What Are Opposite Reciprocals?

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Opposite reciprocals are a phenomenon that you will occasionally experience when working with fractions. Learn about opposite reciprocals with help from a longtime mathematics educator in this free video clip.

Part of the Video Series: Number Theory Education
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Video Transcript

Hi, I'm Jimmy Chang, and we're here to answer the question what are opposite reciprocals? Now, you may already be familiar with what reciprocals are, and that's basically the numerator and denominator flipped in the original fraction. But, all opposite reciprocals are is that they're also reciprocals. They're just opposite in sign. So, for example, if you have three-fifths, for example, the opposite reciprocal is going to be the same thing as the reciprocal, but different signs. So, we're going to flip the fraction so it becomes five-thirds, but the opposite means we're going to change the sign. So, the opposite reciprocal of three-fifths is going to be negative five-thirds. The same holds true if you started out with a negative fraction. Let's just say, negative one-seventh, ok? So, what you're going to do is you're going to flip the fraction so it becomes seven over one, but the opposite is going to be opposite in sign. So, the opposite of negative is going to be positive. So, it's going to be positive seven over one, which is going to be, of course, just seven. So, real quickly, if you have ten over thirteen, same kind of idea. Opposite reciprocal, flip it first. So, it would be thirteen over ten, but then, because it was positive originally, opposite means negative. So, opposite reciprocals are simply reciprocals of the original fraction, but the opposite in sign. So, I'm Jimmy Chang, and that answers the question, what are opposite reciprocals?


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