Saturday, January 5, 2008

Multiplication made easy:multiply with 7

Multiplication by 7: Going from right to left, we use this rule: Double each number and add half the neighbor (digit to the right, dropping any fraction); add 5 if the number (not the neighbor) is odd. And of course, we have to deal with carries:
3852 x 7 = 26964
Starting at the right (2), we double the first number (it has no neighbor) and write down the right-most digit of that (4) and we have no carry. Then we double the next number (2x5=10), add five (+5=15), and add half the neighbor (+1=16), and write down the right digit (6) of that and carry the 1. Then we double the next number (2x8=16), and add half the neighbor (+2=1, and add the carry (+1=19). Then we double the next number (2x3=6), add five (+5=11), add half the neighbor (+4=15), and add the carry (+1=16). Now we double a zero off to the left of our 3852
(Trachtenberg wrote the zero out there: 03852) and add
half the neighbor (0+1=1), and add the carry (+1=2).
And we have our answer.
Notice that the carries are smaller than they were in
normal multiplication by 7. The above rule is not
simple, but once mastered, it is easy to use. It
should be about as fast as multiplying normally (which
requires memorizing the multiplication table).
Multiplication by other small numbers (3 through 12)
uses similar rules.

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