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## Monday, July 1, 2013

### More on Long Division (and short division, too)

There has been an article out for a few years titled "Long division is so last century" (find it here), In this article she quotes Lawrence Spector of Manhattan Community College as follows: "Spector says that long division "belongs in the history of mathematics" because short division is so much simpler and faster.  I have to say I absolutely agree with him!"

This is absolutely scary! Not because short division is incorrect or improper or not effective, but because it is merely a short way of writing long division, which in itself was shortened by leaving out some trailing zeroes.

I am of the strong belief that long division can be understood better as it relates more directly to the commonly known distributive law of multiplication over division (more on that in a future blog entry.)

The web site Ask.com, in response to the question "What is the Difference Between Short and Long Division?" replies by stating: "The difference between long division and short division is that Long division is a typical procedure suitable for dividing simple or complex multi-digit numbers. It breaks down a division problem into a series of easier steps, whereas short division requires neither complex technology nor mental gymnastics; it is only suitable if the divisor is small - typically less than 10."

I believe this reply to be extremely misleading in three ways: it fails to recognize that the "mental gymnastics" in short and long division is exactly the same, it claims that long division "breaks" a problem down, when that is exactly what short division is also doing, and it confuses "small" divisors with single digits divisors (after all, .674327 is much smaller than 1)

Wikipedia is a bit more precise, when it says "Short division is an abbreviated form of long division."

Needless to say, long division is greatly misrepresented, misunderstood, belittled, and unappreciated. Could it be that no one got rich teaching long division but a lot of people got rich selling calculators?