WEEKLY WHINE

# But who’s multiplying: Peasant multiplication

The methods we have seen so far – long multiplication and lattice multiplication – both require knowledge of the 9×9 multiplication table. But that’s not the only way to do it. The ancient Egyptians, much like GoobNet, were fans of powers of two, and so they developed a multiplication method so based. Here is a variation on that method, often called peasant multiplication.

78 | 29 |

39 | 58 |

19 | 116 |

9 | 232 |

4 | 464 |

2 | 928 |

1 | 1856 |

2262 | |

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All that is required is to halve one multiplicand, truncating any fractions, and double the other. Continue until a one ends up in the first column. Then sum all of the multiples of the second multiplicand that are paired with odd fractions of the first.

The fun part of this method is that the multiplication tables are optional. If they are unavailable, multiplying and dividing by two are easy enough. This method can also be done if paper isn’t available, but markers like Monopoly houses are.

As can be seen below, this is a fairly straightforward process that only requires heavy work when it comes time to sum the appropriate intermediate products. But when one multiplicand is fairly small, this is clearly a good approach that has little overhead.

9318 | 861270 |

4659 | 1722540 |

2329 | 3445080 |

1164 | 6890160 |

582 | 13780320 |

291 | 27560640 |

145 | 55121280 |

72 | 110242560 |

36 | 220485120 |

18 | 440970240 |

9 | 881940480 |

4 | 1763880960 |

2 | 3527761920 |

1 | 7055523840 |

8025313860 | |

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