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Lattice algorithm for multiplication

Lattice algorithm for multiplication

Author: Christopher Danielson

To master the lattice algorithm.

This packet is intended to be an introduction to the lattice multiplication algorithm. This algorithm is sometimes taught in elementary schools, but many adults are unfamiliar with it.

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The lattice algorithm is used for multiplying multi-digit numbers. Some important features of the algorithm include:

  • We do not pay attention to the values of the numbers as we work through the algorithm-only to the digits themselves,
  • We do all of the multiplications first, followed by the additions (in contrast to the standard algorithm), meaning...
  • There is no carrying in the multiplication phase of the algorithm, and
  • We have to take a little bit of time to set up the lattice before we can begin multiplying.

In this packet, I will solve two problems:

  1. A 2-digit by 2-digit problem, and
  2. A 3-digit by 2-digit problem


Two-digit by two-digit example

This video demonstrates the lattice algorithm with two two-digit numbers.

Three-digit by two-digit example

This video demonstrates the lattice algorithm with larger numbers.

Lattice v. standard algorithm smackdown

So you spend a lot of time setting up the lattice, right? It must take a lot longer than the standard algorithm, right?
Let's see.
I'll multiply two 10-digit numbers. Which will be completed first? And by how much?
(Note: While the video is sped up, it still takes two minutes...feel free to fast forward to the end!)