### Trachtenberg Multiplication

*1. always place one zero in front of the first multiplier for each digit of the second multiplier. *

*2. apply the rule acording to the second multiplier, working through the digits of the first multiplier from right to left *

*The rule will call for doubling or taking half. Taking half of even numbers presents no problem. Uneven numbers ("odd" numbers) are divided as: half of 1 is 0, half of 3 is 1, half of 5 is 2, half of 7 is 3, half of 9 is 4. For odd numbers the rule will sometimes call for a special procedure. *

Multiply by | Rule |

11 | Add the neighbor |

12 | Double, add the neighbor |

6 | Add half the neighbor plus 5 if number is odd |

7 | Double, add half the neighbor, add 5 if number is odd |

5 | Take half of the neighbor, add 5 if the number is odd |

9 | 1. Last digit: subtract from 10 2. Middle digits: subtract from 9 and add the neighbor 3. First digit: (the leading zero) subtract 1 from the neighbor. |

8 | 1. Last digit: subtract from 10 and double 2. Middle digits: subtract from 9 and double, add the neighbor 3. First digit: (the leading zero) subtract 2 from the neighbor. |

4 | 1. Last digit: subtract from 10, add 5 if odd 2. Middle digits: subtract from 9, add half neighbor, +5 if odd 3. First digit: (the leading zero): half the neighbor less 1. |

3 | 1. Last digit: subtract from 10, double, +5 if odd 2. Middle digits: subtract from 9, double, add half neighbor, +5 if odd. 3. First digit: (the leading zero) half the neighbor and subtract 2. |

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