Reciprocals of Negative FractionsDate: 03/19/2002 at 02:01:47 From: Melissa Subject: Reciprocals What is a reciprocal, and what is the reciprocal of negative 1/2? What is the reciprocal of 10? Date: 03/19/2002 at 09:06:09 From: Doctor Rick Subject: Re: Reciprocals Hi, Melissa. You have learned that the reciprocal of, say, 2/3 is 3/2, right? To get the reciprocal of a fraction, you just switch the numerator and the denominator. So what happens if the fraction is negative? You can consider the negative sign to be part of the numerator: think of -1/2 as -1 over 2. Then the reciprocal is 2/(-1). But you can make an equivalent fraction by multiplying the numerator and denominator by the same quantity. Try multiplying both by -1: 2 2*-1 -2 --- = ----- = --- -1 -1*-1 1 Now, a fraction with a denominator of 1 is just a whole number, so the reciprocal of -1/2 is -2. This last part gives us a clue as to how to find the reciprocal of whole numbers like 10. We can write the number with a denominator of 1: 10 = 10/1 Then we take the reciprocal of this fraction: switch the numerator and denominator to get 1/10. Does this help? - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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