Finally there's always an invisible "0" at the start of each number. So it's double 0 plus 1 = 1.
Answer: 12 x 123,456 = 1,481,472.
It looks complicated the way I've explained it, but I promise it's not!