Why Does Order of Operations Work the Way It Does?
Date: 05/04/2004 at 19:48:01 From: Aviv Subject: Logic for the Order of Operations In order of operations, it is understandable that brackets are focused on initially since they represent individual terms. However, why do exponents then come before the other possible operations? And most importantly, why are multiplication and division done before addition and subtraction? What would happen otherwise? What are the reasons and logic for this, if any? I imagine that mathematicians a long time ago didn't just decide on it for the sake of agreement.
Date: 05/04/2004 at 22:43:14 From: Doctor Peterson Subject: Re: Logic for the Order of Operations Hi, Aviv. I don't know that anyone ever said just why they did what they did, but I give my impressions in these pages, each of which points out a slightly different aspect: History of the Order of Operations http://mathforum.org/library/drmath/view/52582.html Explaining Order of Operations http://mathforum.org/library/drmath/view/57199.html Why Rules? http://mathforum.org/library/drmath/view/57031.html Negative Squared, or Squared Negative? http://mathforum.org/library/drmath/view/61633.html The basic idea, as I see it, is that exponentiation is in a sense more powerful than multiplication, in that it distributes over multiplication; and likewise multiplication is more powerful than addition. Another aspect is that the order we use makes the most interesting expressions, such as polynomials, as easy as possible to write. Finally, there is a good chance that the order just arose naturally out of the way human language tends to express arithmetic, as the symbolism developed gradually from abbreviations of Latin or other languages; for example, "two cats and three dogs" naturally means (2c) + (3d) rather than 2(c + 3)d! If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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