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Partial differences subtraction algorithm

Partial differences subtraction algorithm

Author: Christopher Danielson

To demonstrate the partial differences algorithm for multi-digit subtraction.

This packet consists of a series of videos demonstrating the partial differences algorithm. This algorithm is common in current elementary curriculum, but was not typically taught before the mid-1990's. Adults may be unfamiliar with the algorithm and the reasoning behind it.

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There are many reasons to learn a new subtraction algorithm. Perhaps you are:

  • A teacher teaching an unfamiliar curriculum,
  • A parent of a child in an unfamiliar curriculum,
  • A student in one of my math courses,
  • A student who never quite understood why the standard algorithm works, or
  • A person who is simply interested in this sort of stuff.

This packet does not attempt to present the case that alternate algorithms are better than the standard algorithm. It is instead intended to demonstrate a particular algorithm-the partial differences subtraction algorithm-in sufficient detail that the reader will be able to do it on his/her own, and to demonstrate important features of the algorithm and its relationship to the standard algorithm.

The reader is also invited to perform an Internet search on "partial differences algorithm" for more demonstration, debate and information.


Example 1: All differences positive

This video demonstrates the algorithm in the least complicated case-all differences are positive; there is no regrouping.

Case 2: A negative difference appears

This video demonstrates how the algorithm handles the case where one digit being subtracted is larger than the digit it is being subtracted from. In the standard algorithm, this would require "regrouping" or "borrowing".

Example 3: More negative differences

This video extends the demonstration to show how to handle situations where there is more than one negative partial difference.

Example 4: A difficult computation

This video demonstrates subtraction involving many digits and several negative partial differences.