Lattice Method of Subtraction?
Date: 06/13/2006 at 14:43:43 From: Ashley Subject: Lattice Method I'm studying the Lattice Method in my math class, and I was wondering if it is possible to use the lattice for subtraction problems? I know that there is lattice addition and multiplication, but what about subtraction?
Date: 06/14/2006 at 15:06:16 From: Doctor Peterson Subject: Re: Lattice Method Hi, Ashley. You're right, lattice addition uses the format of the lattice to "hide" the "carrying". Here's a typical problem: 2 3 4 4 + 7 2 6 3 ------------ 0/ 0/ 1/ 0/ /9 /5 /0 /7 ------------ 0 9 6 0 7 The number in the upper left of each cell is really the digit you "carry", just written in a somewhat different location. An equivalent method without the lattice would look like 2344 or 2344 + 7263 + 7263 ------ ------ 09 07 05 10 10 05 07 09 ------ ------ 09607 09607 I can't see any way to do the equivalent for subtraction, since subtraction works backwards, requiring you to pull a "carry" digit OUT of the column to the left when needed, rather than just overflowing INTO that column naturally. To put it another way, in addition you do the "carries" AFTER the additions, but in subtraction you have to do the "borrowing" BEFORE subtracting, in order to set things up to subtract a smaller number from a larger one. There may be a way based on the method used in computers to turn binary subtractions into additions so the same hardware can do both; but that would be very awkward for humans using decimal notation! That's not to say that there aren't other ways to do subtraction; I've heard of a number of them. But none that I have heard of, or can invent easily, look anything like a lattice. If you haven't seen the Austrian Subtraction method, you might like it; there is some resemblance to the lattice, though because the "carry" is used in two different ways, it couldn't be isolated in a cell: Austrian Subtraction http://www.sonoma.edu/users/w/wilsonst/Courses/Math_300/Groupwork/ altsub/aust.html - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Date: 06/14/2006 at 16:10:36 From: Ashley Subject: Thank you (Lattice Method) Thank you so much for your help! I really appreciate it. Your answer makes sense to me, and has helped me figure this concept out. You are the best! Thanks! :-)
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