Can Negative Fractions Also Be Proper or Improper?Date: 03/31/2004 at 17:11:53 From: Laurel Subject: proper and improper fractions How do you classify negative fractions? Is a fraction like -3/4 considered a proper fraction? Is -8/3 considered an improper fraction? I've generally thought that all proper fractions lie between 0 and 1 on a number line. However, what about the negatives? Date: 03/31/2004 at 23:27:43 From: Doctor Peterson Subject: Re: proper and improper fractions Hi, Laurel. The usual definitions are aimed at kids who don't know about negative numbers; it's rare to see a definition that takes negatives into account. When you consider negative fractions, it is the absolute value that has to be less than 1 for a proper fraction; a fraction between -1 and 1 therefore is proper. An alternative way to deal with this might be to restrict the word "fraction" to positive numbers, and use "negative improper fraction" to refer to "the negative of an improper fraction". That avoids the question, but might sound too tricky to kids. I can't be sure which way people generally think of it when they do talk about negative fractions; I just know that -8/3 is improper and -2/3 is proper. I like to confirm my impression in cases like this, so I searched on Google for "negative improper fraction", but I found nothing but this, which doesn't clarify the exact meaning: Positive and negative numbers http://www.mathleague.com/help/posandneg/posandneg.htm What is the reciprocal of -5 1/8? First, we convert to a negative improper fraction: -5 1/8 = -41/8, then we switch the numerator and denominator, and keep the same sign: -8/41. Unfortunately, the Math League's definition of improper fractions ignores negatives: Fractions http://www.mathleague.com/help/fractions/fractions.htm Improper fractions have numerators that are larger than or equal to their denominators. Examples: 11/4, 5/5, and 13/2 are improper fractions. I'm inclined to interpret "larger than" here as "greater in absolute value" in order to make the definition work with negatives. That is, p/q is improper if |p| >= |q|. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ Date: 03/31/2004 at 23:48:46 From: Laurel Brenner Subject: Thank you (proper and improper fractions) Thank you, Dr. Peterson! I am a 6th grade math teacher of a top level class. When I asked the students to write where all proper fractions lie on a number line, the answer I expected was between 0 and 1. But one student claimed that they were between -1 and 1. I'd never thought of that, and I wanted to be sure before I saw her again that it was, in fact, correct. I appreciate your very prompt reply. |
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